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The spatial regions that continuant fiat boundaries occupy #76

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michaelrabenberg opened this issue Dec 13, 2023 · 77 comments
Open

The spatial regions that continuant fiat boundaries occupy #76

michaelrabenberg opened this issue Dec 13, 2023 · 77 comments
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@michaelrabenberg
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Fiat points, lines, and surfaces occupy zero-, one-, and two-dimensional spatial regions, respectively. I think, however, that the axioms don't imply as much. Am I right about this?
@alanruttenberg
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I believe you are correct. I will add axioms for this. Thanks, good catch!

@alanruttenberg alanruttenberg added the bug Something isn't working label Dec 14, 2023
@michaelrabenberg
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OK, thanks. One question relevant to how best to formulate the axioms is whether a given (say) fiat boundary can occupy different spatial regions at different times; some conceivable ways of formulating the axioms would rule out this possibility and some wouldn't.

@alanruttenberg
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alanruttenberg commented Dec 14, 2023 via email

@wceusters
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As long as Scotty cannot beam anybody up, I think I do agree.

@alanruttenberg
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Draft axiom

(forall (m s)
 (if
  (exists (t)
   (and (occupies-spatial m s t)
    (or (= s three-dimensional-spatial-region)
     (= s two-dimensional-spatial-region)
     (= s one-dimensional-spatial-region)
     (= s zero-dimensional-spatial-region))))
  (forall (t1 s1)
   (if (occupies-spatial m s1 t1) (instance-of m s t1)))))

@alanruttenberg
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Draft axiom for boundaries

(forall (x)
 (if (exists (t) (instance-of x fiat-surface t))
  (exists (t s)
   (and (occupies-spatial-region x s t)
    (instance-of s two-dimensional-spatial-region t)))))

Similar for fiat-point, fiat-line.

We only need to check and assert with exists since fiat-line is rigid and the dimension of space occupied by something is rigid per #76 (comment)

@michaelrabenberg
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Alan says: Boundaries can definitely occupy different spatial regions at different
times.

I think there are puzzles but this might not be the best occasion to discuss the matter.

Alan says: Do we agree that nothing changes the dimension of the space
something occupies. So if you occupy a 2d spatial region at some point, at
any time you exist you occupy a 2d spatial region.

That does sound plausible, given certain background assumptions. One such assumption is the proposition that every material entity occupies a 3d spatial region. (If you could "shave" a 3d material entity to make it "perfectly thin," say, then this sort of assumption wouldn't be right.) Another is the proposition that there are no aggregates that can have differently dimensioned independent continuants among their constituents. (If there were a "boundary aggregate," say, with four points and a line for member parts at t1 and with just the points for member parts at t2, then we'd also seem to have a counterexample.)

Another thing: Some of the axioms pertaining to fiat points might be streamlinable. For example, given [jgo-1] (a fiat point has no parts other than itself), [jqd-1] (if a has continuant part b then if a is an instance of fiat point then b is an instance of fiat point) could be discarded.

@michaelrabenberg
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Alan wrote:
(forall (m s)
(if
(exists (t)
(and (occupies-spatial m s t)
(or (= s three-dimensional-spatial-region)
(= s two-dimensional-spatial-region)
(= s one-dimensional-spatial-region)
(= s zero-dimensional-spatial-region))))
(forall (t1 s1)
(if (occupies-spatial m s1 t1) (instance-of m s t1)))))

I assume the boldfaced 'm' should be 's', right?

@michaelrabenberg
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Ugh--I meant "s1," not "s."

@michaelrabenberg
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Alan wrote:

(forall (x)
(if (exists (t) (instance-of x fiat-surface t))
(exists (t s)
(and (occupies-spatial-region x s t)
(instance-of s two-dimensional-spatial-region t)))))

This looks good to me.

@alanruttenberg
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Alan wrote: (forall (m s) (if (exists (t) (and (occupies-spatial m s t) (or (= s three-dimensional-spatial-region) (= s two-dimensional-spatial-region) (= s one-dimensional-spatial-region) (= s zero-dimensional-spatial-region)))) (forall (t1 s1) (if (occupies-spatial m s1 t1) (instance-of m s t1)))))

I assume the boldfaced 'm' should be 's', right?

Yes, thanks.

@alanruttenberg
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I think there are puzzles but this might not be the best occasion to discuss the matter.

