BFO-2020
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BFO-ontology
The spatial regions that continuant fiat boundaries occupy
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?
I believe you are correct. I will add axioms for this. Thanks, good catch!
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.
Boundaries can definitely occupy different spatial regions at different times. 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.
On Wed, Dec 13, 2023 at 7:31 PM Michael Rabenberg @.***> wrote:
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.
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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)))))
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 https://github.com/BFO-ontology/BFO-2020/issues/76#issuecomment-1856429861
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.
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?
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.
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.
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.
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.
The aggregate example is cute. Can you think of a plausible situation in which that would make sense?
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.
Note that we do not want to adopt for aggregates analogues of formation principles of the sort accepted in set theory Aggregates are entities which exist in time. We want aggregates to be capable of ceasing to exist even though all their members remain in existence BS
From: Michael Rabenberg @.> Sent: Saturday, December 16, 2023 7:36 AM To: BFO-ontology/BFO-2020 @.> Cc: Subscribed @.***> Subject: Re: [BFO-ontology/BFO-2020] The spatial regions that continuant fiat boundaries occupy (Issue #76)
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.
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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.)
On Wed, Dec 13, 2023 at 10:33 PM Alan Ruttenberg @.***> wrote:
Boundaries can definitely occupy different spatial regions at different times. 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.
Absolutely
On Wed, Dec 13, 2023 at 7:31 PM Michael Rabenberg < @.***> wrote:
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.
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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.
There is a demarcation zone and demarcation line 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. @.*** https://res.cloudinary.com/korea-konsult-ab/image/upload/c_limit,f_auto,q_auto,w_800,dpr_auto/DMZ/Korea_DMZ.jpg
From: John Beverley @.> Sent: Tuesday, December 19, 2023 5:06 PM To: BFO-ontology/BFO-2020 @.> Cc: Barry Smith @.>; Comment @.> Subject: Re: [BFO-ontology/BFO-2020] The spatial regions that continuant fiat boundaries occupy (Issue #76)
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.
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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.
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. BS
From: Alan Ruttenberg @.> Sent: Tuesday, December 19, 2023 7:02 PM To: BFO-ontology/BFO-2020 @.> Cc: Barry Smith @.>; Comment @.> Subject: Re: [BFO-ontology/BFO-2020] The spatial regions that continuant fiat boundaries occupy (Issue #76)
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.
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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.
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.
@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).
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.
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.
^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.
From: Michael Rabenberg @.> Sent: Wednesday, December 20, 2023 10:52 AM To: BFO-ontology/BFO-2020 @.> Cc: Barry Smith @.>; Mention @.> Subject: Re: [BFO-ontology/BFO-2020] The spatial regions that continuant fiat boundaries occupy (Issue #76)
^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.
This is surely a matter of logic.
Compare
the fact that prime numbers don't have factors other than themselvs and 1 and non-prime numbers do isn't great evidence that prime numbers aren't non-prime numbers.
BS
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This is surely a matter of logic. Compare the fact that prime numbers don't have factors other than themselvs and 1 and non-prime numbers do isn't great evidence that prime numbers aren't non-prime numbers.
This isn't an apt analogy to what I said. I said (among other things) that 0D, 1D, and 2D CFBs are infinitely thin, not that all CFBs are infinitely thin. Whether all CFBs are infinitely thin is precisely the issue that John is raising.