diff --git a/cylc/flow/cfgspec/workflow.py b/cylc/flow/cfgspec/workflow.py
index d22f0f415bb..8575980707a 100644
--- a/cylc/flow/cfgspec/workflow.py
+++ b/cylc/flow/cfgspec/workflow.py
@@ -996,6 +996,136 @@ def get_script_common_text(this: str, example: Optional[str] = None):
             can be explicitly configured to provide or override default
             settings for all tasks in the workflow.
         '''):
+            Conf('completion', VDR.V_STRING, desc='''
+                Define the condition for task completion.
+
+                The completion condition is evaluated when a task is finished.
+                It is a validation check which confirms that the task has
+                generated the outputs it was expected to.
+
+                If the task fails this check it is considered
+                :term:`incomplete` and may cause the workflow to
+                :term:`stall`, alerting you that something has gone wrong which
+                requires investigation.
+
+                By default, the completion condition ensures that all required
+                outputs, i.e. outputs which appear in the graph but are not
+                marked as optional with the ``?`` character, are completed.
+
+                E.g., in this example, the task ``foo`` must generate the
+                required outputs ``succeeded`` and ``x``, it may or may not
+                generate the optional output ``y``:
+
+                .. code-block:: cylc-graph
+
+                   foo => bar
+                   foo:x => x
+                   foo:y? => y
+
+                In Python syntax that condition looks like this:
+
+                .. code-block:: python
+
+                   # the task must succeeded and generate the custom output "x"
+                   succeeded and x
+
+                The ``completion`` configuration allows you to override the
+                default completion to suit your needs.
+
+                E.G., in this example, the task ``foo`` has three optional
+                outputs, ``x``, ``y`` and ``z``:
+
+                .. code-block:: cylc-graph
+
+                   foo:x? => x
+                   foo:y? => y
+                   foo:z? => z
+                   x | y | z => bar
+
+                Because all three of these outputs are optional, if none of
+                them are generated, the task will still be marked as complete.
+
+                If you wanted to require that at least one of these outputs is
+                generated you could configure the completion confition like so:
+
+                .. code-block:: python
+
+                   # the task must succeeded and generate at least one of the
+                   # outputs "x" or "y" or "z":
+                   succeeded and (x or y or z)
+
+                .. note::
+
+                   For the completion expression, hyphens in task outputs
+                   are converted into underscores e.g:
+
+                   .. code-block:: cylc
+
+                      [runtime]
+                          [[foo]]
+                              completion = succeeded and my_output # underscore
+                              [[[outputs]]]
+                                  my-output = 'my custom task output' # hyphen
+
+                .. note::
+
+                   In some cases the succeeded output might not explicitly
+                   appear in the graph, e.g:
+
+                   .. code-block:: cylc-graph
+
+                      foo:x? => x
+
+                   In these cases succeess is presumed to be required unless
+                   explicitly stated otherwise, either in the graph:
+
+                   .. code-block:: cylc-graph
+
+                      foo?
+                      foo:x? => x
+
+                   Or in the completion expression:
+
+                   .. code-block:: cylc
+
+                      completion = x  # no reference to succeeded here
+
+
+                .. hint::
+
+                   If task outputs are optional in the graph they must also
+                   be optional in the completion condition and vice versa.
+
+                   .. code-block:: cylc
+
+                      [scheduling]
+                          [[graph]]
+                              R1 = """
+                                  # ERROR: this should be "a? => b"
+                                  a => b
+                              """
+                      [runtime]
+                          [[a]]
+                              # this completion condition implies that the
+                              # succeeded output is optional
+                              completion = succeeded or failed
+
+                .. rubric:: Examples
+
+                ``succeeded``
+                   The task must succeed.
+                ``succeeded or (failed and my_error)``
+                   The task can fail, but only if it also yields the custom
+                   output ``my_error``.
+                ``succeeded and (x or y or z)``
+                   The task must succeed and yield at least one of the
+                   custom outputs, x, y or z.
+                ``(a and b) or (c and d)``
+                   One pair of these outputs must be yielded for the task
+                   to be complete.
+
+                .. versionadded:: 8.3.0
+            ''')
             Conf('platform', VDR.V_STRING, desc='''
                 The name of a compute resource defined in
                 :cylc:conf:`global.cylc[platforms]` or
diff --git a/cylc/flow/config.py b/cylc/flow/config.py
index ad87315c4c1..cfaa4b1df30 100644
--- a/cylc/flow/config.py
+++ b/cylc/flow/config.py
@@ -90,7 +90,11 @@
 from cylc.flow.task_id import TaskID
 from cylc.flow.task_outputs import (
     TASK_OUTPUT_SUCCEEDED,
-    TaskOutputs
+    TASK_OUTPUT_FINISHED,
+    TaskOutputs,
+    get_completion_expression,
+    get_optional_outputs,
+    trigger_to_completion_variable,
 )
 from cylc.flow.task_trigger import TaskTrigger, Dependency
 from cylc.flow.taskdef import TaskDef
@@ -519,6 +523,8 @@ def __init__(
         self.load_graph()
         self.mem_log("config.py: after load_graph()")
 
+        self._set_completion_expressions()
+
         self.process_runahead_limit()
 
         if self.run_mode('simulation', 'dummy'):
@@ -1007,6 +1013,197 @@ def _check_sequence_bounds(self):
                 )
             LOG.warning(msg)
 
+    def _set_completion_expressions(self):
+        """Sets and checks completion expressions for each task.
+
+        If a task does not have a user-defined completion expression, then set
+        one according to the default rules.
+
+        If a task does have a used-defined completion expression, then ensure
+        it is consistent with the use of outputs in the graph.
+        """
+        for name, taskdef in self.taskdefs.items():
+            expr = taskdef.rtconfig['completion']
+            if expr:
+                # check the user-defined expression
+                self._check_completion_expression(name, expr)
+            else:
+                # derive a completion expression for this taskdef
+                expr = get_completion_expression(taskdef)
+
+            if name not in self.taskdefs:
+                # this is a family -> nothing more to do here
+                continue
+
+            # update both the sparse and dense configs to make these values
+            # visible to "cylc config" to make the completion expression more
+            # transparent to users.
+            # NOTE: we have to update both because we are setting this value
+            # late on in the process after the dense copy has been made
+            self.pcfg.sparse.setdefault(
+                'runtime', {}
+            ).setdefault(
+                name, {}
+            )['completion'] = expr
+            self.pcfg.dense['runtime'][name]['completion'] = expr
+
+            # update the task's runtime config to make this value visible to
+            # the data store
+            # NOTE: we have to do this because we are setting this value late
+            # on after the TaskDef has been created
+            taskdef.rtconfig['completion'] = expr
+
+    def _check_completion_expression(self, task_name: str, expr: str) -> None:
+        """Checks a user-defined completion expression.
+
+        Args:
+            task_name:
+                The name of the task we are checking.
+            expr:
+                The completion expression as defined in the config.
+
+        """
+        # check completion expressions are not being used in compat mode
+        if cylc.flow.flags.cylc7_back_compat:
+            raise WorkflowConfigError(
+                '[runtime][<namespace>]completion cannot be used'
+                ' in Cylc 7 compatibility mode.'
+            )
+
+        # check for invalid triggers in the expression
+        if 'submit-failed' in expr:
+            raise WorkflowConfigError(
+                f'Error in [runtime][{task_name}]completion:'
+                f'\nUse "submit_failed" rather than "submit-failed"'
+                ' in completion expressions.'
+            )
+        elif '-' in expr:
+            raise WorkflowConfigError(
+                f'Error in [runtime][{task_name}]completion:'
+                f'\n  {expr}'
+                '\nReplace hyphens with underscores in task outputs when'
+                ' used in completion expressions.'
+            )
+
+        # get the outputs and completion expression for this task
+        try:
+            outputs = self.taskdefs[task_name].outputs
+        except KeyError:
+            # this is a family -> we'll check integrity for each task that
+            # inherits from it
+            return
+
+        # get the optional/required outputs defined in the graph
+        graph_optionals = {
+            # completion_variable: is_optional
+            trigger_to_completion_variable(output): (
+                None if is_required is None else not is_required
+            )
+            for output, (_, is_required)
+            in outputs.items()
+        }
+
+        # get the optional/required outputs defined in the expression
+        try:
+            # this involves running the expression which also validates it
+            expression_optionals = get_optional_outputs(expr, outputs)
+        except NameError as exc:
+            # expression references an output which has not been registered
+            error = exc.args[0][5:]
+
+            if f"'{TASK_OUTPUT_FINISHED}'" in error:
+                # the finished output cannot be used in completion expressions
+                # see proposal point 5::
+                # https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+                raise WorkflowConfigError(
+                    f'Error in [runtime][{task_name}]completion:'
+                    f'\n  {expr}'
+                    '\nThe "finished" output cannot be used in completion'
+                    ' expressions, use "succeeded or failed".'
+                )
+
+            raise WorkflowConfigError(
+                # NOTE: str(exc) == "name 'x' is not defined" tested in
+                # tests/integration/test_optional_outputs.py
+                f'Error in [runtime][{task_name}]completion:'
+                f'\nInput {error}'
+            )
+        except Exception as exc:  # includes InvalidCompletionExpression
+            # expression contains non-whitelisted syntax or any other error in
+            # the expression e.g. SyntaxError
+            raise WorkflowConfigError(
+                f'Error in [runtime][{task_name}]completion:'
+                f'\n{str(exc)}'
+            )
+
+        # ensure consistency between the graph and the completion expression
+        for compvar in (
+            {
+                *graph_optionals,
+                *expression_optionals
+            }
+        ):
+            # is the output optional in the graph?
+            graph_opt = graph_optionals.get(compvar)
+            # is the output optional in the completion expression?
+            expr_opt = expression_optionals.get(compvar)
+
+            # True = is optional
+            # False = is required
+            # None = is not referenced
+
+            # graph_opt  expr_opt
+            # True       True       ok
+            # True       False      not ok
+            # True       None       not ok [1]
+            # False      True       not ok [1]
+            # False      False      ok
+            # False      None       not ok
+            # None       True       ok
+            # None       False      ok
+            # None       None       ok
+
+            # [1] applies only to "submit-failed" and "expired"
+
+            output = compvar  # TODO
+
+            if graph_opt is True and expr_opt is False:
+                raise WorkflowConfigError(
+                    f'{task_name}:{output} is optional in the graph'
+                    ' (? symbol), but required in the completion'
+                    f' expression:\n{expr}'
+                )
+
+            if graph_opt is False and expr_opt is None:
+                raise WorkflowConfigError(
+                    f'{task_name}:{output} is required in the graph,'
+                    ' but not referenced in the completion'
+                    f' expression\n{expr}'
+                )
+
+            if (
+                graph_opt is True
+                and expr_opt is None
+                and compvar in {'submit_failed', 'expired'}
+            ):
+                raise WorkflowConfigError(
+                    f'{task_name}:{output} is permitted in the graph'
+                    ' but is not referenced in the completion'
+                    ' expression (so is not permitted by it).'
+                    f'\nTry: completion = "{expr} or {output}"'
+                )
+
+            if (
+                graph_opt is False
+                and expr_opt is True
+                and compvar not in {'submit_failed', 'expired'}
+            ):
+                raise WorkflowConfigError(
+                    f'{task_name}:{output} is required in the graph,'
+                    ' but optional in the completion expression'
+                    f'\n{expr}'
+                )
+
     def _expand_name_list(self, orig_names):
         """Expand any parameters in lists of names."""
         name_expander = NameExpander(self.parameters)
diff --git a/cylc/flow/data_messages.proto b/cylc/flow/data_messages.proto
index 6068bb1c5df..bc0355e6d4c 100644
--- a/cylc/flow/data_messages.proto
+++ b/cylc/flow/data_messages.proto
@@ -127,6 +127,7 @@ message PbRuntime {
     optional string directives = 15;
     optional string environment = 16;
     optional string outputs = 17;
+    optional string completion = 18;
 }
 
 
diff --git a/cylc/flow/data_messages_pb2.py b/cylc/flow/data_messages_pb2.py
index 82c620bcacf..5ecb96fc122 100644
--- a/cylc/flow/data_messages_pb2.py
+++ b/cylc/flow/data_messages_pb2.py
@@ -2,6 +2,7 @@
 # -*- coding: utf-8 -*-
 # Generated by the protocol buffer compiler.  DO NOT EDIT!
 # source: data_messages.proto
+# Protobuf Python Version: 4.25.3
 """Generated protocol buffer code."""
 from google.protobuf import descriptor as _descriptor
 from google.protobuf import descriptor_pool as _descriptor_pool
@@ -14,7 +15,7 @@
 
 
 