Regarding aggregates, there's precedent. The choice for temporal regions is that the highest dimension of a part is the dimension of the sum.

Another thing: Some of the axioms pertaining to fiat points might be streamlinable

I ran my leave-on-out code yesterday. The code takes each axiom, one at a time, and tries to prove it from the rest of the axioms. It had been a while since I had last run it. It found 60 examples! It has relatively tight time limits - it gives prover9 a chance for 10 seconds and if it times out give z3 10 seconds. Maybe I'll try again with raised limit. I'll try to organize this and share it and maybe you and Werner can help me sort through them.

@michaelrabenberg
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Regarding aggregates, there's precedent. The choice for temporal regions is that the highest dimension of a part is the dimension of the sum.

I assumed something like that would be the case--intuitively the aggregate of a line and a point, say, is 1D--but that's why I imagined a case in which the aggregate first contains some 0D individuals (four fiat points) and a 1D individual (a fiat line) and later loses the 1D individual. If there were such an aggregate (and it persisted through this loss of an individual) then it'd undergo a change in dimension even by the standard you mentioned. So there can't be things that meet that description if the "once xD always xD" assumption is to be maintained.

Another thing: Some of the axioms pertaining to fiat points might be streamlinable

I ran my leave-on-out code yesterday. The code takes each axiom, one at a time, and tries to prove it from the rest of the axioms. It had been a while since I had last run it. It found 60 examples! It has relatively tight time limits - it gives prover9 a chance for 10 seconds and if it times out give z3 10 seconds. Maybe I'll try again with raised limit. I'll try to organize this and share it and maybe you and Werner can help me sort through them.

Very interesting! Would be eager to hear more about it.

@alanruttenberg
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The aggregate example is cute. Can you think of a plausible situation in which that would make sense?

@michaelrabenberg
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No, I can't imagine a case in which I'd want to say there is an aggregate like that. But there'd be no contradiction in positing such an aggregate, and some imaginable aggregation/composition principles (like "any two individuals form an aggregate") would imply that there is such an aggregate.

@phismith
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phismith commented Dec 16, 2023 via email

@michaelrabenberg
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Barry, I agree but the case I was imagining was one where an aggregate persists though the loss of one of its members (like the persistence of a school of fish through the loss of one of the fish), not one where an aggregate ceases to be due to the loss of one of its members. Because BFO allows for some cases of the former sort (like school-of-fish cases), my point was that some specific tailoring is required to rule out cases of the former sort involving aggregates of differently dimensioned entities such that the dimensions of the aggregate would count as changing over time. (Such tailoring could take a very straightforward form, such as never saying anything that implies that there are aggregates like that.)

@alanruttenberg
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alanruttenberg commented Dec 19, 2023 via email

@johnbeve
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if you occupy a 2d spatial region at some point, at any time you exist you occupy a 2d spatial region.

A 2D continuant fiat boundary occupying a 2D spatial region that later becomes a site occupying a 3D spatial region would be a counterexample. Here's a shot: 38th parallel north border (not the latitude, the border) was the boundary between N and S Korea during the Korean War, prior to the establishment of a 160x2.5 mile buffer zone that acts as the current border.

Is this a case of one border expanding dimension or a case in which one border stops existing and is replaced by another that occupies a higher dimension? I lean towards the latter for this example, but I suspect there are more compelling cases that presently escape me.

@phismith
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phismith commented Dec 19, 2023 via email

@alanruttenberg
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In general there is no BFO class such that one and the same entity can instantiate it and not instantiate it at different times in its existence.

The exceptions being object aggregate, fiat object part, and object.

@phismith
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phismith commented Dec 20, 2023 via email

@johnbeve
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An egg and a sperm fuse. An object aggregate is replaced by (does not become) an object. The tail of a cat is chopped off. A new object is created thereby.

@alanruttenberg what was the motivation for object, object aggregate, and fiat object being exceptions to the general rule? My suspicion is that it might apply equally to cases of dimension change.

@alanruttenberg
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It has to do with granularity. The triad represents 3 levels of granularity. Data integration across OBO spanned something like 8 or 10 different granularities. A muscle is either a fiat part, or an object aggregate depending on which discipline of biology. Absent a larger scale, workable, theory of granularity we make do with object, fiat part, object aggregate, but don't have to have different disciplines arguing about whether that muscle is object, aggregate, or part.

