README.md: first order logic analysis using predicate calculus

README.md

@@ -8,12 +8,13 @@ with highly modifiable system-specific registration using platform predicates.
 
 | Item                            | Description | Predicate Calculus | 
 |---------------------------------|-------------|--------------------|
-| _Problem Definition_            | The main problem that entailed building this project had been to have something similar to the JME's `NativeLibraryLoader`, but for a better version with more capabilities (such as: loading libraries from external Jars and having a generic file extraction interface). |                    |
-| _Generalized Approach_          | The generalized approach was deemed insufficient; as it will not add on the JME's `NativeLibraryLoader`, and thus the project will be insignificant. The generalized approach entails building something that directly encapsulates concrete buffered byte stream calls to _ZipFileSystem_ interfaces for the native libraries only within the same classpath, and that actually is a bad practice to build APIs on concretions, instead as the Ontology entails, abstractions and using levels of indirections should play the most part in developing a new system. | |
-| _jSnapLoader-specific Approach_ | The jSnapLoader-specific approach is quite ingenuine, nevertheless it's not unique. The essential design entails the basic use of the System-Entity-Structure (SES) Framework; which essentially decomposes the the bulky actions of the library, first from the perspective of behavior into deterministic finite-states, and then from the structural perspective into the components that execute these states; the net result is having a freely-floating decomposed components. The next step was regrouping those components (using common properties from predicate calculus) and finding abstractions for them, and finally capturing relations between those components and similar systems (i.e., FileSystem APIs). This structural way of thinking has resulted in the production of beneficial compilation units that could serve other purposes and not entailed specifically to serve native library extraction and loading. |                    |
-| _Framework Decomposition_ | The decomposition had been successfully inducted into a `FileLocator` interface with a validation strategy, a `FileExtractor` interface with the full ability to control native IO resources, and a `LibraryLoader` interface with the ability to build and register platform predicates to support any new unsupported systems. |                    |
-| _Framework Enhancements_ | The `PlatformPredicate` interface wasn't planned from the start; it has been added as an enhancement for the library to accomodate the changes and the addition of new platforms robustly without changing the internal API. In fact, I give credits to [Jolt-jni](https://github.com/stephengold/jolt-jni/tree/master) for implicitly opening the vision to add them. Furthermore, the addition of the `FileLocalizingListener`, the `FileExtractionListener`, and the `NativeLibraryLoadingListener` binds the user API to the framework API giving jSnapLoader a more added robustness value overtime. |                    |
-| _Credits for other systems_ | Credits should go for the jSnapLoader's users, [Serial4j](https://github.com/Electrostat-Lab/Serial4j), [Jolt-jni](https://github.com/stephengold/jolt-jni/tree/master), and [Electrostatic4j](https://github.com/Electrostat-Lab/Electrostatic-Sandbox). Those implicitly and continously have pushed the API over to become better. | |
+| _Problem Definition_            | The main problem that entailed building this project had been to have something similar to the JME's `NativeLibraryLoader`, but for a better version with more capabilities (such as: loading libraries from external Jars and having a generic file extraction interface). | Sample = $P = [\cup_{n = 0}^N P_n]$ - Formula (Mapping relations in the form antecedents to descendants) = $\forall{P}\exists{S}\ F(P, S)$                  |
+| _Generalized Approach_          | The generalized approach was deemed insufficient; as it will not add on the JME's `NativeLibraryLoader`, and thus the project will be insignificant. The generalized approach entails building something that directly encapsulates concrete buffered byte stream calls to _ZipFileSystem_ interfaces for the native libraries only within the same classpath, and that actually is a bad practice to build APIs on concretions, instead as the Ontology entails, abstractions and using levels of indirections should play the most part in developing a new system. | Sample = $S = [\cup_{n = 0}^N S_n]$ - Formula (Mapping relations in the form descendants to antecedents) = $\forall{S}\exists{P}\ F(S, P)$ |
+| _jSnapLoader-specific Approach_ | The jSnapLoader-specific approach is quite ingenuine, nevertheless it's not unique. The essential design entails the basic use of the System-Entity-Structure (SES) Framework; which essentially decomposes the the bulky actions of the library, first from the perspective of behavior into deterministic finite-states, and then from the structural perspective into the components that execute these states; the net result is having a freely-floating decomposed components. The next step was regrouping those components (using common properties from predicate calculus) and finding abstractions for them, and finally capturing relations between those components and similar systems (i.e., FileSystem APIs). This structural way of thinking has resulted in the production of beneficial compilation units that could serve other purposes and not entailed specifically to serve native library extraction and loading. | $\forall{P_loader}\ \exists{S_loader}\ F(P_loader, S_loader)$          |
+| _Framework Decomposition_ | The decomposition had been successfully inducted into a `FileLocator` interface with a validation strategy, a `FileExtractor` interface with the full ability to control native IO resources, and a `LibraryLoader` interface with the ability to build and register platform predicates to support any new unsupported systems. | $$F = \cup_{n = 0}^N \ (P_{loader}, S_{loader})\_{n}$$ $$= [(P_{file-locator}, S_{file-locator}), (P_{file-extractor}, S_{file-extractor}),$$ $$(P_{library-locator}, S'\_{file-locator}), (P_{library-extractor}, S'\_{file-extractor}), (P_{library-loader}, S_{library-loader})]$$ ;where $S'_{clazz}$ S prime represents a solution of class 'clazz'.  |
+| _Common problems, robustness, and re-usability of solutions_ | To extend the robustness (rigidity) of the solution, multiple similar problems could utilize classes of solutions from the same kind; for instance, the problem `library-locator` could use a solution of the class `file-locator`; thus this could be explained by a uniqueness formula as regard to the formal language. | $$\forall{p}\ \in{P},\ \exists{s} \in{S}\,\ \forall{s'} \in{S} [(p_{loader}, s_{loader}) \land\ (p_{loader}, s'\_{loader})\ \implies\ [s_{loader} = s'\_{loader}]$$ |
+| _Framework Enhancements_ | The `PlatformPredicate` interface wasn't planned from the start; it has been added as an enhancement for the library to accomodate the changes and the addition of new platforms robustly without changing the internal API. In fact, I give credits to [Jolt-jni](https://github.com/stephengold/jolt-jni/tree/master) for implicitly opening the vision to add them. Furthermore, the addition of the `FileLocalizingListener`, the `FileExtractionListener`, and the `NativeLibraryLoadingListener` binds the user API to the framework API giving jSnapLoader a more added robustness value overtime. | $$E = \cup_{n = 0}^N \ (E_{loader}, S_{loader})\_{n}$$ $$= [(E_{system-detection-listeners}, S_{system-detection-listeners}), (E_{locator-listeners}, S_{locator-listeners}), (E_{extractor-listeners}, S_{extractor-listeners}),$$ $$(E_{loader-listeners}, S\_{loader-listeners}), (E_{system-exception}, S\_{system-exception})]$$   |
+| _Credits for other systems_ | Credits should go for the jSnapLoader's users, [Serial4j](https://github.com/Electrostat-Lab/Serial4j), [Jolt-jni](https://github.com/stephengold/jolt-jni/tree/master), and [Electrostatic4j](https://github.com/Electrostat-Lab/Electrostatic-Sandbox). Those implicitly and continously have pushed the API over to become better. | --- |
 
 ## Software Architectural Paradigm: 
 <img src="https://github.com/Electrostat-Lab/jSnapLoader/blob/master/architecture/architectural-paradigm.png" alt="Architectural-Paradigm-Placement"/>