-DESCRIPTOR = _descriptor_pool.Default().AddSerializedFile(b'\n\x13\x64\x61ta_messages.proto\"\x96\x01\n\x06PbMeta\x12\x12\n\x05title\x18\x01 \x01(\tH\x00\x88\x01\x01\x12\x18\n\x0b\x64\x65scription\x18\x02 \x01(\tH\x01\x88\x01\x01\x12\x10\n\x03URL\x18\x03 \x01(\tH\x02\x88\x01\x01\x12\x19\n\x0cuser_defined\x18\x04 \x01(\tH\x03\x88\x01\x01\x42\x08\n\x06_titleB\x0e\n\x0c_descriptionB\x06\n\x04_URLB\x0f\n\r_user_defined\"\xaa\x01\n\nPbTimeZone\x12\x12\n\x05hours\x18\x01 \x01(\x05H\x00\x88\x01\x01\x12\x14\n\x07minutes\x18\x02 \x01(\x05H\x01\x88\x01\x01\x12\x19\n\x0cstring_basic\x18\x03 \x01(\tH\x02\x88\x01\x01\x12\x1c\n\x0fstring_extended\x18\x04 \x01(\tH\x03\x88\x01\x01\x42\x08\n\x06_hoursB\n\n\x08_minutesB\x0f\n\r_string_basicB\x12\n\x10_string_extended\"\'\n\x0fPbTaskProxyRefs\x12\x14\n\x0ctask_proxies\x18\x01 \x03(\t\"\xd4\x0c\n\nPbWorkflow\x12\x12\n\x05stamp\x18\x01 \x01(\tH\x00\x88\x01\x01\x12\x0f\n\x02id\x18\x02 \x01(\tH\x01\x88\x01\x01\x12\x11\n\x04name\x18\x03 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\x03(\x0b\x32\x0c.PbTaskProxy\x12\x0e\n\x06pruned\x18\x05 \x03(\t\x12\x15\n\x08reloaded\x18\x06 \x01(\x08H\x02\x88\x01\x01\x42\x07\n\x05_timeB\x0b\n\t_checksumB\x0b\n\t_reloaded\"\xc3\x01\n\x07WDeltas\x12\x11\n\x04time\x18\x01 \x01(\x01H\x00\x88\x01\x01\x12\x1f\n\x05\x61\x64\x64\x65\x64\x18\x02 \x01(\x0b\x32\x0b.PbWorkflowH\x01\x88\x01\x01\x12!\n\x07updated\x18\x03 \x01(\x0b\x32\x0b.PbWorkflowH\x02\x88\x01\x01\x12\x15\n\x08reloaded\x18\x04 \x01(\x08H\x03\x88\x01\x01\x12\x13\n\x06pruned\x18\x05 \x01(\tH\x04\x88\x01\x01\x42\x07\n\x05_timeB\x08\n\x06_addedB\n\n\x08_updatedB\x0b\n\t_reloadedB\t\n\x07_pruned\"\xd1\x01\n\tAllDeltas\x12\x1a\n\x08\x66\x61milies\x18\x01 \x01(\x0b\x32\x08.FDeltas\x12!\n\x0e\x66\x61mily_proxies\x18\x02 \x01(\x0b\x32\t.FPDeltas\x12\x16\n\x04jobs\x18\x03 \x01(\x0b\x32\x08.JDeltas\x12\x17\n\x05tasks\x18\x04 \x01(\x0b\x32\x08.TDeltas\x12\x1f\n\x0ctask_proxies\x18\x05 \x01(\x0b\x32\t.TPDeltas\x12\x17\n\x05\x65\x64ges\x18\x06 \x01(\x0b\x32\x08.EDeltas\x12\x1a\n\x08workflow\x18\x07 \x01(\x0b\x32\x08.WDeltasb\x06proto3')
 
 _globals = globals()
 _builder.BuildMessageAndEnumDescriptors(DESCRIPTOR, _globals)
@@ -46,55 +47,55 @@
   _globals['_PBWORKFLOW_LATESTSTATETASKSENTRY']._serialized_start=1493
   _globals['_PBWORKFLOW_LATESTSTATETASKSENTRY']._serialized_end=1566
   _globals['_PBRUNTIME']._serialized_start=2014
-  _globals['_PBRUNTIME']._serialized_end=2839
-  _globals['_PBJOB']._serialized_start=2842
-  _globals['_PBJOB']._serialized_end=3511
-  _globals['_PBTASK']._serialized_start=3514
-  _globals['_PBTASK']._serialized_end=3868
-  _globals['_PBPOLLTASK']._serialized_start=3871
-  _globals['_PBPOLLTASK']._serialized_end=4087
-  _globals['_PBCONDITION']._serialized_start=4090
-  _globals['_PBCONDITION']._serialized_end=4293
-  _globals['_PBPREREQUISITE']._serialized_start=4296
-  _globals['_PBPREREQUISITE']._serialized_end=4446
-  _globals['_PBOUTPUT']._serialized_start=4449
-  _globals['_PBOUTPUT']._serialized_end=4589
-  _globals['_PBTRIGGER']._serialized_start=4592
-  _globals['_PBTRIGGER']._serialized_end=4757
-  _globals['_PBTASKPROXY']._serialized_start=4760
-  _globals['_PBTASKPROXY']._serialized_end=5801
-  _globals['_PBTASKPROXY_OUTPUTSENTRY']._serialized_start=5411
-  _globals['_PBTASKPROXY_OUTPUTSENTRY']._serialized_end=5468
-  _globals['_PBTASKPROXY_EXTERNALTRIGGERSENTRY']._serialized_start=5470
-  _globals['_PBTASKPROXY_EXTERNALTRIGGERSENTRY']._serialized_end=5537
-  _globals['_PBTASKPROXY_XTRIGGERSENTRY']._serialized_start=5539
-  _globals['_PBTASKPROXY_XTRIGGERSENTRY']._serialized_end=5599
-  _globals['_PBFAMILY']._serialized_start=5804
-  _globals['_PBFAMILY']._serialized_end=6132
-  _globals['_PBFAMILYPROXY']._serialized_start=6135
-  _globals['_PBFAMILYPROXY']._serialized_end=6949
+  _globals['_PBRUNTIME']._serialized_end=2879
+  _globals['_PBJOB']._serialized_start=2882
+  _globals['_PBJOB']._serialized_end=3551
+  _globals['_PBTASK']._serialized_start=3554
+  _globals['_PBTASK']._serialized_end=3908
+  _globals['_PBPOLLTASK']._serialized_start=3911
+  _globals['_PBPOLLTASK']._serialized_end=4127
+  _globals['_PBCONDITION']._serialized_start=4130
+  _globals['_PBCONDITION']._serialized_end=4333
+  _globals['_PBPREREQUISITE']._serialized_start=4336
+  _globals['_PBPREREQUISITE']._serialized_end=4486
+  _globals['_PBOUTPUT']._serialized_start=4489
+  _globals['_PBOUTPUT']._serialized_end=4629
+  _globals['_PBTRIGGER']._serialized_start=4632
+  _globals['_PBTRIGGER']._serialized_end=4797
+  _globals['_PBTASKPROXY']._serialized_start=4800
+  _globals['_PBTASKPROXY']._serialized_end=5841
+  _globals['_PBTASKPROXY_OUTPUTSENTRY']._serialized_start=5451
+  _globals['_PBTASKPROXY_OUTPUTSENTRY']._serialized_end=5508
+  _globals['_PBTASKPROXY_EXTERNALTRIGGERSENTRY']._serialized_start=5510
+  _globals['_PBTASKPROXY_EXTERNALTRIGGERSENTRY']._serialized_end=5577
+  _globals['_PBTASKPROXY_XTRIGGERSENTRY']._serialized_start=5579
+  _globals['_PBTASKPROXY_XTRIGGERSENTRY']._serialized_end=5639
+  _globals['_PBFAMILY']._serialized_start=5844
+  _globals['_PBFAMILY']._serialized_end=6172
+  _globals['_PBFAMILYPROXY']._serialized_start=6175
+  _globals['_PBFAMILYPROXY']._serialized_end=6989
   _globals['_PBFAMILYPROXY_STATETOTALSENTRY']._serialized_start=1441
   _globals['_PBFAMILYPROXY_STATETOTALSENTRY']._serialized_end=1491
-  _globals['_PBEDGE']._serialized_start=6952
-  _globals['_PBEDGE']._serialized_end=7140
-  _globals['_PBEDGES']._serialized_start=7142
-  _globals['_PBEDGES']._serialized_end=7265
-  _globals['_PBENTIREWORKFLOW']._serialized_start=7268
-  _globals['_PBENTIREWORKFLOW']._serialized_end=7510
-  _globals['_EDELTAS']._serialized_start=7513
-  _globals['_EDELTAS']._serialized_end=7688
-  _globals['_FDELTAS']._serialized_start=7691
-  _globals['_FDELTAS']._serialized_end=7870
-  _globals['_FPDELTAS']._serialized_start=7873
-  _globals['_FPDELTAS']._serialized_end=8063
-  _globals['_JDELTAS']._serialized_start=8066
-  _globals['_JDELTAS']._serialized_end=8239
-  _globals['_TDELTAS']._serialized_start=8242
-  _globals['_TDELTAS']._serialized_end=8417
-  _globals['_TPDELTAS']._serialized_start=8420
-  _globals['_TPDELTAS']._serialized_end=8606
-  _globals['_WDELTAS']._serialized_start=8609
-  _globals['_WDELTAS']._serialized_end=8804
-  _globals['_ALLDELTAS']._serialized_start=8807
-  _globals['_ALLDELTAS']._serialized_end=9016
+  _globals['_PBEDGE']._serialized_start=6992
+  _globals['_PBEDGE']._serialized_end=7180
+  _globals['_PBEDGES']._serialized_start=7182
+  _globals['_PBEDGES']._serialized_end=7305
+  _globals['_PBENTIREWORKFLOW']._serialized_start=7308
+  _globals['_PBENTIREWORKFLOW']._serialized_end=7550
+  _globals['_EDELTAS']._serialized_start=7553
+  _globals['_EDELTAS']._serialized_end=7728
+  _globals['_FDELTAS']._serialized_start=7731
+  _globals['_FDELTAS']._serialized_end=7910
+  _globals['_FPDELTAS']._serialized_start=7913
+  _globals['_FPDELTAS']._serialized_end=8103
+  _globals['_JDELTAS']._serialized_start=8106
+  _globals['_JDELTAS']._serialized_end=8279
+  _globals['_TDELTAS']._serialized_start=8282
+  _globals['_TDELTAS']._serialized_end=8457
+  _globals['_TPDELTAS']._serialized_start=8460
+  _globals['_TPDELTAS']._serialized_end=8646
+  _globals['_WDELTAS']._serialized_start=8649
+  _globals['_WDELTAS']._serialized_end=8844
+  _globals['_ALLDELTAS']._serialized_start=8847
+  _globals['_ALLDELTAS']._serialized_end=9056
 # @@protoc_insertion_point(module_scope)
diff --git a/cylc/flow/data_store_mgr.py b/cylc/flow/data_store_mgr.py
index 744daeb4dda..f49c5bd9eaa 100644
--- a/cylc/flow/data_store_mgr.py
+++ b/cylc/flow/data_store_mgr.py
@@ -247,6 +247,7 @@ def runtime_from_config(rtconfig):
     return PbRuntime(
         platform=platform,
         script=rtconfig['script'],
+        completion=rtconfig['completion'],
         init_script=rtconfig['init-script'],
         env_script=rtconfig['env-script'],
         err_script=rtconfig['err-script'],
@@ -1440,7 +1441,7 @@ def apply_task_proxy_db_history(self):
                     )
             ):
                 for message in json.loads(outputs_str):
-                    itask.state.outputs.set_completion(message, True)
+                    itask.state.outputs.set_message_complete(message)
             # Gather tasks with flow id.
             prereq_ids.add(f'{relative_id}/{flow_nums_str}')
 
@@ -1502,7 +1503,7 @@ def _process_internal_task_proxy(self, itask, tproxy):
         del tproxy.prerequisites[:]
         tproxy.prerequisites.extend(prereq_list)
 
-        for label, message, satisfied in itask.state.outputs.get_all():
+        for label, message, satisfied in itask.state.outputs:
             output = tproxy.outputs[label]
             output.label = label
             output.message = message
@@ -2393,10 +2394,8 @@ def delta_task_output(
         tp_id, tproxy = self.store_node_fetcher(itask.tokens)
         if not tproxy:
             return
-        item = itask.state.outputs.get_item(message)
-        if item is None:
-            return
-        label, _, satisfied = item
+        outputs = itask.state.outputs
+        label = outputs.get_trigger(message)
         # update task instance
         update_time = time()
         tp_delta = self.updated[TASK_PROXIES].setdefault(
@@ -2405,7 +2404,7 @@ def delta_task_output(
         output = tp_delta.outputs[label]
         output.label = label
         output.message = message
-        output.satisfied = satisfied
+        output.satisfied = outputs.is_message_complete(message)
         output.time = update_time
         self.updates_pending = True
 
@@ -2425,9 +2424,10 @@ def delta_task_outputs(self, itask: TaskProxy) -> None:
         tp_delta = self.updated[TASK_PROXIES].setdefault(
             tp_id, PbTaskProxy(id=tp_id))
         tp_delta.stamp = f'{tp_id}@{update_time}'
-        for label, _, satisfied in itask.state.outputs.get_all():
-            output = tp_delta.outputs[label]
-            output.label = label
+        for trigger, message, satisfied in itask.state.outputs:
+            output = tp_delta.outputs[trigger]
+            output.label = trigger
+            output.message = message
             output.satisfied = satisfied
             output.time = update_time
 
diff --git a/cylc/flow/exceptions.py b/cylc/flow/exceptions.py
index 0800a914888..9881631484b 100644
--- a/cylc/flow/exceptions.py
+++ b/cylc/flow/exceptions.py
@@ -487,3 +487,16 @@ def __str__(self):
             )
         else:
             return "Installed workflow is not compatible with Cylc 8."
+
+
+class InvalidCompletionExpression(CylcError):
+    """For the [runtime][<namespace>]completion configuration.
+
+    Raised when non-whitelisted syntax is present.
+    """
+    def __init__(self, message, expr=None):
+        self.message = message
+        self.expr = expr
+
+    def __str__(self):
+        return self.message
diff --git a/cylc/flow/graph_parser.py b/cylc/flow/graph_parser.py
index 3dbab9261b7..ac8968dc213 100644
--- a/cylc/flow/graph_parser.py
+++ b/cylc/flow/graph_parser.py
@@ -745,9 +745,14 @@ def _set_output_opt(
         if suicide:
             return
 