I don't think it transfers to boundaries/sites. I see them as completely different things. A boundary is infinitely thin. A site isn't.

@alanruttenberg
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@phismith we settled on these not being disjoint. Given that, the choice is either that all material entities are all three forever, or they can be one thing at one time and another at another (but also both, as appropriate).

@johnbeve
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Thank you for clarifying the motivation @alanruttenberg.

I don't think it transfers to boundaries/sites. I see them as completely different things. A boundary is infinitely thin. A site isn't.

You get Sites as completely different from CFBs from:

  • 0D CFB is infinitely thin along 3 axes
  • 1D CFB is infinitely thin along 2 axes
  • 2D CFB is infinitely thin along 1 axis
  • Site is infinitely thin along 0 axis

Whereas I could equally get 0D CFB as completely different from Sites, 1D, and 2D CFBs from:

  • Site has 3 dimensions
  • 2D CFB has 2 dimensions
  • 1D CFB has 1 dimension
  • 0D CFB has 0 dimensions

Rather than take either direction, I've leaned towards treating Sites as essentially 3D CFBs. I see no defensible differentia distinguishing Sites and CFBs.

I don't mean to suggest here though that I think the granularity-based motivation for flexibility wrt object, aggregate, and fiat object part transfers to Sites and CFBs. I'll need to think more about that. I only mean to suggest that if it doesn't transfer, I don't think it's because Sites and CFBs are completely different things.

@michaelrabenberg
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I agree with John that the fact that sites are infinitely thin and 0D, 1D, and 2D continuant fiat boundaries aren't isn't great evidence that sites aren't continuant fiat boundaries.

What about this, though: A given site crowds out material-entity proper parts of the material entity relative to which the site's boundaries are determined (to adapt the language from the site elucidation on the GitHub); no parallel fact obtains for a continent fiat boundary. So, crudely, some of the "matter" of the earth is where the surface of the earth is, but none of the "matter" of a ship is where any part of the hull of a ship is. (That could surely be put more precisely but I hope the idea is reasonably clear.)

Problem case (Werner presented this one to me a while ago): A ship has a hull at t1; at t2 a ceiling lamp is installed within the hull that (just assume) counts as a material entity proper part of the ship. So, it might be thought, the hull doesn't crowd out the matter of the ship at all times. I guess my response is that the hull changes shape to accommodate the ceiling lamp.

Perhaps this doesn't seem like a sufficiently deep difference to call for classifying sites as non-CFBs. But note that there's no contradiction in positing an immaterial entity that is 3D, that isn't a spatial region, that has its location determined relative to some material entity, and that is exactly co-located with a material proper part of this material entity. For example, there's no contradiction in saying I have a 3D immaterial proper part that is located precisely where my entire left arm is. I'd be more inclined to classify such an outré thing as a "3D continuant fiat boundary" than to classify the hull of a ship as one. So the "crowding out" feature of a site seems like a deep feature of it that isn't just (say) a by-product of its three-dimensionality.

@michaelrabenberg
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^Mistyped. Correction: I agree with John that the fact that sites aren't infinitely thin and 0D, 1D, and 2D continuant fiat boundaries are isn't great evidence that sites aren't continuant fiat boundaries.

@phismith
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phismith commented Dec 20, 2023 via email

@johnbeve
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don't you mean to ask whether a site can meet this description?

Thank you for catching that, I did mean Site; you've my intent correct, I'm hoping clause (1) in the elucidation of Site might provide a more robust way to distinguish them from CFBs.

I still like my proposal

I like the spirit; still trying to grok how the 'crowding out' metaphor works, especially with the problem case.

Some sites are CFBs, and some aren't. One way of fleshing that view out: Sites that have their location determined relative to a material entity are 3d CFBs, but sites (if there are any) that don't have their locations determined relative to a material entity are 3d immaterial entities that aren't CFBs.

I've the same worry about the disjunctive elucidation for Site. I see the plausibility of your suggestion trading on whether we can distinguish "(partially or wholly) coincide with the boundaries of one or more material entities" from "have locations determined in relation to some material entity" in a sensible way, e.g. specifying what 'coincides with the boundaries of' and 'determined in relation to' mean. More to chew on.