-        if output == TASK_OUTPUT_EXPIRED and not optional:
-            raise GraphParseError(
-                f"Expired-output {name}:{output} must be optional")
+        if (
+            output in {TASK_OUTPUT_EXPIRED, TASK_OUTPUT_SUBMIT_FAILED}
+            and not optional
+        ):
+            # ":expire" and ":submit-fail" cannot be required
+            # proposal point 4:
+            # https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+            raise GraphParseError(f"{name}:{output} must be optional")
 
         if output == TASK_OUTPUT_FINISHED:
             # Interpret :finish pseudo-output
diff --git a/cylc/flow/loggingutil.py b/cylc/flow/loggingutil.py
index 35884729ea0..e3f1b82d47b 100644
--- a/cylc/flow/loggingutil.py
+++ b/cylc/flow/loggingutil.py
@@ -53,10 +53,10 @@ class CylcLogFormatter(logging.Formatter):
     """
 
     COLORS = {
-        'CRITICAL': cparse('<red><bold>{0}</bold></red>'),
-        'ERROR': cparse('<red>{0}</red>'),
-        'WARNING': cparse('<yellow>{0}</yellow>'),
-        'DEBUG': cparse('<fg #888888>{0}</fg #888888>')
+        'CRITICAL': '<red><bold>{0}</bold></red>',
+        'ERROR': '<red>{0}</red>',
+        'WARNING': '<yellow>{0}</yellow>',
+        'DEBUG': '<fg #888888>{0}</fg #888888>'
     }
 
     # default hard-coded max width for log entries
@@ -99,7 +99,7 @@ def format(self, record):  # noqa: A003 (method name not local)
         if not self.timestamp:
             _, text = text.split(' ', 1)  # ISO8601 time points have no spaces
         if self.color and record.levelname in self.COLORS:
-            text = self.COLORS[record.levelname].format(text)
+            text = cparse(self.COLORS[record.levelname].format(text))
         if self.max_width:
             return '\n'.join(
                 line
@@ -329,7 +329,7 @@ def _filter(self, record):
 def re_formatter(log_string):
     """Read in an uncoloured log_string file and apply colour formatting."""
     for sub, repl in LOG_LEVEL_REGEXES:
-        log_string = sub.sub(repl, log_string)
+        log_string = cparse(sub.sub(repl, log_string))
     return log_string
 
 
diff --git a/cylc/flow/network/schema.py b/cylc/flow/network/schema.py
index a1ae2ea26f7..e2e0d8f9422 100644
--- a/cylc/flow/network/schema.py
+++ b/cylc/flow/network/schema.py
@@ -807,6 +807,7 @@ class Meta:
         """)
     platform = String(default_value=None)
     script = String(default_value=None)
+    completion = String(default_value=None)
     init_script = String(default_value=None)
     env_script = String(default_value=None)
     err_script = String(default_value=None)
diff --git a/cylc/flow/scripts/show.py b/cylc/flow/scripts/show.py
index dae42f637b8..80180964cc5 100755
--- a/cylc/flow/scripts/show.py
+++ b/cylc/flow/scripts/show.py
@@ -40,6 +40,7 @@
 import re
 import json
 import sys
+from textwrap import indent
 from typing import Any, Dict, TYPE_CHECKING
 
 from ansimarkup import ansiprint
@@ -51,6 +52,7 @@
 from cylc.flow.id import Tokens
 from cylc.flow.id_cli import parse_ids
 from cylc.flow.network.client_factory import get_client
+from cylc.flow.task_outputs import TaskOutputs
 from cylc.flow.task_state import (
     TASK_STATUSES_ORDERED,
     TASK_STATUS_RUNNING
@@ -60,6 +62,7 @@
     ID_MULTI_ARG_DOC,
 )
 from cylc.flow.terminal import cli_function
+from cylc.flow.util import BOOL_SYMBOLS
 
 
 if TYPE_CHECKING:
@@ -135,16 +138,39 @@
       label
       satisfied
     }
+    runtime {
+      completion
+    }
   }
 }
 '''
 
 
+SATISFIED = BOOL_SYMBOLS[True]
+UNSATISFIED = BOOL_SYMBOLS[False]
+
+
 def print_msg_state(msg, state):
     if state:
-        ansiprint(f'<green>  + {msg}</green>')
+        ansiprint(f'<green>  {SATISFIED} {msg}</green>')
     else:
-        ansiprint(f'<red>  - {msg}</red>')
+        ansiprint(f'<red>  {UNSATISFIED} {msg}</red>')
+
+
+def print_completion_state(t_proxy):
+    # create task outputs object
+    outputs = TaskOutputs(t_proxy["runtime"]["completion"])
+
+    for output in t_proxy['outputs']:
+        outputs.add(output['label'], output['message'])
+        if output['satisfied']:
+            outputs.set_message_complete(output['message'])
+
+    ansiprint(
+        f'<bold>completion:</bold>'
+        f' {"complete" if outputs.is_complete() else "incomplete"}'
+        f'\n{indent(outputs.format_completion_status(ansimarkup=2), "  ")}'
+    )
 
 
 def flatten_data(data, flat_data=None):
@@ -316,14 +342,16 @@ async def prereqs_and_outputs_query(
                     ansiprint(f"{pre_txt} (n/a for past tasks)")
                 else:
                     ansiprint(
-                        f"{pre_txt} ('<red>-</red>': not satisfied)")
+                        f"{pre_txt}"
+                        f"('<red>{UNSATISFIED}</red>': not satisfied)"
+                    )
                     for _, prefix, msg, state in prereqs:
                         print_msg_state(f'{prefix}{msg}', state)
 
                 # outputs
                 ansiprint(
                     '<bold>outputs:</bold>'
-                    " ('<red>-</red>': not completed)")
+                    f" ('<red>{UNSATISFIED}</red>': not completed)")
                 if not t_proxy['outputs']:  # (Not possible - standard outputs)
                     print('  (None)')
                 for output in t_proxy['outputs']:
@@ -334,7 +362,9 @@ async def prereqs_and_outputs_query(
                         or t_proxy['xtriggers']
                 ):
                     ansiprint(
-                        "<bold>other:</bold> ('<red>-</red>': not satisfied)")
+                        "<bold>other:</bold>"
+                        f"('<red>{UNSATISFIED}</red>': not satisfied)"
+                    )
                     for ext_trig in t_proxy['externalTriggers']:
                         state = ext_trig['satisfied']
                         print_msg_state(
@@ -346,6 +376,9 @@ async def prereqs_and_outputs_query(
                         print_msg_state(
                             f'xtrigger "{xtrig["label"]} = {label}"',
                             state)
+
+                print_completion_state(t_proxy)
+
     if not results['taskProxies']:
         ansiprint(
             f"<red>No matching active tasks found: {', '.join(ids_list)}",
diff --git a/cylc/flow/task_events_mgr.py b/cylc/flow/task_events_mgr.py
index a7f16e04498..70342d4ab59 100644
--- a/cylc/flow/task_events_mgr.py
+++ b/cylc/flow/task_events_mgr.py
@@ -662,6 +662,7 @@ def process_message(
             True: if polling is required to confirm a reversal of status.
 
         """
+
         # Log messages
         if event_time is None:
             event_time = get_current_time_string()
@@ -699,8 +700,7 @@ def process_message(
 
         completed_output = None
         if msg0 not in [TASK_OUTPUT_SUBMIT_FAILED, TASK_OUTPUT_FAILED]:
-            completed_output = itask.state.outputs.set_msg_trg_completion(
-                message=msg0, is_completed=True)
+            completed_output = itask.state.outputs.set_message_complete(msg0)
             if completed_output:
                 self.data_store_mgr.delta_task_output(itask, msg0)
 
@@ -1315,8 +1315,7 @@ def _process_message_failed(self, itask, event_time, message, forced):
             if itask.state_reset(TASK_STATUS_FAILED, forced=forced):
                 self.setup_event_handlers(itask, self.EVENT_FAILED, message)
                 self.data_store_mgr.delta_task_state(itask)
-                itask.state.outputs.set_msg_trg_completion(
-                    message=TASK_OUTPUT_FAILED, is_completed=True)
+                itask.state.outputs.set_message_complete(TASK_OUTPUT_FAILED)
                 self.data_store_mgr.delta_task_output(
                     itask, TASK_OUTPUT_FAILED)
                 self.data_store_mgr.delta_task_state(itask)
@@ -1417,8 +1416,9 @@ def _process_message_submit_failed(
                 self.setup_event_handlers(
                     itask, self.EVENT_SUBMIT_FAILED,
                     f'job {self.EVENT_SUBMIT_FAILED}')
-                itask.state.outputs.set_msg_trg_completion(
-                    message=TASK_OUTPUT_SUBMIT_FAILED, is_completed=True)
+                itask.state.outputs.set_message_complete(
+                    TASK_OUTPUT_SUBMIT_FAILED
+                )
                 self.data_store_mgr.delta_task_output(
                     itask, TASK_OUTPUT_SUBMIT_FAILED)
                 self.data_store_mgr.delta_task_state(itask)
@@ -1462,7 +1462,7 @@ def _process_message_submitted(
             itask.set_summary_time('started', event_time)
             if itask.state_reset(TASK_STATUS_RUNNING, forced=forced):
                 self.data_store_mgr.delta_task_state(itask)
-            itask.state.outputs.set_completion(TASK_OUTPUT_STARTED, True)
+            itask.state.outputs.set_message_complete(TASK_OUTPUT_STARTED)
             self.data_store_mgr.delta_task_output(itask, TASK_OUTPUT_STARTED)
 
         else:
diff --git a/cylc/flow/task_outputs.py b/cylc/flow/task_outputs.py
index 644b7b0dd3c..0ca7a2345d6 100644
--- a/cylc/flow/task_outputs.py
+++ b/cylc/flow/task_outputs.py
@@ -15,7 +15,29 @@
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 """Task output message manager and constants."""
 
-from typing import List
+import ast
+import re
+from typing import (
+    Dict,
+    Iterable,
+    Iterator,
+    List,
+    Optional,
+    TYPE_CHECKING,
+    Tuple,
+    Union,
+)
+
+from cylc.flow.exceptions import InvalidCompletionExpression
+from cylc.flow.util import (
+    BOOL_SYMBOLS,
+    get_variable_names,
+    restricted_evaluator,
+)
+
+if TYPE_CHECKING:
+    from cylc.flow.taskdef import TaskDef
+
 
 # Standard task output strings, used for triggering.
 TASK_OUTPUT_EXPIRED = "expired"
@@ -32,7 +54,8 @@
     TASK_OUTPUT_SUBMIT_FAILED,
     TASK_OUTPUT_STARTED,
     TASK_OUTPUT_SUCCEEDED,
-    TASK_OUTPUT_FAILED)
+    TASK_OUTPUT_FAILED,
+)
 
 TASK_OUTPUTS = (
     TASK_OUTPUT_EXPIRED,
@@ -44,226 +67,305 @@
     TASK_OUTPUT_FINISHED,
 )
 
-_TRIGGER = 0
-_MESSAGE = 1
-_IS_COMPLETED = 2
+# this evaluates task completion expressions
+CompletionEvaluator = restricted_evaluator(
+    # expressions
+    ast.Expression,
+    # variables
+    ast.Name, ast.Load,
+    # operations
+    ast.BoolOp, ast.And, ast.Or, ast.BinOp,
+    error_class=InvalidCompletionExpression,
+)
 
+# regex for splitting expressions into individual parts for formatting
+RE_EXPR_SPLIT = re.compile(r'([\(\) ])')
 
-class TaskOutputs:
-    """Task output message manager.
 
-    Manage standard task outputs and custom outputs, e.g.:
-    [scheduling]
-        [[graph]]
-            R1 = t1:trigger1 => t2
-    [runtime]
-        [[t1]]
-            [[[outputs]]]
-                trigger1 = message 1
+def trigger_to_completion_variable(output: str) -> str:
+    """Turn a trigger into something that can be used in an expression.
 
-    Can search item by message string or by trigger string.
-    """
+    Examples:
+        >>> trigger_to_completion_variable('succeeded')
+        'succeeded'
+        >>> trigger_to_completion_variable('submit-failed')
+        'submit_failed'
 
-    # Memory optimization - constrain possible attributes to this list.
-    __slots__ = ["_by_message", "_by_trigger", "_required"]
+    """
+    return output.replace('-', '_')
 
-    def __init__(self, tdef):
-        self._by_message = {}
-        self._by_trigger = {}
-        self._required = {}  # trigger: message
 
-        # Add outputs from task def.
-        for trigger, (message, required) in tdef.outputs.items():
-            self._add(message, trigger, required=required)
+def get_completion_expression(tdef: 'TaskDef') -> str:
+    """Return a completion expression for this task definition.
 