@alanruttenberg
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(forall (m s) (if (exists (t) (and (occupies-spatial m s t) (or (= s three-dimensional-spatial-region) (= s two-dimensional-spatial-region) (= s one-dimensional-spatial-region) (= s zero-dimensional-spatial-region)))) (forall (t1 s1) (if (occupies-spatial m s1 t1) (instance-of m s t1)))))

I assume the boldfaced 'm' should be 's', right?

s1, right?

@wceusters
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(forall (m s) (if (exists (t) (and (occupies-spatial m s t) (or (= s three-dimensional-spatial-region) (= s two-dimensional-spatial-region) (= s one-dimensional-spatial-region) (= s zero-dimensional-spatial-region)))) (forall (t1 s1) (if (occupies-spatial m s1 t1) (instance-of m s t1)))))
I assume the boldfaced 'm' should be 's', right?

s1, right?

There is much more wrong: you are claiming here the particular 's' to be identical with one or other universal

@alanruttenberg
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There is much more wrong: you are claiming here the particular 's' to be identical with one or other universal

Oh, you are right @wceusters , thanks!

Let me try again:

(forall (m s u)
 (if
  (exists (t)
   (and (occupies-spatial m s t) (instance-of s u t)
    (or (= u three-dimensional-spatial-region)
     (= u two-dimensional-spatial-region)
     (= u one-dimensional-spatial-region)
     (= u zero-dimensional-spatial-region))))
  (forall (t1 s1)
   (if (occupies-spatial m s1 t1) (instance-of s1 u t1)))))

And actually, I think I can move s down to the existential, yes?

(forall (m u)
 (if
  (exists (s t)
   (and (occupies-spatial m s t) (instance-of s u t)
    (or (= u three-dimensional-spatial-region)
     (= u two-dimensional-spatial-region)
     (= u one-dimensional-spatial-region)
     (= u zero-dimensional-spatial-region))))
  (forall (t1 s1)
   (if (occupies-spatial m s1 t1) (instance-of s1 u t1)))))

@michaelrabenberg
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Yeah I think that does it. Thanks for catching the other thing, Werner.

Perhaps the 'u' could be eliminated by breaking the axiom into four separate smaller axioms--don't know if that'd improve efficiency or not. The first could go as follows, I think (not sure if I got the parentheses right but I hope the idea is clear enough):

(forall (m)
(if
(exists (s t)
(and (occupies-spatial-region m s t) (instance-of s three-dimensional-spatial-region t)))
(forall (t1 s1)
(if (occupies-spatial-region m s1 t1) (instance-of s1 three-dimensional-spatial-region t1)))))

And similarly for the other three spatial region universals.

@alanruttenberg
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@johnbeve said:

I've the same worry about the disjunctive elucidation for Site. I see the plausibility of your suggestion trading on whether we can distinguish "(partially or wholly) coincide with the boundaries of one or more material entities" from "have locations determined in relation to some material entity" in a sensible way, e.g. specifying what 'coincides with the boundaries of' and 'determined in relation to' mean. More to chew on.

The disjunctive definition was kind of after the fact, IIRC. The original version of site was that it was in part bounded by a material entity. It was extended to support air corridors as in air traffic control. Since then another case where I think it is relevant is for the sites around Lagrange points, that can be used by spacecraft as "parking spots" in space to remain in a fixed position with minimal fuel consumption.. Anyone know of other plausible cases of a site not being partially bounded by a material entity

As an aside, the only use there is for spatial regions, as far as I can tell, is as support for the theory. I don't think you ever want to have particular spatial regions asserted (as opposed to inferred) to exist. But if any of you know of cases where that would be useful I'd be curious to hear. I know that they are used in some cases to, e.g, represent ground tracks(like the path a mountain bike travels through the woods), but I think that's an error and that boundaries must be the correct representation. Minimally because spatial regions can't have qualities like length or direction, and because they are attached to a material entity. Although even boundary feels a little suspect in that case - should that be an information entity? Or a 'continuant profile' ;-)

@wceusters
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I ran this one after correcting the 'occupies-spatial' mistake:

(cl:comment "test [ttt-1]"
(forall (m u)
(if
(exists (s t)
(and (occupies-spatial-region m s t) (instance-of s u t)
(or (= u three-dimensional-spatial-region)
(= u two-dimensional-spatial-region)
(= u one-dimensional-spatial-region)
(= u zero-dimensional-spatial-region))))
(forall (t1 s1)
(if (occupies-spatial-region m s1 t1) (instance-of s1 u t1)))))
)

and I obtain the following 4 very straigthforward clauses:

r(458,4,[],[],"BFO-ttt-1",kow(if([[identical,F,'three-dimensional-spatial-region'],['instance-of',A,F,B],['occupies-spatial-region',E,A,B],['occupies-spatial-region',E,D,C]]),then(['instance-of',D,F,C]))).
r(459,4,[],[],"BFO-ttt-1",kow(if([[identical,F,'two-dimensional-spatial-region'],['instance-of',A,F,B],['occupies-spatial-region',E,A,B],['occupies-spatial-region',E,D,C]]),then(['instance-of',D,F,C]))).
r(460,4,[],[],"BFO-ttt-1",kow(if([[identical,F,'one-dimensional-spatial-region'],['instance-of',A,F,B],['occupies-spatial-region',E,A,B],['occupies-spatial-region',E,D,C]]),then(['instance-of',D,F,C]))).
r(461,4,[],[],"BFO-ttt-1",kow(if([[identical,F,'zero-dimensional-spatial-region'],['instance-of',A,F,B],['occupies-spatial-region',E,A,B],['occupies-spatial-region',E,D,C]]),then(['instance-of',D,F,C]))).

So you could indeed get rid of variable for the universal.

@michaelrabenberg
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Thank you for catching that, I did mean Site; you've my intent correct, I'm hoping clause (1) in the elucidation of Site might provide a more robust way to distinguish them from CFBs.

I do worry that every site has its location determined in relation to a ME; all the canonical examples of sites in the literature that I can think of (cargo hold, joey pouch, etc) seem like that.

I like the spirit; still trying to grok how the 'crowding out' metaphor works, especially with the problem case.

Suppose the cargo hold is perfectly cubical at t1 and the lamp is installed at t2. My proposal would have to say that the shape of the cargo hold has a lamp-shaped dent in one of its faces at t2. So a site, S, can have its location, dimensions, etc. influenced by the ME proper parts of the ME, X, relative to which S has its location, dimensions, etc. determined; but ME proper parts of X can't occupy spatial regions that parts of S occupy. This isn't true of CFBs (as I understand them)--a surface, for example, occupies a spatial region that's a part of a spatial region occupied by a ME proper part of the material entity that determines the surface's location.

I've the same worry about the disjunctive elucidation for Site. I see the plausibility of your suggestion trading on whether we can distinguish "(partially or wholly) coincide with the boundaries of one or more material entities" from "have locations determined in relation to some material entity" in a sensible way, e.g. specifying what 'coincides with the boundaries of' and 'determined in relation to' mean. More to chew on.

I have to think more about this too.

@alanruttenberg
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Perhaps the 'u' could be eliminated by breaking the axiom into four separate smaller axioms--don't know if that'd improve efficiency or not.

Probably a better idea as I've had reasoning performance problems traced to quantifying over universals. In some other cases I've had both, with the latter marked as theorems. I think I may have shown some proof attempts that use *everything-theory+theorems*, which lets those be used. In this case I'm fine to split it into separate axioms. I'm not sure which would be more efficient in @wceusters engine, since adding some theorems was found to reduce performance. Do you have a preference Werner?

In some cases they can't be expanded, like in the axiom that says all subuniversals of occurrent are rigid. There's a similar axiom that will be in the next release for roles.

@wceusters
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In my system, the complexity of the axiom is reduced by the parser/generator which translates it in the 4 clauses above. You could write indeed 4 separate axioms and do it without the variable for the universal (in the above examples, the first condition would be removed, and 'F' where used substituted by x-dimensional-region for each clause). I don't think it poses a problem.

@alanruttenberg
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but ME proper parts of X can't occupy spatial regions that parts of S occupy. This isn't true of CFBs (as I understand them)

Yes, that would be my understanding as well. The ME with the lamp you are talking about is an aggregate, yes?

a surface, for example, occupies a spatial region that's a part of a spatial region occupied by a ME proper part of the material entity that determines the surface's location.

I guess formally there's an open question which is whether the spaces occupied by material entities are closed - we don't have the distinction between open and closed (or mixed) spatial regions. But even outside that corner case there's nothing that forces the boundary spatial region to be part of any ME's spatial region. For instance, a geoid of a planet is a fiat surface everywhere which the gravitational potential is the same, but that surface isn't part of any ME. Also sites can have boundaries as in the boundary of an air traffic corridor. Even with a site partially bounded by a ME some parts of the boundary are definitely not part of that ME.