-        # Handle implicit submit requirement
-        if (
-            # "submitted" is not declared as optional/required
-            tdef.outputs[TASK_OUTPUT_SUBMITTED][1] is None
-            # and "submit-failed" is not declared as optional/required
-            and tdef.outputs[TASK_OUTPUT_SUBMIT_FAILED][1] is None
-        ):
-            self._add(
-                TASK_OUTPUT_SUBMITTED,
-                TASK_OUTPUT_SUBMITTED,
-                required=True,
-            )
+    If there is *not* a user provided completion statement:
 
-    def _add(self, message, trigger, is_completed=False, required=False):
-        """Add a new output message"""
-        self._by_message[message] = [trigger, message, is_completed]
-        self._by_trigger[trigger] = self._by_message[message]
-        if required:
-            self._required[trigger] = message
-
-    def set_completed_by_msg(self, message):
-        """For flow trigger --wait: set completed outputs from the DB."""
-        for trig, msg, _ in self._by_trigger.values():
-            if message == msg:
-                self._add(message, trig, True, trig in self._required)
-                break
-
-    def all_completed(self):
-        """Return True if all all outputs completed."""
-        return all(val[_IS_COMPLETED] for val in self._by_message.values())
-
-    def exists(self, message=None, trigger=None):
-        """Return True if message/trigger is identified as an output."""
-        try:
-            return self._get_item(message, trigger) is not None
-        except KeyError:
-            return False
-
-    def get_all(self):
-        """Return an iterator for all output messages."""
-        return sorted(self._by_message.values(), key=self.msg_sort_key)
-
-    def get_completed(self):
-        """Return all completed output messages."""
-        ret = []
-        for value in self.get_all():
-            if value[_IS_COMPLETED]:
-                ret.append(value[_MESSAGE])
-        return ret
-
-    def get_completed_all(self):
-        """Return all completed outputs.
-
-        Return a list in this form: [(trigger1, message1), ...]
-        """
-        ret = []
-        for value in self.get_all():
-            if value[_IS_COMPLETED]:
-                ret.append((value[_TRIGGER], value[_MESSAGE]))
-        return ret
-
-    def has_custom_triggers(self):
-        """Return True if it has any custom triggers."""
-        return any(key not in SORT_ORDERS for key in self._by_trigger)
-
-    def _get_custom_triggers(self, required: bool = False) -> List[str]:
-        """Return list of all, or required, custom trigger messages."""
-        custom = [
-            out[1] for trg, out in self._by_trigger.items()
-            if trg not in SORT_ORDERS
-        ]
+    1. Create a completion expression that ensures all required ouputs are
+       completed.
+    2. If succeess is optional add "or succeeded or failed" onto the end.
+    3. If submission is optional add "or submit-failed" onto the end of it.
+    4. If expiry is optional add "or expired" onto the end of it.
+    """
+    # check if there is a user-configured completion expression
+    completion = tdef.rtconfig.get('completion')
+    if completion:
+        # completion expression is defined in the runtime -> return it
+        return completion
+
+    # (1) start with an expression that ensures all required outputs are
+    # generated (if the task runs)
+    required = {
+        trigger_to_completion_variable(trigger)
+        for trigger, (_message, required) in tdef.outputs.items()
+        if required
+    }
+    parts = []
+    if required:
+        _part = ' and '.join(sorted(required))
+        if len(required) > 1:
+            # wrap the expression in brackets for clarity
+            parts.append(f'({_part})')
+        else:
+            parts.append(_part)
+
+    # (2) handle optional success
+    if (
+        tdef.outputs[TASK_OUTPUT_SUCCEEDED][1] is False
+        or tdef.outputs[TASK_OUTPUT_FAILED][1] is False
+    ):
+        # failure is tolerated -> ensure the task succeess OR fails
         if required:
-            custom = [out for out in custom if out in self._required.values()]
-        return custom
-
-    def get_not_completed(self):
-        """Return all not-completed output messages."""
-        ret = []
-        for value in self.get_all():
-            if not value[_IS_COMPLETED]:
-                ret.append(value[_MESSAGE])
-        return ret
-
-    def is_completed(self, message=None, trigger=None):
-        """Return True if output of message is completed."""
-        try:
-            return self._get_item(message, trigger)[_IS_COMPLETED]
-        except KeyError:
-            return False
-
-    def remove(self, message=None, trigger=None):
-        """Remove an output by message, if it exists."""
-        try:
-            trigger, message = self._get_item(message, trigger)[:2]
-        except KeyError:
-            pass
+            # required outputs are required only if the task actually runs
+            parts = [
+                f'({parts[0]} and {TASK_OUTPUT_SUCCEEDED})'
+                f' or {TASK_OUTPUT_FAILED}'
+            ]
         else:
-            del self._by_message[message]
-            del self._by_trigger[trigger]
+            parts.append(
+                f'{TASK_OUTPUT_SUCCEEDED} or {TASK_OUTPUT_FAILED}'
+            )
 
-    def set_all_completed(self):
-        """Set all outputs to complete."""
-        for value in self._by_message.values():
-            value[_IS_COMPLETED] = True
+    # (3) handle optional submission
+    if (
+        tdef.outputs[TASK_OUTPUT_SUBMITTED][1] is False
+        or tdef.outputs[TASK_OUTPUT_SUBMIT_FAILED][1] is False
+    ):
+        # submit-fail tolerated -> ensure the task executes OR submit-fails
+        parts.append(
+            trigger_to_completion_variable(TASK_OUTPUT_SUBMIT_FAILED)
+        )
 
-    def set_all_incomplete(self):
-        """Set all outputs to incomplete."""
-        for value in self._by_message.values():
-            value[_IS_COMPLETED] = False
+    # (4) handle optional expiry
+    if tdef.outputs[TASK_OUTPUT_EXPIRED][1] is False:
+        # expiry tolerated -> ensure the task executes OR expires
+        parts.append(TASK_OUTPUT_EXPIRED)
+
+    return ' or '.join(parts)
+
+
+def get_optional_outputs(
+    expression: str,
+    outputs: Iterable[str],
+) -> Dict[str, Optional[bool]]:
+    """Determine which outputs in an expression are optional.
+
+    Args:
+        expression:
+            The completion expression.
+        outputs:
+            All outputs that apply to this task.
+
+    Returns:
+        dict: compvar: is_optional
+
+        compvar:
+            The completion variable, i.e. the trigger as used in the completion
+            expression.
+        is_optional:
+            * True if var is optional.
+            * False if var is required.
+            * None if var is not referenced.
+
+    Examples:
+        >>> sorted(get_optional_outputs(
+        ...     '(succeeded and (x or y)) or failed',
+        ...     {'succeeded', 'x', 'y', 'failed', 'expired'}
+        ... ).items())
+        [('expired', None), ('failed', True), ('succeeded', True),
+         ('x', True), ('y', True)]
+
+        >>> sorted(get_optional_outputs(
+        ...     '(succeeded and x and y) or expired',
+        ...     {'succeeded', 'x', 'y', 'failed', 'expired'}
+        ... ).items())
+        [('expired', True), ('failed', None), ('succeeded', False),
+         ('x', False), ('y', False)]
 
-    def set_completion(self, message, is_completed):
-        """Set output message completion status to is_completed (bool)."""
-        if message in self._by_message:
-            self._by_message[message][_IS_COMPLETED] = is_completed
+    """
+    # determine which triggers are used in the expression
+    used_compvars = get_variable_names(expression)
+
+    # all completion vairables which could appear in the expression
+    all_compvars = {trigger_to_completion_variable(out) for out in outputs}
+
+    return {  # output: is_optional
+        # the outputs that are used in the expression
+        **{
+            output: CompletionEvaluator(
+                expression,
+                **{
+                    **{out: out != output for out in all_compvars},
+                    # don't consider pre-execution conditions as optional
+                    # (pre-conditions are considered separately)
+                    'expired': False,
+                    'submit_failed': False,
+                },
+            )
+            for output in used_compvars
+        },
+        # the outputs that are not used in the expression
+        **{
+            output: None
+            for output in all_compvars - used_compvars
+        },
+    }
 
-    def set_msg_trg_completion(self, message=None, trigger=None,
-                               is_completed=True):
-        """Set the output identified by message/trigger to is_completed.
 
-        Return:
-            - Value of trigger (True) if completion flag is changed,
-            - False if completion is unchanged, or
-            - None if message/trigger is not found.
+class TaskOutputs:
+    """Represents a collection of outputs for a task.
 
-        """
-        try:
-            item = self._get_item(message, trigger)
-            old_is_completed = item[_IS_COMPLETED]
-            item[_IS_COMPLETED] = is_completed
-        except KeyError:
-            return None
-        else:
-            if bool(old_is_completed) == bool(is_completed):
-                return False
-            else:
-                return item[_TRIGGER]
-
-    def is_incomplete(self):
-        """Return True if any required outputs are not complete."""
-        return any(
-            not completed
-            and trigger in self._required
-            for trigger, (_, _, completed) in self._by_trigger.items()
-        )
+    Task outputs have a trigger and a message:
+    * The trigger is used in the graph and with "cylc set".
+    * Messages map onto triggers and are used with "cylc message", they can
+      provide additional context to an output which will appear in the workflow
+      log.
 
-    def get_incomplete(self):
-        """Return a list of required outputs that are not complete.
+    [scheduling]
+        [[graph]]
+            R1 = t1:trigger1 => t2
+    [runtime]
+        [[t1]]
+            [[[outputs]]]
+                trigger1 = message 1
 
-        A task is incomplete if:
+    Args:
+        tdef:
+            The task definition for the task these outputs represent.
 
-        * it finished executing without completing all required outputs
-        * or if job submission failed and the :submit output was not optional
+            For use outside of the scheduler, this argument can be completion
+            expression string.
 
-        https://github.com/cylc/cylc-admin/blob/master/docs/proposal-new-output-syntax.md#output-syntax
+    """
 
+    __slots__ = (
+        "_message_to_trigger",
+        "_message_to_compvar",
+        "_completed",
+        "_completion_expression",
+    )
+
+    _message_to_trigger: Dict[str, str]  # message: trigger
+    _message_to_compvar: Dict[str, str]  # message: completion variable
+    _completed: Dict[str, bool]  # message: is_complete
+    _completion_expression: str
+
+    def __init__(self, tdef: 'Union[TaskDef, str]'):
+        self._message_to_trigger = {}
+        self._message_to_compvar = {}
+        self._completed = {}
+
+        if isinstance(tdef, str):
+            # abnormal use e.g. from the "cylc show" command
+            self._completion_expression = tdef
+        else:
+            # normal use e.g. from within the scheduler
+            self._completion_expression = get_completion_expression(tdef)
+            for trigger, (message, _required) in tdef.outputs.items():
+                self.add(trigger, message)
+
+    def add(self, trigger: str, message: str) -> None:
+        """Register a new output.
+
+        Note, normally outputs are listed automatically from the provided
+        TaskDef so there is no need to call this interface. It exists for cases
+        where TaskOutputs are used outside of the scheduler where there is no
+        TaskDef object handy so outputs must be listed manually.
         """
-        return [
+        self._message_to_trigger[message] = trigger
+        self._message_to_compvar[message] = trigger_to_completion_variable(
             trigger
-            for trigger, (_, _, is_completed) in self._by_trigger.items()
-            if not is_completed and trigger in self._required
-        ]
+        )
+        self._completed[message] = False
 
-    def get_item(self, message):
-        """Return output item by message.
+    def get_trigger(self, message: str) -> str:
+        """Return the trigger associated with this message."""
+        return self._message_to_trigger[message]
 
-        Args:
-            message (str): Output message.
+    def set_message_complete(self, message):
+        """Set the provided task message as complete."""
+        if (
+            # Note, this interface sometimes gets called erroneously, so we
+            # have to check that the message being set actually applies to
+            # these outputs before setting it
+            message in self._completed
+            and self._completed[message] is False
+        ):
+            self._completed[message] = True
+            return True
+        return False
+
+    def is_message_complete(self, message: str) -> Optional[bool]:
+        """Return True if this messages is complete.
 
         Returns:
-            item (tuple):
-                label (str), message (str), satisfied (bool)
+            * True if the message is complete.
+            * False if the message is not complete.
+            * None if the message does not apply to these outputs.
+        """
+        if message in self._completed:
+            return self._completed[message]
+        return None
+
+    def iter_completed_messages(self) -> Iterator[str]:
+        """A generator that yields completed messages.
+
+        Yields:
+            message: A completed task message.
 
         """
-        if message in self._by_message:
-            return self._by_message[message]
+        for message, is_completed in self._completed.items():
+            if is_completed:
+                yield message
+
+    def __iter__(self) -> Iterator[Tuple[str, str, bool]]:
+        """A generator that yields all outputs.
+
+        Yields:
+            (trigger, message, is_complete)
 
-    def _get_item(self, message, trigger):
-        """Return self._by_trigger[trigger] or self._by_message[message].
+            trigger:
+                The output trigger.
+            message:
+                The output message.
+            is_complete:
+                True if the output is complete, else False.
 
-        whichever is relevant.
         """
-        if message is None:
-            return self._by_trigger[trigger]
-        else:
-            return self._by_message[message]
+        for message, is_complete in self._completed.items():
+            yield self._message_to_trigger[message], message, is_complete
+
+    def is_complete(self) -> bool:
+        """Return True if the outputs are complete."""
+        return CompletionEvaluator(
+            self._completion_expression,
+            **{
+                self._message_to_compvar[message]: completed
+                for message, completed in self._completed.items()
+            },
+        )
 
-    def get_incomplete_implied(self, output: str) -> List[str]:
-        """Return an ordered list of incomplete implied outputs.
+    def get_incomplete_implied(self, message: str) -> List[str]:
+        """Return an ordered list of incomplete implied messages.
 
         Use to determined implied outputs to complete automatically.
 
@@ -276,41 +378,141 @@ def get_incomplete_implied(self, output: str) -> List[str]:
         """
         implied: List[str] = []
 
-        if output in [TASK_OUTPUT_SUCCEEDED, TASK_OUTPUT_FAILED]:
+        if message in [TASK_OUTPUT_SUCCEEDED, TASK_OUTPUT_FAILED]:
             # Finished, so it must have submitted and started.
             implied = [TASK_OUTPUT_SUBMITTED, TASK_OUTPUT_STARTED]
-
-        elif output == TASK_OUTPUT_STARTED:
+        elif message == TASK_OUTPUT_STARTED:
             # It must have submitted.
             implied = [TASK_OUTPUT_SUBMITTED]
 
-        return [out for out in implied if not self.is_completed(out)]
+        return [
+            message
+            for message in implied
+            if not self.is_message_complete(message)
+        ]
+
+    def format_completion_status(
+        self,
+        indent: int = 2,
+        gutter: int = 2,
+        ansimarkup: int = 0,
+    ) -> str:
+        """Return a text representation of the status of these outputs.
+
+        Returns a multiline string representing the status of each output used
+        in the expression within the context of the expression itself.
+
+        Args:
+            indent:
+                Number of spaces to indent each level of the expression.
+            gutter:
+                Number of spaces to pad the left column from the expression.
+            ansimarkup:
+                Turns on colour coding using ansimarkup tags. These will need
+                to be parsed before display. There are three options
+
+                0:
+                    No colour coding.
+                1:
+                    Only success colours will be used. This is easier to read
+                    in colour coded logs.
+                2:
+                    Both success and fail colours will be used.
+
+        Returns:
+            A multiline textural representation of the completion status.
+
+        """
+        indent_space: str = ' ' * indent
+        _gutter: str = ' ' * gutter
+
+        def color_wrap(string, is_complete):
+            nonlocal ansimarkup
+            if ansimarkup == 0:
+                return string
+            if is_complete:
+                return f'<green>{string}</green>'
+            if ansimarkup == 2:
+                return f'<red>{string}</red>'
+            return string
+
+        ret: List[str] = []
+        indent_level: int = 0
+        op: Optional[str] = None
+        for part in RE_EXPR_SPLIT.split(self._completion_expression):
+            if not part.strip():
+                continue
+
+            if part in {'and', 'or'}:
+                op = part
+                continue
+
+            elif part == '(':
+                if op:
+                    ret.append(
+                        f'  |{_gutter}{op}'
+                        f' {(indent_space * indent_level)}{part}'
+                    )
+                else:
+                    ret.append(
+                        f'  |{_gutter}{(indent_space * indent_level)}{part}'
+                    )
+                indent_level += 1
+            elif part == ')':
+                indent_level -= 1
+                ret.append(
+                    f'  |{_gutter}{(indent_space * indent_level)}{part}'
+                )
+
+            else:
+                _symbol = BOOL_SYMBOLS[
+                    self._is_compvar_complete(part)  # type: ignore
+                ]
+                is_complete = self._is_compvar_complete(part)
+                _pre = (
+                    f'{color_wrap(_symbol, is_complete)} |'
+                    f'{_gutter}{(indent_space * indent_level)}'
+                )
+                if op:
+                    ret.append(f'{_pre}{op} {color_wrap(part, is_complete)}')
+                else:
+                    ret.append(f'{_pre}{color_wrap(part, is_complete)}')
+
+            op = None
+
+        return '\n'.join(ret)
 
     @staticmethod
-    def is_valid_std_name(name):
+    def is_valid_std_name(name: str) -> bool:
         """Check name is a valid standard output name."""
         return name in SORT_ORDERS
 
     @staticmethod
-    def msg_sort_key(item):
-        """Compare by _MESSAGE."""
-        try:
-            ind = SORT_ORDERS.index(item[_MESSAGE])
-        except ValueError:
-            ind = 999
-        return (ind, item[_MESSAGE] or '')
-
-    @staticmethod
-    def output_sort_key(item):
+    def output_sort_key(item: Iterable[str]) -> float:
         """Compare by output order.
 
         Examples:
-
             >>> this = TaskOutputs.output_sort_key
             >>> sorted(['finished', 'started',  'custom'], key=this)
             ['started', 'custom', 'finished']
+
         """
         if item in TASK_OUTPUTS:
             return TASK_OUTPUTS.index(item)
         # Sort custom outputs after started.
         return TASK_OUTPUTS.index(TASK_OUTPUT_STARTED) + .5
+
+    def _is_compvar_complete(self, compvar: str) -> Optional[bool]:
+        """Return True if the completion variable is complete.
+
+        Returns:
+            * True if var is optional.
+            * False if var is required.
+            * None if var is not referenced.
+
+        """
+        for message, _compvar in self._message_to_compvar.items():
+            if _compvar == compvar:
+                return self.is_message_complete(message)
+        else:
+            raise KeyError(compvar)
diff --git a/cylc/flow/task_pool.py b/cylc/flow/task_pool.py
index 2b214d70943..cb245d800b3 100644
--- a/cylc/flow/task_pool.py
+++ b/cylc/flow/task_pool.py
@@ -19,6 +19,7 @@
 from contextlib import suppress
 from collections import Counter
 import json
+from textwrap import indent
 from typing import (
     Dict,
     Iterable,
@@ -526,7 +527,7 @@ def load_db_task_pool_for_restart(self, row_idx, row):
                     TASK_STATUS_SUCCEEDED
             ):
                 for message in json.loads(outputs_str):
-                    itask.state.outputs.set_completion(message, True)
+                    itask.state.outputs.set_message_complete(message)
                     self.data_store_mgr.delta_task_output(itask, message)
 
             if platform_name and status != TASK_STATUS_WAITING:
@@ -1146,15 +1147,22 @@ def log_incomplete_tasks(self) -> bool:
         for itask in self.get_tasks():
             if not itask.state(*TASK_STATUSES_FINAL):
                 continue
-            outputs = itask.state.outputs.get_incomplete()
-            if outputs:
-                incomplete.append((itask.identity, outputs))
+            if not itask.state.outputs.is_complete():
+                incomplete.append(
+                    (
+                        itask.identity,
+                        itask.state.outputs.format_completion_status(
+                            ansimarkup=1
+                        ),
+                    )
+                )
 
         if incomplete:
             LOG.error(
                 "Incomplete tasks:\n"
                 + "\n".join(
-                    f"  * {id_} did not complete required outputs: {outputs}"
+                    f"* {id_} did not complete the required outputs:"
+                    f"\n{indent(outputs, '  ')}"
                     for id_, outputs in incomplete
                 )
             )
@@ -1441,22 +1449,17 @@ def remove_if_complete(
                 self.release_runahead_tasks()
             return ret
 
-        if itask.state(TASK_STATUS_EXPIRED):
-            self.remove(itask, "expired")
-            if self.compute_runahead():
-                self.release_runahead_tasks()
-            return True
-
-        incomplete = itask.state.outputs.get_incomplete()
-        if incomplete:
+        if not itask.state.outputs.is_complete():
             # Keep incomplete tasks in the pool.
             if output in TASK_STATUSES_FINAL:
                 # Log based on the output, not the state, to avoid warnings
                 # due to use of "cylc set" to set internal outputs on an
                 # already-finished task.
                 LOG.warning(
-                    f"[{itask}] did not complete required outputs:"
-                    f" {incomplete}"
+                    f"[{itask}] did not complete the required outputs:\n"
+                    + itask.state.outputs.format_completion_status(
+                        ansimarkup=1
+                    )
                 )
             return False
 
@@ -1482,14 +1485,12 @@ def spawn_on_all_outputs(
         """
         if not itask.flow_nums:
             return
-        if completed_only:
-            outputs = itask.state.outputs.get_completed()
-        else:
-            outputs = itask.state.outputs._by_message
 
-        for output in outputs:
+        for _trigger, message, is_completed in itask.state.outputs:
+            if completed_only and not is_completed:
+                continue
             try:
-                children = itask.graph_children[output]
+                children = itask.graph_children[message]
             except KeyError:
                 continue
 
@@ -1509,7 +1510,7 @@ def spawn_on_all_outputs(
                     continue
                 if completed_only:
                     c_task.satisfy_me(
-                        [itask.tokens.duplicate(task_sel=output)]
+                        [itask.tokens.duplicate(task_sel=message)]
                     )
                     self.data_store_mgr.delta_task_prerequisite(c_task)
                 self.add_to_pool(c_task)
@@ -1595,7 +1596,7 @@ def _load_historical_outputs(self, itask):
             for outputs_str, fnums in info.items():
                 if itask.flow_nums.intersection(fnums):
                     for msg in json.loads(outputs_str):
-                        itask.state.outputs.set_completed_by_msg(msg)
+                        itask.state.outputs.set_message_complete(msg)
 
     def spawn_task(
         self,
@@ -1744,7 +1745,7 @@ def _get_task_proxy_db_outputs(
         for outputs_str, fnums in info.items():
             if flow_nums.intersection(fnums):
                 for msg in json.loads(outputs_str):
-                    itask.state.outputs.set_completed_by_msg(msg)
+                    itask.state.outputs.set_message_complete(msg)
         return itask
 
     def _standardise_prereqs(
@@ -1887,7 +1888,6 @@ def _set_outputs_itask(
         outputs: List[str],
     ) -> None:
         """Set requested outputs on a task proxy and spawn children."""
-
         if not outputs:
             outputs = itask.tdef.get_required_output_messages()
         else:
@@ -1896,7 +1896,7 @@ def _set_outputs_itask(
 
         outputs = sorted(outputs, key=itask.state.outputs.output_sort_key)
         for output in outputs:
-            if itask.state.outputs.is_completed(output):
+            if itask.state.outputs.is_message_complete(output):
                 LOG.info(f"output {itask.identity}:{output} completed already")
                 continue
             self.task_events_mgr.process_message(
@@ -2410,7 +2410,7 @@ def merge_flows(self, itask: TaskProxy, flow_nums: 'FlowNums') -> None:
 
         if (
             itask.state(*TASK_STATUSES_FINAL)
-            and itask.state.outputs.get_incomplete()
+            and not itask.state.outputs.is_complete()
         ):
             # Re-queue incomplete task to run again in the merged flow.
             LOG.info(f"[{itask}] incomplete task absorbed by new flow.")
diff --git a/cylc/flow/task_proxy.py b/cylc/flow/task_proxy.py
index 898017c8da1..dbb6efc6db9 100644
--- a/cylc/flow/task_proxy.py
+++ b/cylc/flow/task_proxy.py
@@ -38,19 +38,11 @@
 from cylc.flow.flow_mgr import stringify_flow_nums
 from cylc.flow.platforms import get_platform
 from cylc.flow.task_action_timer import TimerFlags
-from cylc.flow.task_outputs import (
-    TASK_OUTPUT_FAILED,
-    TASK_OUTPUT_EXPIRED,
-    TASK_OUTPUT_SUCCEEDED,
-    TASK_OUTPUT_SUBMIT_FAILED
-)
 from cylc.flow.task_state import (
     TaskState,
     TASK_STATUS_WAITING,
     TASK_STATUS_EXPIRED,
-    TASK_STATUS_SUCCEEDED,
-    TASK_STATUS_SUBMIT_FAILED,
-    TASK_STATUS_FAILED
+    TASK_STATUSES_FINAL,
 )
 from cylc.flow.taskdef import generate_graph_children
 from cylc.flow.wallclock import get_unix_time_from_time_string as str2time
@@ -578,32 +570,8 @@ def clock_expire(self) -> bool:
 
     def is_finished(self) -> bool:
         """Return True if a final state achieved."""
-        return (
-            self.state(
-                TASK_STATUS_EXPIRED,
-                TASK_STATUS_SUBMIT_FAILED,
-                TASK_STATUS_FAILED,
-                TASK_STATUS_SUCCEEDED
-            )
-        )
+        return self.state(*TASK_STATUSES_FINAL)
 
     def is_complete(self) -> bool:
         """Return True if complete or expired."""
-        return (
-            self.state(TASK_STATUS_EXPIRED)
-            or not self.state.outputs.is_incomplete()
-        )
-
-    def set_state_by_outputs(self) -> None:
-        """Set state according to which final output is completed."""
-        for output in (
-            TASK_OUTPUT_EXPIRED, TASK_OUTPUT_SUBMIT_FAILED,
-            TASK_OUTPUT_FAILED, TASK_OUTPUT_SUCCEEDED
-        ):
-            if self.state.outputs.is_completed(output, output):
-                # This assumes status and output strings are the same:
-                self.state_reset(
-                    status=output,
-                    silent=True, is_queued=False, is_runahead=False
-                )
-                break
+        return self.state.outputs.is_complete()
diff --git a/cylc/flow/taskdef.py b/cylc/flow/taskdef.py
index 1da5101306b..22315b0e78e 100644
--- a/cylc/flow/taskdef.py
+++ b/cylc/flow/taskdef.py
@@ -23,9 +23,7 @@
 from cylc.flow.exceptions import TaskDefError
 from cylc.flow.task_id import TaskID
 from cylc.flow.task_outputs import (
-    TASK_OUTPUT_EXPIRED,
     TASK_OUTPUT_SUBMITTED,
-    TASK_OUTPUT_SUBMIT_FAILED,
     TASK_OUTPUT_SUCCEEDED,
     TASK_OUTPUT_FAILED,
     SORT_ORDERS
@@ -75,7 +73,7 @@ def generate_graph_children(tdef, point):
 
 
 def generate_graph_parents(tdef, point, taskdefs):
-    """Determine concrent graph parents of task tdef at point.
+    """Determine concrete graph parents of task tdef at point.
 