@phismith
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phismith commented Dec 25, 2023 via email

@michaelrabenberg
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but ME proper parts of X can't occupy spatial regions that parts of S occupy. This isn't true of CFBs (as I understand them)

Yes, that would be my understanding as well. The ME with the lamp you are talking about is an aggregate, yes?

I was assuming that the ship is not an aggregate but an object, and that the ship's "matter" (so to speak) is enlarged with the ship's installation, b/c I was assuming (if only for argument's sake) that the lamp, once installed, is a part of the ship. If the lamp isn't a part of the ship, then the view of site dimensions that I find attractive wouldn't imply that the cargo hold changes shape upon the lamp's installation; in that case the lamp would relevantly be like a cargo crate that is placed in the hold. So the point is that a site crowds out material-entity proper parts of the material entity that determines the site's location; it's not the case that a site crowds out material entities full stop.

a surface, for example, occupies a spatial region that's a part of a spatial region occupied by a ME proper part of the material entity that determines the surface's location.

I guess formally there's an open question which is whether the spaces occupied by material entities are closed - we don't have the distinction between open and closed (or mixed) spatial regions. But even outside that corner case there's nothing that forces the boundary spatial region to be part of any ME's spatial region. For instance, a geoid of a planet is a fiat surface everywhere which the gravitational potential is the same, but that surface isn't part of any ME. Also sites can have boundaries as in the boundary of an air traffic corridor. Even with a site partially bounded by a ME some parts of the boundary are definitely not part of that ME.

My mistake, I was speaking a bit loosely. My thinking was that, sometimes, part of a CFB is where a material-entity part of a material entity relative to which the CFB's location is determined; but a parallel thing never happens with a site and a material entity that determines its location.

@michaelrabenberg
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Here's a point David Limbaugh made in conversation w/ me the other day (he asked me to post this and said he might add to this thread some time soon):

CFBs are, pretty obviously, all fiat (otherwise they're very, very poorly named); but, plausibly, at least some sites are non-fiat. So, at least some sites just can't be CFB's.

Add the thought--questioned above, but reasonable--that if some sites aren't CFB's, then no sites are CFB's, and you get the conclusion that no sites are CFB's. So that's a possible justification for the current classification.

@alanruttenberg
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My mistake, I was speaking a bit loosely. My thinking was that, sometimes, part of a CFB is where a material-entity part of a material entity relative to which the CFB's location is determined; but a parallel thing never happens with a site and a material entity that determines its location.

Don't forget that things can be located in sites, in which case both the site's and the occupant's spatial regions overlap. Something can also be located in a material entity, though in that case the thing located carves out a site which is part of the ME.

With the lamp and the ship I think it a reasonable alternative story is that that the lamp is located in the hold, and the hold is part of the ship. On the view that the lamp is located but not part, the part of the lamp that is installed - the screw holes, for example, are distinct sites also part of the ship and the screws are located in those holes.

Or consider a bullet lodged in a leg muscle. The bullet is located in a site that it has forcibly created. The site is part of the body. The bullet is not. The bullet is also located in the body. If you are located in a part then you are located in anything the part is of ([evu-1]).

With the cases of the bullet and the screws there's a potential ambiguity in what ME the sites is determined in relation to. There's the boundary of the bullet or screws and there's the boundaries of the larger surrounding ME that do or almost coincide. I'm not sure you can say unambiguously that the site is only determined relative to the larger ME.

So this isn't exactly a counterexample in that the bullet and screws are not part of the person/ship. Here's a potential example where a part is located in the site it bounds. Suppose you have an object aggregate consisting of balls that are magnetized and one ball that is wooden. Suppose the magnetic balls are arranged in a sphere and the wooden ball is enclosed - could be a toy. In that case a reasonable interpretation is that the metal ball members of the aggregate are the ME relative to which the site is determined and the wooden ball is located in that site.

Another example. You bleed into your stomach cavity. The stomach cavity is part of a person and the blood is part of the person, but the blood is located in the stomach cavity. I don't think the site is diminished by the volume of the blood.

I'll still maintain that there's no need to search for additional justifications for the classification of site vs CFB, since the minimal differentia are clear. However if you want one, it could be that material entities can''t be located in CFBs but can be located in sites.