     Infer parents be reversing upstream triggers that lead to point/task.
     """
@@ -204,21 +202,13 @@ def get_required_output_messages(self):
 
     def tweak_outputs(self):
         """Output consistency checking and tweaking."""
-
         # If :succeed or :fail not set, assume success is required.
-        # Unless submit (and submit-fail) is optional (don't stall
-        # because of missing succeed if submit is optional).
         if (
             self.outputs[TASK_OUTPUT_SUCCEEDED][1] is None
             and self.outputs[TASK_OUTPUT_FAILED][1] is None
-            and self.outputs[TASK_OUTPUT_SUBMITTED][1] is not False
-            and self.outputs[TASK_OUTPUT_SUBMIT_FAILED][1] is not False
         ):
             self.set_required_output(TASK_OUTPUT_SUCCEEDED, True)
 
-        # Expired must be optional
-        self.set_required_output(TASK_OUTPUT_EXPIRED, False)
-
         # In Cylc 7 back compat mode, make all success outputs required.
         if cylc.flow.flags.cylc7_back_compat:
             for output in [
diff --git a/cylc/flow/util.py b/cylc/flow/util.py
index b167cb33a84..ac10bab9b54 100644
--- a/cylc/flow/util.py
+++ b/cylc/flow/util.py
@@ -25,9 +25,12 @@
     Callable,
     List,
     Sequence,
+    Tuple,
 )
 
 
+BOOL_SYMBOLS: List[str] = ['x', '✓']
+
 _NAT_SORT_SPLIT = re.compile(r'([\d\.]+)')
 
 
@@ -336,3 +339,35 @@ def _get_exception(
     }
 
     return error_class(message, **context)
+
+
+class NameWalker(ast.NodeVisitor):
+    """AST node visitor which records all variable names in an expression.
+
+    Examples:
+        >>> tree = ast.parse('(foo and bar) or baz or qux')
+        >>> walker = NameWalker()
+        >>> walker.visit(tree)
+        >>> sorted(walker.names)
+        ['bar', 'baz', 'foo', 'qux']
+
+    """
+
+    def __init__(self):
+        super().__init__()
+        self._names = set()
+
+    def visit(self, node):
+        if isinstance(node, ast.Name):
+            self._names.add(node.id)
+        return super().visit(node)
+
+    @property
+    def names(self):
+        return self._names
+
+
+def get_variable_names(expression):
+    walker = NameWalker()
+    walker.visit(ast.parse(expression))
+    return walker.names
diff --git a/cylc/flow/workflow_db_mgr.py b/cylc/flow/workflow_db_mgr.py
index 128cfd45126..0a92e7312bf 100644
--- a/cylc/flow/workflow_db_mgr.py
+++ b/cylc/flow/workflow_db_mgr.py
@@ -630,11 +630,10 @@ def put_update_task_jobs(self, itask, set_args):
 
     def put_update_task_outputs(self, itask):
         """Put UPDATE statement for task_outputs table."""
-        outputs = []
-        for _, message in itask.state.outputs.get_completed_all():
-            outputs.append(message)
         set_args = {
-            "outputs": json.dumps(outputs)
+            "outputs": json.dumps(
+                list(itask.state.outputs.iter_completed_messages())
+            )
         }
         where_args = {
             "cycle": str(itask.point),
diff --git a/tests/integration/conftest.py b/tests/integration/conftest.py
index d575f2a6af2..edfe56e2a1f 100644
--- a/tests/integration/conftest.py
+++ b/tests/integration/conftest.py
@@ -360,6 +360,28 @@ def _validate(id_: Union[str, Path], **kwargs) -> WorkflowConfig:
     return _validate
 
 
+@pytest.fixture(scope='module')
+def mod_validate(run_dir):
+    """Provides a function for validating workflow configurations.
+
+    Attempts to load the configuration, will raise exceptions if there are
+    errors.
+
+    Args:
+        id_ - The flow to validate
+        kwargs - Arguments to pass to ValidateOptions
+    """
+    def _validate(id_: Union[str, Path], **kwargs) -> WorkflowConfig:
+        id_ = str(id_)
+        return WorkflowConfig(
+            id_,
+            str(Path(run_dir, id_, 'flow.cylc')),
+            ValidateOptions(**kwargs)
+        )
+
+    return _validate
+
+
 @pytest.fixture
 def capture_submission():
     """Suppress job submission and capture submitted tasks.
diff --git a/tests/integration/test_optional_outputs.py b/tests/integration/test_optional_outputs.py
new file mode 100644
index 00000000000..d897fc4ce6d
--- /dev/null
+++ b/tests/integration/test_optional_outputs.py
@@ -0,0 +1,380 @@
+# THIS FILE IS PART OF THE CYLC WORKFLOW ENGINE.
+# Copyright (C) NIWA & British Crown (Met Office) & Contributors.
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+"""Tests optional output and task completion logic.
+
+This functionality is defined by the "optional-output-extension" proposal:
+
+https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+"""
+
+from itertools import combinations
+from typing import TYPE_CHECKING
+
+import pytest
+
+from cylc.flow.cycling.integer import IntegerPoint
+from cylc.flow.cycling.iso8601 import ISO8601Point
+from cylc.flow.network.resolvers import TaskMsg
+from cylc.flow.scheduler import Scheduler
+from cylc.flow.task_events_mgr import (
+    TaskEventsManager,
+)
+from cylc.flow.task_outputs import (
+    TASK_OUTPUTS,
+    TASK_OUTPUT_EXPIRED,
+    TASK_OUTPUT_FINISHED,
+    TASK_OUTPUT_SUCCEEDED,
+    get_completion_expression,
+)
+from cylc.flow.task_state import (
+    TASK_STATUS_EXPIRED,
+    TASK_STATUS_PREPARING,
+    TASK_STATUS_WAITING,
+)
+
+if TYPE_CHECKING:
+    from cylc.flow.task_proxy import TaskProxy
+
+
+def reset_outputs(itask: 'TaskProxy'):
+    """Undo the consequences of setting task outputs.
+
+    This assumes you haven't completed the task.
+    """
+    itask.state.outputs._completed = {
+        message: False
+        for message in itask.state.outputs._completed
+    }
+    itask.state_reset(
+        TASK_STATUS_WAITING,
+        is_queued=False,
+        is_held=False,
+        is_runahead=False,
+    )
+
+
+@pytest.mark.parametrize(
+    'graph, completion_outputs',
+    [
+        pytest.param(
+            'a:x',
+            [{TASK_OUTPUT_SUCCEEDED, 'x'}],
+            id='1',
+        ),
+        pytest.param(
+            'a\na:x\na:expired?',
+            [{TASK_OUTPUT_SUCCEEDED, 'x'}, {TASK_OUTPUT_EXPIRED}],
+            id='2',
+        ),
+    ],
+)
+async def test_task_completion(
+    flow,
+    scheduler,
+    start,
+    graph,
+    completion_outputs,
+    capcall,
+):
+    """Ensure that task completion is watertight.
+
+    Run through every possible permutation of outputs MINUS the ones that would
+    actually complete a task to ensure that task completion is correctly
+    handled.
+
+    Note, the building and evaluation of completion expressions is also tested,
+    this is more of an end-to-end test to ensure everything is connected
+    properly.
+    """
+    # prevent tasks from being removed from the pool when complete
+    capcall(
+        'cylc.flow.task_pool.TaskPool.remove_if_complete'
+    )
+    id_ = flow({
+        'scheduling': {
+            'graph': {'R1': graph},
+        },
+        'runtime': {
+            'a': {
+                'outputs': {
+                    'x': 'xxx',
+                },
+            },
+        },
+    })
+    schd = scheduler(id_)
+    all_outputs = {
+        # all built-in outputs
+        *TASK_OUTPUTS,
+        # all registered custom outputs
+        'x'
+        # but not the finished psudo output
+    } - {TASK_OUTPUT_FINISHED}
+
+    async with start(schd):
+        a1 = schd.pool.get_task(IntegerPoint('1'), 'a')
+
+        # try every set of outputs that *shouldn't* complete the task
+        for combination in {
+            comb
+            # every possible combination of outputs
+            for _length in range(1, len(all_outputs))
+            for comb in combinations(all_outputs, _length)
+            # that doesn't contain the outputs that would satisfy the task
+            if not any(
+                set(comb) & output_set == output_set
+                for output_set in completion_outputs
+            )
+        }:
+            # set the combination of outputs
+            schd.pool.set_prereqs_and_outputs(
+                ['1/a'],
+                combination,
+                [],
+                ['1'],
+            )
+
+            # ensure these outputs do *not* complete the task
+            assert not a1.state.outputs.is_complete()
+
+            # reset any changes
+            reset_outputs(a1)
+
+        # now try the outputs that *should* satisfy the task
+        for combination in completion_outputs:
+            # set the combination of outputs
+            schd.pool.set_prereqs_and_outputs(
+                ['1/a'],
+                combination,
+                [],
+                ['1'],
+            )
+
+            # ensure the task *is* completed
+            assert a1.state.outputs.is_complete()
+
+            # reset any changes
+            reset_outputs(a1)
+
+
+async def test_expire_orthogonality(flow, scheduler, start):
+    """Ensure "expired?" does not infer "succeeded?".
+
+    Asserts proposal point 2:
+    https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+    """
+    id_ = flow({
+        'scheduling': {
+            'graph': {
+                'R1': 'a:expire? => e'
+            },
+        },
+    })
+    schd: 'Scheduler' = scheduler(id_, paused_start=False)
+    async with start(schd):
+        a_1 = schd.pool.get_task(IntegerPoint('1'), 'a')
+
+        # wait for the task to submit
+        while not a_1.state(TASK_STATUS_WAITING, TASK_STATUS_PREPARING):
+            schd.release_queued_tasks()
+
+        # NOTE: The submit number isn't presently incremented via this code
+        # pathway so we have to hack it here. If the task messages in this test
+        # get ignored because of some future change, then you can safely remove
+        # this line (it's not what this test is testing).
+        a_1.submit_num += 1
+
+        # tell the scheduler that the task *submit-failed*
+        schd.message_queue.put(
+            TaskMsg(
+                '1/a/01',
+                '2000-01-01T00:00:00+00',
+                'INFO',
+                TaskEventsManager.EVENT_SUBMIT_FAILED
+            ),
+        )
+        schd.process_queued_task_messages()
+        # ensure that the scheduler is stalled
+        assert not a_1.state.outputs.is_complete()
+        assert schd.pool.is_stalled()
+
+        # tell the scheduler that the task *failed*
+        schd.message_queue.put(
+            TaskMsg(
+                '1/a/01',
+                '2000-01-01T00:00:00+00',
+                'INFO',
+                TaskEventsManager.EVENT_FAILED,
+            ),
+        )
+        schd.process_queued_task_messages()
+        # ensure that the scheduler is stalled
+        assert not a_1.state.outputs.is_complete()
+        assert schd.pool.is_stalled()
+
+        # tell the scheduler that the task *expired*
+        schd.message_queue.put(
+            TaskMsg(
+                '1/a/01',
+                '2000-01-01T00:00:00+00',
+                'INFO',
+                TaskEventsManager.EVENT_EXPIRED,
+            ),
+        )
+        schd.process_queued_task_messages()
+        # ensure that the scheduler is *not* stalled
+        assert a_1.state.outputs.is_complete()
+        assert not schd.pool.is_stalled()
+
+
+@pytest.fixture(scope='module')
+def implicit_completion_config(mod_flow, mod_validate):
+    id_ = mod_flow({
+        'scheduling': {
+            'graph': {
+                'R1': '''
+                    a
+
+                    b?
+
+                    c:x
+
+                    d:x?
+                    d:y?
+                    d:z?
+
+                    e:x
+                    e:y
+                    e:z
+
+                    f?
+                    f:x
+
+                    g:expired?
+
+                    h:succeeded?
+                    h:expired?
+
+                    i:expired?
+                    i:submitted
+
+                    j:expired?
+                    j:submitted?
+
+                    k:submit-failed?
+                    k:succeeded?
+
+                    l:expired?
+                    l:submit-failed?
+                    l:succeeded?
+                '''
+            }
+        },
+        'runtime': {
+            'root': {
+                'outputs': {
+                    'x': 'xxx',
+                    'y': 'yyy',
+                    'z': 'zzz',
+                }
+            }
+        }
+    })
+    return mod_validate(id_)
+
+
+@pytest.mark.parametrize(
+    'task, condition',
+    [
+        pytest.param('a', 'succeeded', id='a'),
+        pytest.param('b', 'succeeded or failed', id='b'),
+        pytest.param('c', '(succeeded and x)', id='c'),
+        pytest.param('d', 'succeeded', id='d'),
+        pytest.param('e', '(succeeded and x and y and z)', id='e'),
+        pytest.param('f', '(x and succeeded) or failed', id='f'),
+        pytest.param('g', 'succeeded or expired', id='h'),
+        pytest.param('h', 'succeeded or failed or expired', id='h'),
+        pytest.param('i', '(submitted and succeeded) or expired', id='i'),
+        pytest.param('j', 'succeeded or submit_failed or expired', id='j'),
+        pytest.param('k', 'succeeded or failed or submit_failed', id='k'),
+        pytest.param(
+            'l', 'succeeded or failed or submit_failed or expired', id='l'
+        ),
+    ],
+)
+async def test_implicit_completion_expression(
+    implicit_completion_config,
+    task,
+    condition,
+):
+    """It should generate a completion expression from the graph.
+
+    If no completion expression is provided in the runtime section, then it
+    should auto generate one inferring whether outputs are required or not from
+    the graph.
+    """
+    completion_expression = get_completion_expression(
+        implicit_completion_config.taskdefs[task]
+    )
+    assert completion_expression == condition
+
+
+async def test_clock_expire_partially_satisfied_task(
+    flow,
+    scheduler,
+    start,
+):
+    """Clock expire should take effect on a partially satisfied task.
+
+    Tests proposal point 8:
+    https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+    """
+    id_ = flow({
+        'scheduling': {
+            'initial cycle point': '2000',
+            'runahead limit': 'P0',
+            'special tasks': {
+                'clock-expire': 'e',
+            },
+            'graph': {
+                'P1D': '''
+                    # this prerequisite we will satisfy
+                    a => e
+
+                    # this prerequisite we will leave unsatisfied creating a
+                    # partially-satisfied task
+                    b => e
+                '''
+            },
+        },
+    })
+    schd = scheduler(id_)
+    async with start(schd):
+        # satisfy one of the prerequisites
+        a = schd.pool.get_task(ISO8601Point('20000101T0000Z'), 'a')
+        assert a
+        schd.pool.spawn_on_output(a, TASK_OUTPUT_SUCCEEDED)
+
+        # the task "e" should now be spawned
+        e = schd.pool.get_task(ISO8601Point('20000101T0000Z'), 'e')
+        assert e
+
+        # check for clock-expired tasks
+        schd.pool.clock_expire_tasks()
+
+        # the task should now be in the expired state
+        assert e.state(TASK_STATUS_EXPIRED)
diff --git a/tests/integration/test_simulation.py b/tests/integration/test_simulation.py
index 72cf23996a4..66842fade25 100644
--- a/tests/integration/test_simulation.py
+++ b/tests/integration/test_simulation.py
@@ -184,11 +184,10 @@ def test_task_finishes(sim_time_check_setup, monkeytime, caplog):
 
     # After simulation time is up it Fails and records custom outputs:
     assert sim_time_check(schd.task_events_mgr, [fail_all_1066], '') is True
-    outputs = {
-        o[0]: (o[1], o[2]) for o in fail_all_1066.state.outputs.get_all()}
-    assert outputs['succeeded'] == ('succeeded', False)
-    assert outputs['foo'] == ('bar', True)
-    assert outputs['failed'] == ('failed', True)
+    outputs = fail_all_1066.state.outputs
+    assert outputs.is_message_complete('succeeded') is False
+    assert outputs.is_message_complete('bar') is True
+    assert outputs.is_message_complete('failed') is True
 
 
 def test_task_sped_up(sim_time_check_setup, monkeytime):
@@ -334,7 +333,7 @@ async def test_settings_reload(
         one_1066 = schd.pool.get_tasks()[0]
 
         itask = run_simjob(schd, one_1066.point, 'one')
-        assert ['failed', 'failed', False] in itask.state.outputs.get_all()
+        assert itask.state.outputs.is_message_complete('failed') is False
 
         # Modify config as if reinstall had taken place:
         conf_file = Path(schd.workflow_run_dir) / 'flow.cylc'
@@ -346,8 +345,7 @@ async def test_settings_reload(
 
         # Submit second psuedo-job and "run" to success:
         itask = run_simjob(schd, one_1066.point, 'one')
-        assert [
-            'succeeded', 'succeeded', True] in itask.state.outputs.get_all()
+        assert itask.state.outputs.is_message_complete('succeeded') is True
 
 
 async def test_settings_broadcast(
diff --git a/tests/integration/test_task_pool.py b/tests/integration/test_task_pool.py
index 3d75074cf15..7623ba0a797 100644
--- a/tests/integration/test_task_pool.py
+++ b/tests/integration/test_task_pool.py
@@ -1178,9 +1178,10 @@ async def test_detect_incomplete_tasks(
     start,
     log_filter,
 ):
-    """Finished but incomplete tasks should be retains as incomplete."""
-
-    final_task_states = {
+    """Finished but incomplete tasks should be retained as incomplete."""
+    incomplete_final_task_states = {
+        # final task states that would leave a task with
+        # completion=succeeded incomplete
         TASK_STATUS_FAILED: TaskEventsManager.EVENT_FAILED,
         TASK_STATUS_EXPIRED: TaskEventsManager.EVENT_EXPIRED,
         TASK_STATUS_SUBMIT_FAILED: TaskEventsManager.EVENT_SUBMIT_FAILED
@@ -1192,7 +1193,7 @@ async def test_detect_incomplete_tasks(
         'scheduling': {
             'graph': {
                 # a workflow with one task for each of the final task states
-                'R1': '\n'.join(final_task_states.keys())
+                'R1': '\n'.join(incomplete_final_task_states.keys())
             }
         }
     })
@@ -1204,28 +1205,18 @@ async def test_detect_incomplete_tasks(
             # spawn the output corresponding to the task
             schd.pool.task_events_mgr.process_message(
                 itask, 1,
-                final_task_states[itask.tdef.name]
+                incomplete_final_task_states[itask.tdef.name]
             )
             # ensure that it is correctly identified as incomplete
-            assert itask.state.outputs.get_incomplete()
-            assert itask.state.outputs.is_incomplete()
-            if itask.tdef.name == TASK_STATUS_EXPIRED:
-                assert log_filter(
-                    log,
-                    contains=f"[{itask}] removed (expired)"
-                )
-                # the task should have been removed
-                assert itask not in schd.pool.get_tasks()
-            else:
-                assert log_filter(
-                    log,
-                    contains=(
-                        f"[{itask}] did not complete "
-                        "required outputs:"
-                    )
-                )
-                # the task should not have been removed
-                assert itask in schd.pool.get_tasks()
+            assert not itask.state.outputs.is_complete()
+            assert log_filter(
+                log,
+                contains=(
+                    f"[{itask}] did not complete the required outputs:"
+                ),
+            )
+            # the task should not have been removed
+            assert itask in schd.pool.get_tasks()
 
 
 async def test_future_trigger_final_point(
diff --git a/tests/integration/tui/screenshots/test_show.success.html b/tests/integration/tui/screenshots/test_show.success.html
index 5f9c192b04b..8982956d523 100644
--- a/tests/integration/tui/screenshots/test_show.success.html
+++ b/tests/integration/tui/screenshots/test_show.success.html
@@ -8,7 +8,6 @@
 <span style="color:#000000;background:#e5e5e5">                                                                                </span>
 <span style="color:#000000;background:#e5e5e5">                                                                                </span>
 <span style="color:#000000;background:#e5e5e5">                                                                                </span>
-<span style="color:#000000;background:#e5e5e5">                                                                                </span>
 <span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">┌</span><span style="color:#000000;background:#e5e5e5">────────────────────────</span><span style="color:#000000;background:#e5e5e5">────────────────────────</span><span style="color:#000000;background:#e5e5e5">┐</span><span style="color:#000000;background:#e5e5e5">               </span>
 <span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">title: Foo                                  </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
 <span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">description: The first metasyntactic        </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
@@ -16,13 +15,15 @@
 <span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">URL: (not given)                            </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
 <span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">state: waiting                              </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
 <span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">prerequisites: (None)                       </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
-<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">outputs: (&#x27;-&#x27;: not completed)               </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
-<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  - 1/foo expired                           </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
-<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  - 1/foo submitted                         </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
-<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  - 1/foo submit-failed                     </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
-<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  - 1/foo started                           </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
-<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  - 1/foo succeeded                         </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
-<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  - 1/foo failed                            </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
+<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">outputs: (&#x27;x&#x27;: not completed)               </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
+<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  x 1/foo expired                           </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
+<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  x 1/foo submitted                         </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
+<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  x 1/foo submit-failed                     </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
+<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  x 1/foo started                           </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
+<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  x 1/foo succeeded                         </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
+<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  x 1/foo failed                            </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
+<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">completion: incomplete                      </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
+<span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">  x |  succeeded                            </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
 <span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">                                            </span><span style="color:#000000;background:#e5e5e5">  </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
 <span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">                                                </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
 <span style="color:#000000;background:#e5e5e5">               </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5"> q to close                                     </span><span style="color:#000000;background:#e5e5e5">│</span><span style="color:#000000;background:#e5e5e5">               </span>
@@ -35,7 +36,6 @@
 <span style="color:#000000;background:#e5e5e5">                                                                                </span>
 <span style="color:#000000;background:#e5e5e5">                                                                                </span>
 <span style="color:#000000;background:#e5e5e5">                                                                                </span>
-<span style="color:#000000;background:#e5e5e5">                                                                                </span>
 <span style="color:#ffffff;background:#0000ee">quit: </span><span style="color:#00ffff;background:#0000ee">q</span><span style="color:#ffffff;background:#0000ee">  help: </span><span style="color:#00ffff;background:#0000ee">h</span><span style="color:#ffffff;background:#0000ee">  context: </span><span style="color:#00ffff;background:#0000ee">enter</span><span style="color:#ffffff;background:#0000ee">  tree: </span><span style="color:#00ffff;background:#0000ee">- ← + → </span><span style="color:#ffffff;background:#0000ee"> navigation: </span><span style="color:#00ffff;background:#0000ee">↑ ↓ ↥ ↧ Home End </span><span style="color:#ffffff;background:#0000ee">  </span>
 <span style="color:#ffffff;background:#0000ee">filter tasks: </span><span style="color:#00ffff;background:#0000ee">T f s r R </span><span style="color:#ffffff;background:#0000ee"> filter workflows: </span><span style="color:#00ffff;background:#0000ee">W E p </span><span style="color:#ffffff;background:#0000ee">                               </span>
 </pre>
\ No newline at end of file
diff --git a/tests/integration/validate/test_outputs.py b/tests/integration/validate/test_outputs.py
index 5675372a09f..8bfd9b546ee 100644
--- a/tests/integration/validate/test_outputs.py
+++ b/tests/integration/validate/test_outputs.py
@@ -32,7 +32,6 @@
                 'foo',
                 'foo-bar',
                 'foo_bar',
-                'foo.bar',
                 '0foo0',
                 '123',
             ],
@@ -152,7 +151,7 @@ def test_messages(messages, valid, flow, validate):
         'runtime': {
             'foo': {
                 'outputs': {
-                    str(random()): message
+                    str(random())[2:]: message
                     for message in messages
                 }
             }
@@ -164,3 +163,111 @@ def test_messages(messages, valid, flow, validate):
     else:
         with pytest.raises(WorkflowConfigError):
             val()
+
+
+@pytest.mark.parametrize(
+    'graph, expression, message', [
+        pytest.param(
+            'foo:x',
+            'succeeded and (x or y)',
+            r'foo:x is required in the graph.*'
+            r' but optional in the completion expression',
+            id='required-in-graph-optional-in-completion',
+        ),
+        pytest.param(
+            'foo:x?',
+            'succeeded and x',
+            r'foo:x is optional in the graph.*'
+            r' but required in the completion expression',
+            id='optional-in-graph-required-in-completion',
+        ),
+        pytest.param(
+            'foo:x',
+            'succeeded',
+            'foo:x is required in the graph.*'
+            'but not referenced in the completion expression',
+            id='required-in-graph-not-referenced-in-completion',
+        ),
+        pytest.param(
+            # tests proposal point 4:
+            # https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+            'foo:expired',
+            'succeeded',
+            'foo:expired must be optional',
+            id='expire-required-in-graph',
+        ),
+        pytest.param(
+            'foo:expired?',
+            'succeeded',
+            'foo:expired is permitted in the graph.*'
+            '\nTry: completion = "succeeded or expired"',
+            id='expire-optional-in-graph-but-not-used-in-completion'
+        ),
+        pytest.param(
+            # tests part of proposal point 5:
+            # https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+            'foo',
+            'finished and x',
+            '"finished" output cannot be used in completion expressions',
+            id='finished-output-used-in-completion-expression',
+        ),
+    ]
+)
+def test_completion_expression_invalid(
+    flow,
+    validate,
+    graph,
+    expression,
+    message,
+):
+    """It should ensure the completion is logically consistent with the graph.
+
+    Tests proposal point 5:
+    https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+    """
+    id_ = flow({
+        'scheduling': {
+            'graph': {'R1': graph},
+        },
+        'runtime': {
+            'foo': {
+                'completion': expression,
+                'outputs': {
+                    'x': 'xxx',
+                    'y': 'yyy',
+                },
+            },
+        },
+    })
+    with pytest.raises(WorkflowConfigError, match=message):
+        validate(id_)
+
+
+@pytest.mark.parametrize(
+    'graph, expression', [
+        ('foo', 'succeeded and (x or y or z)'),
+        ('foo?', 'succeeded and (x or y or z) or failed or expired'),
+        ('foo', '(succeeded and x) or (expired and y)'),
+    ]
+)
+def test_completion_expression_valid(
+    flow,
+    validate,
+    graph,
+    expression,
+):
+    id_ = flow({
+        'scheduling': {
+            'graph': {'R1': graph},
+        },
+        'runtime': {
+            'foo': {
+                'completion': expression,
+                'outputs': {
+                    'x': 'xxx',
+                    'y': 'yyy',
+                },
+            },
+        },
+    })
+    validate(id_)
diff --git a/tests/unit/test_config.py b/tests/unit/test_config.py
index 98d9fc2f4ce..a69ab176412 100644
--- a/tests/unit/test_config.py
+++ b/tests/unit/test_config.py
@@ -1317,28 +1317,6 @@ def test_implicit_success_required(tmp_flow_config, graph):
     assert cfg.taskdefs['foo'].outputs[TASK_OUTPUT_SUCCEEDED][1]
 