@michaelrabenberg
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I guess formally there's an open question which is whether the spaces occupied by material entities are closed - we don't have the distinction between open and closed (or mixed) spatial regions.

Could you explain why this is a complication for the idea that, sometimes, a fiat surface occupies a spatial region that's a proper part of the spatial region that a material entity occupies? If some material entity, x, occupies some open spatial region, osr, then would there be any issue with saying that there's a fiat-surface, fs, that occupies a proper part of osr? Or have I just missed your point?

@michaelrabenberg
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michaelrabenberg commented Jan 1, 2024 •
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Another example. You bleed into your stomach cavity. The stomach cavity is part of a person and the blood is part of the person, but the blood is located in the stomach cavity. I don't think the site is diminished by the volume of the blood.

This is indeed an awkward case for the view I was proposing.

@alanruttenberg
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I guess formally there's an open question which is whether the spaces occupied by material entities are closed - we don't have the distinction between open and closed (or mixed) spatial regions.

Could you explain why this is a complication for the idea that, sometimes, a fiat surface occupies a spatial region that's a proper part of the spatial region that a material entity occupies? If some material entity, x, occupies some open spatial region, osr, then would there be any issue with saying that there's a fiat-surface, fs, that occupies a proper part of osr? Or have I just missed your point?

I was thinking about the question of whether a boundary is part of the thing it bounds. Consider the open interval (0,1) vs the closed interval [0,1], with the "boundaries" being 0,1. In the closed interval the boundaries are part of the interval. With the open interval, the boundaries are not part of the interval.

@phismith
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phismith commented Jan 1, 2024 via email

@alanruttenberg
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Consider a scallop S under water The external boundary of the scallop is a part of the scallop Where is the external boundary of the body of water, a scallop-shaped portion of which is displaced by the scallop. Best answer: The boundaries are in the same place, and this is possible because S is closed (as [0,1] is closed), but the body of water in the neighborhood of S is open. BS

What's the argument against the alternatives

  • That the boundary is part of neither
  • The the boundary is part of both - they overlap at the boundary
  • There are two boundaries, one bounding the water and one bounding the scallop, which don't overlap

An argument for it being neither is that if you look down to the molecular level, there are molecules that are part of the mussel, and their are molecules that are part of the water. Some of the water molecules even nestle themselves within the near-boundary portion of the scallop. The boundary is a fiat surface chosen somewhat arbitrarily to best segregate the scallop molecules from the water molecules and doesn't need to be part of either.

An argument for it being both is that if you ignore the molecular level and choose some more granular view it seems like things are symmetric. How do you decide which side the boundary belongs to, assuming the boundary should be part of some material entity.

An argument for there being two boundaries that don't overlap is that, being fiat, one boundary, could be chosen to "hug" one side and the other the other. I guess this is easier to see if you are thinking at the molecular level, where the notion of touching isn't well-defined. I'm not really certain how one reasons about boundaries at a coarser granularity, but maybe there's an argument for this even at a coarser granularity.

@phismith
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phismith commented Jan 2, 2024 via email

@michaelrabenberg
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Consider a scallop S under water The external boundary of the scallop is a part of the scallop Where is the external boundary of the body of water, a scallop-shaped portion of which is displaced by the scallop. Best answer: The boundaries are in the same place, and this is possible because S is closed (as [0,1] is closed), but the body of water in the neighborhood of S is open. BS

What's the argument against the alternatives

  • That the boundary is part of neither
  • The the boundary is part of both - they overlap at the boundary
  • There are two boundaries, one bounding the water and one bounding the scallop, which don't overlap

Regarding Barry's argument that the boundary is part of S (and so that option 1 is incorrect): Is there a reason to think S's spatial region is closed and the water's is open, rather than vice-versa (or for that matter rather than their both being open)?

Wouldn't option 2 imply that there's an individual partly composed of the scallop and the water? If A is part of B and A is part of C then isn't there an individual of which B and C are each parts?

I'm attracted to 3, because it doesn't require there to be (for example) a happy open/closed or open/open coincidence whenever a scallop is in some water.

@michaelrabenberg
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Consider a scallop S under water The external boundary of the scallop is a part of the scallop Where is the external boundary of the body of water, a scallop-shaped portion of which is displaced by the scallop. Best answer: The boundaries are in the same place, and this is possible because S is closed (as [0,1] is closed), but the body of water in the neighborhood of S is open. BS

Is the water's boundary not a part of the water? If it is a part of the water, then I don't see how this view could be correct.