 
-@pytest.mark.parametrize(
-    'graph',
-    [
-        "foo:submit? => bar",
-        "foo:submit-fail? => bar",
-    ]
-)
-def test_success_after_optional_submit(tmp_flow_config, graph):
-    """Check foo:succeed is not required if foo:submit is optional."""
-    id_ = 'blargh'
-    flow_file = tmp_flow_config(id_, f"""
-    [scheduling]
-        [[graph]]
-            R1 = {graph}
-    [runtime]
-        [[bar]]
-        [[foo]]
-    """)
-    cfg = WorkflowConfig(workflow=id_, fpath=flow_file, options=None)
-    assert not cfg.taskdefs['foo'].outputs[TASK_OUTPUT_SUCCEEDED][1]
-
-
 @pytest.mark.parametrize(
     'allow_implicit_tasks',
     [
diff --git a/tests/unit/test_graph_parser.py b/tests/unit/test_graph_parser.py
index ca19b2060b4..bbd4f85a001 100644
--- a/tests/unit/test_graph_parser.py
+++ b/tests/unit/test_graph_parser.py
@@ -720,7 +720,6 @@ def test_task_optional_outputs():
         ('succeed', TASK_OUTPUT_SUCCEEDED),
         ('fail', TASK_OUTPUT_FAILED),
         ('submit', TASK_OUTPUT_SUBMITTED),
-        ('submit-fail', TASK_OUTPUT_SUBMIT_FAILED),
     ]
 )
 def test_family_optional_outputs(qual, task_output):
@@ -751,6 +750,26 @@ def test_family_optional_outputs(qual, task_output):
         assert gp.task_output_opt[(member, task_output)][0] == optional
 
 
+def test_cannot_be_required():
+    """Is should not allow :expired or :submit-failed to be required.
+
+    See proposal point 4:
+    https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+    """
+    gp = GraphParser({})
+
+    # outputs can be optional
+    gp.parse_graph('a:expired? => b')
+    gp.parse_graph('a:submit-failed? => b')
+
+    # but cannot be required
+    with pytest.raises(GraphParseError, match='must be optional'):
+        gp.parse_graph('a:expired => b')
+    with pytest.raises(GraphParseError, match='must be optional'):
+        gp.parse_graph('a:submit-failed => b')
+
+
+
 @pytest.mark.parametrize(
     'graph, error',
     [
diff --git a/tests/unit/test_subprocpool.py b/tests/unit/test_subprocpool.py
index c72ffc4d094..7da14e9e73c 100644
--- a/tests/unit/test_subprocpool.py
+++ b/tests/unit/test_subprocpool.py
@@ -30,6 +30,13 @@
 from cylc.flow.task_events_mgr import TaskJobLogsRetrieveContext
 from cylc.flow.subprocctx import SubProcContext
 from cylc.flow.subprocpool import SubProcPool, _XTRIG_FUNC_CACHE, _XTRIG_MOD_CACHE, get_xtrig_func
+from cylc.flow.task_outputs import (
+    TASK_OUTPUT_SUBMITTED,
+    TASK_OUTPUT_SUBMIT_FAILED,
+    TASK_OUTPUT_SUCCEEDED,
+    TASK_OUTPUT_FAILED,
+    TASK_OUTPUT_EXPIRED,
+)
 from cylc.flow.task_proxy import TaskProxy
 
 
@@ -316,8 +323,7 @@ def test__run_command_exit_add_to_badhosts(mock_ctx):
 
 
 def test__run_command_exit_add_to_badhosts_log(caplog, mock_ctx):
-    """It gets platform name from the callback args.
-    """
+    """It gets platform name from the callback args."""
     badhosts = {'foo', 'bar'}
     SubProcPool._run_command_exit(
         mock_ctx(cmd=['ssh']),
@@ -330,7 +336,11 @@ def test__run_command_exit_add_to_badhosts_log(caplog, mock_ctx):
                 external_triggers=[], xtrig_labels={},
                 expiration_offset=None,
                 outputs={
-                    'submitted': [None, None], 'submit-failed': [None, None]
+                    TASK_OUTPUT_SUBMITTED: [None, None],
+                    TASK_OUTPUT_SUBMIT_FAILED: [None, None],
+                    TASK_OUTPUT_SUCCEEDED: [None, None],
+                    TASK_OUTPUT_FAILED: [None, None],
+                    TASK_OUTPUT_EXPIRED: [None, None],
                 },
                 graph_children={}, rtconfig={'platform': 'foo'}
 
diff --git a/tests/unit/test_task_outputs.py b/tests/unit/test_task_outputs.py
index 4f61e696fbc..34bd1fde09f 100644
--- a/tests/unit/test_task_outputs.py
+++ b/tests/unit/test_task_outputs.py
@@ -13,30 +13,247 @@
 #
 # You should have received a copy of the GNU General Public License
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
-import random
-import unittest
-
-from cylc.flow.task_outputs import TaskOutputs
-
-
-class TestMessageSorting(unittest.TestCase):
-
-    TEST_MESSAGES = [
-        ['expired', 'expired', False],
-        ['submitted', 'submitted', False],
-        ['submit-failed', 'submit-failed', False],
-        ['started', 'started', False],
-        ['succeeded', 'succeeded', False],
-        ['failed', 'failed', False],
-        [None, None, False],
-        ['foo', 'bar', False],
-        ['foot', 'bart', False],
-        # NOTE: [None, 'bar', False] is unstable under Python2
-    ]
-
-    def test_sorting(self):
-        messages = list(self.TEST_MESSAGES)
-        for _ in range(5):
-            random.shuffle(messages)
-            output = sorted(messages, key=TaskOutputs.msg_sort_key)
-            self.assertEqual(output, self.TEST_MESSAGES, output)
+
+from textwrap import dedent
+from types import SimpleNamespace
+
+import pytest
+
+from cylc.flow.task_outputs import (
+    TASK_OUTPUTS,
+    TASK_OUTPUT_EXPIRED,
+    TASK_OUTPUT_FAILED,
+    TASK_OUTPUT_SUBMITTED,
+    TASK_OUTPUT_SUBMIT_FAILED,
+    TASK_OUTPUT_SUCCEEDED,
+    TaskOutputs,
+    get_completion_expression,
+)
+
+
+def tdef(required, optional, completion=None):
+    """Stuf a task definition.
+
+    Args:
+        required: Collection or required outputs.
+        optional: Collection of optional outputs.
+        completion: User defined execution completion expression.
+
+    """
+    return SimpleNamespace(
+        rtconfig={
+            'completion': completion,
+        },
+        outputs={
+            output: (
+                output,
+                (
+                    # output is required:
+                    True if output in required
+                    # output is optional:
+                    else False if output in optional
+                    # output is ambiguous (i.e. not referenced in graph):
+                    else None
+                )
+            )
+            for output in set(TASK_OUTPUTS) | set(required) | set(optional)
+        },
+    )
+
+
+def test_completion_implicit():
+    """It should generate a completion expression when none is provided.
+
+    The outputs should be considered "complete" according to the logic in
+    proposal point 5:
+    https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+    """
+    # one required output - succeeded
+    outputs = TaskOutputs(tdef([TASK_OUTPUT_SUCCEEDED], []))
+
+    # the completion expression should only contain the one required output
+    assert outputs._completion_expression == 'succeeded'
+    # the outputs should be incomplete - it hasn't run yet
+    assert outputs.is_complete() is False
+
+    # set the submit-failed output
+    outputs.set_message_complete(TASK_OUTPUT_SUBMIT_FAILED)
+    # the outputs should be incomplete - submited-failed is a "final" output
+    assert outputs.is_complete() is False
+
+    # set the submitted and succeeded outputs
+    outputs.set_message_complete(TASK_OUTPUT_SUBMITTED)
+    outputs.set_message_complete(TASK_OUTPUT_SUCCEEDED)
+    # the outputs should be complete - it has run an succeedd
+    assert outputs.is_complete() is True
+
+    # set the expired output
+    outputs.set_message_complete(TASK_OUTPUT_EXPIRED)
+    # the outputs should still be complete - it has run and succeeded
+    assert outputs.is_complete() is True
+
+
+def test_completion_explicit():
+    """It should use the provided completion expression.
+
+    The outputs should be considered "complete" according to the logic in
+    proposal point 5:
+    https://cylc.github.io/cylc-admin/proposal-optional-output-extension.html#proposal
+    """
+    outputs = TaskOutputs(tdef(
+        # no required outputs
+        [],
+        # four optional outputs
+        [
+            TASK_OUTPUT_SUCCEEDED,
+            TASK_OUTPUT_FAILED,
+            'x',
+            'y',
+        ],
+        # one pair must be satisfied for the outputs to be complete
+        completion='(succeeded and x) or (failed and y)',
+    ))
+
+    # the outputs should be incomplete - it hasn't run yet
+    assert outputs.is_complete() is False
+
+    # set the succeeded and failed outputs
+    outputs.set_message_complete(TASK_OUTPUT_SUCCEEDED)
+    outputs.set_message_complete(TASK_OUTPUT_FAILED)
+
+    # the task should be incomplete - it has executed but the completion
+    # expression is not satisfied
+    assert outputs.is_complete() is False
+
+    # satisfy the (failed and y) pair
+    outputs.set_message_complete('y')
+    assert outputs.is_complete() is True
+
+    # satisfy the (succeeded and x) pair
+    outputs._completed['y'] = False
+    outputs.set_message_complete('x')
+    assert outputs.is_complete() is True
+
+
+@pytest.mark.parametrize(
+    'required, optional, expression', [
+        pytest.param(
+            {TASK_OUTPUT_SUCCEEDED},
+            [],
+            'succeeded',
+            id='0',
+        ),
+        pytest.param(
+            {TASK_OUTPUT_SUCCEEDED, 'x'},
+            [],
+            '(succeeded and x)',
+            id='1',
+        ),
+        pytest.param(
+            [],
+            {TASK_OUTPUT_SUCCEEDED},
+            'succeeded or failed',
+            id='2',
+        ),
+        pytest.param(
+            {TASK_OUTPUT_SUCCEEDED},
+            {TASK_OUTPUT_EXPIRED},
+            'succeeded or expired',
+            id='3',
+        ),
+        pytest.param(
+            [],
+            {TASK_OUTPUT_SUCCEEDED, TASK_OUTPUT_EXPIRED},
+            'succeeded or failed or expired',
+            id='4',
+        ),
+        pytest.param(
+            {TASK_OUTPUT_SUCCEEDED},
+            {TASK_OUTPUT_EXPIRED, TASK_OUTPUT_SUBMITTED},
+            'succeeded or submit_failed or expired',
+            id='5',
+        ),
+        pytest.param(
+            {TASK_OUTPUT_SUCCEEDED, TASK_OUTPUT_SUBMITTED},
+            {TASK_OUTPUT_EXPIRED},
+            '(submitted and succeeded) or expired',
+            id='6',
+        ),
+        pytest.param(
+            [],
+            {TASK_OUTPUT_SUCCEEDED, TASK_OUTPUT_SUBMIT_FAILED},
+            'succeeded or failed or submit_failed',
+            id='7',
+        ),
+        pytest.param(
+            {'x'},
+            {
+                TASK_OUTPUT_SUCCEEDED,
+                TASK_OUTPUT_SUBMIT_FAILED,
+                TASK_OUTPUT_EXPIRED,
+            },
+            '(x and succeeded) or failed or submit_failed or expired',
+            id='8',
+        ),
+    ],
+)
+def test_get_completion_expression_implicit(required, optional, expression):
+    """It should generate a completion expression if none is provided."""
+    assert get_completion_expression(tdef(required, optional)) == expression
+
+
+def test_get_completion_expression_explicit():
+    """If a completion expression is used, it should be used unmodified."""
+    assert get_completion_expression(tdef(
+        {'x', 'y'},
+        {TASK_OUTPUT_SUCCEEDED, TASK_OUTPUT_FAILED, TASK_OUTPUT_EXPIRED},
+        '((failed and x) or (succeeded and y)) or expired'
+    )) == '((failed and x) or (succeeded and y)) or expired'
+
+
+def sstrip(text):  # TODO
+    """Simple function to dedent and strip text.
+
+    Examples:
+        >>> print(sstrip('''
+        ...     foo
+        ...       bar
+        ...     baz
+        ... '''))
+        foo
+          bar
+        baz
+
+    """
+    return dedent(text).strip('\n')
+
+
+def test_format_completion_status():
+    outputs = TaskOutputs(
+        tdef(
+            {TASK_OUTPUT_SUCCEEDED, 'x', 'y'},
+            {TASK_OUTPUT_EXPIRED},
+        )
+    )
+    assert outputs.format_completion_status(indent=2, gutter=2) == sstrip(
+        '''
+          |  (
+        x |    succeeded
+        x |    and x
+        x |    and y
+          |  )
+        x |  or expired
+        '''
+    )
+    outputs.set_message_complete('succeeded')
+    outputs.set_message_complete('x')
+    assert outputs.format_completion_status(indent=2, gutter=2) == sstrip(
+        '''
+          |  (
+        ✓ |    succeeded
+        ✓ |    and x
+        x |    and y
+          |  )
+        x |  or expired
+        '''
+    )
diff --git a/tests/unit/test_xtrigger_mgr.py b/tests/unit/test_xtrigger_mgr.py
index 3cfee363d15..5192a7d3dd8 100644
--- a/tests/unit/test_xtrigger_mgr.py
+++ b/tests/unit/test_xtrigger_mgr.py
@@ -154,10 +154,10 @@ def test_housekeeping_with_xtrigger_satisfied(xtrigger_mgr):
     xtrig.out = "[\"True\", {\"name\": \"Yossarian\"}]"
     tdef = TaskDef(
         name="foo",
-        rtcfg=None,
+        rtcfg={'completion': None},
         run_mode="live",
         start_point=1,
-        initial_point=1
+        initial_point=1,
     )
     init()
     sequence = ISO8601Sequence('P1D', '2019')
@@ -197,7 +197,7 @@ def test__call_xtriggers_async(xtrigger_mgr):
     # create a task
     tdef = TaskDef(
         name="foo",
-        rtcfg=None,
+        rtcfg={'completion': None},
         run_mode="live",
         start_point=1,
         initial_point=1