@alanruttenberg
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(forall (x) 
  (if (exists (t) (instance-of x fiat-surface t))
     (exists (t s) 
       (and (occupies-spatial-region x s t) 
            (instance-of s two-dimensional-spatial-region t)))))

So, @johnbeve was asking me a question about this axiom and I realized in answering it that the above is too weak. I think it needs to be

(forall (x t) 
  (if (instance-of x fiat-surface t)
     (exists (s tp) 
       (and (temporal-part-of tp t))
             (occupies-spatial-region x s tp) 
             (instance-of s two-dimensional-spatial-region tp)))))

See #69 (comment)

From the new+theory we can prove the old one, but not the other way around.

One more set of eyes on this would help...

@wceusters
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This one:
(forall (x t)
(if (instance-of x fiat-surface t)
(exists (s tp)
(and (temporal-part-of tp t))
(occupies-spatial-region x s tp)
(instance-of s two-dimensional-spatial-region tp)))))

should be corrected to (the '(and' is closed too early):

(forall (x t)
(if (instance-of x fiat-surface t)
(exists (s tp)
(and (temporal-part-of tp t)
(occupies-spatial-region x s tp)
(instance-of s two-dimensional-spatial-region tp)))))

and then looks acceptable to me, as long as we accept axiom dyv-1 stating that all fiat-surfaces stay fiat-surfaces as long as they exist. But since not much is described in BFO documentation about what fiat-surfaces precisely are, dyv-1 can be challenged. In that case, perhaps the following axiom is better than the one above:

(forall (x t)
(if (instance-of x fiat-surface t)
(forall (tp)
(if (temporal-part-of tp t)
(exists (s)
(and (occupies-spatial-region x s tp)
(instance-of s two-dimensional-spatial-region tp)))))))

@michaelrabenberg
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This one: (forall (x t) (if (instance-of x fiat-surface t) (exists (s tp) (and (temporal-part-of tp t)) (occupies-spatial-region x s tp) (instance-of s two-dimensional-spatial-region tp)))))

should be corrected to (the '(and' is closed too early):

(forall (x t) (if (instance-of x fiat-surface t) (exists (s tp) (and (temporal-part-of tp t) (occupies-spatial-region x s tp) (instance-of s two-dimensional-spatial-region tp)))))

and then looks acceptable to me, as long as we accept axiom dyv-1 stating that all fiat-surfaces stay fiat-surfaces as long as they exist. But since not much is described in BFO documentation about what fiat-surfaces precisely are, dyv-1 can be challenged. In that case, perhaps the following axiom is better than the one above:

(forall (x t) (if (instance-of x fiat-surface t) (forall (tp) (if (temporal-part-of tp t) (exists (s) (and (occupies-spatial-region x s tp) (instance-of s two-dimensional-spatial-region tp)))))))

If I'm reading Alan's replacement axiom correctly, I agree w/ Werner that the extra close-parenthesis after '(temporal-part-of tp t)' should be deleted.

I don't see how Werner's proposed replacement is more responsive to his concern than Alan's replacement axiom. Unless I'm misreading them, neither Alan's replacement axiom nor Werner's proposed replacement entails that if x is ever an instance of fiat-surface, then x is an instance of fiat-surface for all of x's existence.

@michaelrabenberg
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michaelrabenberg commented Jan 9, 2024 •
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A problem for Werner's proposed replacement:

Suppose x is a fiat-surface for all of 12:00 to 1:00. Werner's replacement entails that at 12:00-12:30, there's a 2d spatial region that x occupies. But this needn't be true. Alan's doesn't entail this.

@wceusters
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A problem for Werner's proposed replacement:

Suppose x is a fiat-surface for all of 12:00 to 1:00. Werner's replacement entails that at 12:00-12:30, there's a 2d spatial region that x occupies. But this needn't be true. Alan's doesn't entail this.

I agree,

@alanruttenberg
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should be corrected to (the '(and' is closed too early):

Yes. Had it in the source code but hand-typed the common logic version. Oops.

@ajnelson-nist ajnelson-nist mentioned this issue Mar 8, 2024
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@alanruttenberg @phismith @johnbeve @wceusters @michaelrabenberg