On Jan 9, 2009, at 12:11 AM, Patrick Cassidy wrote: PatH – Just two responses here – about whether the primitives are necessary, and the question of whether 3D and 4D entities can live together in a logically consistent ontology: (1) [full preceding text is below, here just the last paragraphs] [PH] > Well, now, this is certainly a reasonable grand vision to guide future effort and research. What you describe here is very similar to what John Sowa has described as a lattice of theories, and what Cyc has implemented using its 'micro-theory' context mechanism. (Cyc actually has the choice of modules semi-automated, as part of the overall Cyc ontology is a fairly comprehensive ontology of contexts themselves, allowing the inference engine to reason about what assemblages of micro-theories are most suitable for various reasoning tasks or topic areas.) > But allow me to suggest one small amendment. Given the notions of being able to combine mutually consistent modules, why do we need to have a single 'basic' FO at all? This combining-module idea does not depend on there being a single central 'basic' module somewhere in the lattice, or on all concepts being reducible to a smallish set of 'primitives'. It can be a true catalog of various alternatives, with no single 'root', and still provide the interoperability advantages. I have no problem with the lattice of theories notion: it is this mythical single primitive core that is so unconvincing: but your vision here does not seem to depend on that. For example, for some purposes, a discrete time and a continuous space ontology seems useful; for others, it is important to allow temporal limit points, but spatial references can be minimal, and so on. Why do we need to decide which combinations are more 'basic' than others, when it seems that all such decisions will be largely matters of taste, and likely fraught with endless controversy? [PC] (1) Yes, it is true that different independent developers could use different combinations of modules, provided that those modules were known to be (or not disproven to be) logically consistent, and still achieve optimal interoperability. But this still requires that the chosen modules have all of the basic concepts that allow all of the newly created domain terms to be ‘expressed in terms of’ (I am using your phrase) those terms in the modules chosen. This means that *somewhere* in the collection of mutually consistent modules there have to be enough of the basic terms that are used to express the meanings of newly created domain terms, so that any domain can be represented.
OK, lets agree on this for the sake of argument. But note, it does not follow that there is a *single* such set. That is the point. That set of modules would then contain what I think of as the minimum set of primitives
By using the word "the" here, you beg the central question: whether there is a *single* set of primitives out of which all other meanings can be formed. , though the modules can also have other ontology elements in them. It is not clear to me that we can have a *stable* set of modules to serve the purpose of interoperability unless we have some confidence that all or most of the terms needed to express the meanings of domain terms are there at the start.
Seems clear to me that if we impose this condition as a requirement, we have shot ourselves in the foot. And why should the set of concepts be "stable" ? Isn't it more realistic to assume that new concepts will always be being constructed, that knowledge is always open-ended? The hypothesis of a finite set of primitives (whether in a core ‘BaseKB’ or in a set of consistent modules) provides a target number that is as small as possible, largely **to make the task of agreement as easy as possible**. If it turns out that there is no such thing as a finite set of primitives, and it becomes necessary to continue adding new primitives indefinitely as new domains are derived from the FO, then the FO will not be fully stable.
True, but I find this a feature rather than a bug. It may nevertheless be stable enough to achieve a practical level of semantic interoperability. In any case, I expect that actively seeking out what look like the basic semantic primitives will drive the FO to its most stable state as quickly as possible. In sum, I agree that the existence of a finite set of semantic primitives is *not* a condition for success for a collaboratively developed Foundation Ontology, but (a) if it does exist, the resulting ontology will be more stable than one that starts out with fewer than the full number of primitives; and (b) aiming to represent all the primitives is likely to make the FO as stable as possible as quickly as possible. That’s why I think that emphasizing the search for the semantic primitives is a good approach. Of course, the most *essential* factor is the collaborative development by a large consortium, to quickly create a large user community. (2) Concerning the question of whether 3D and 4D versions of an Object can both exist in a logically consistent ontology: [PH] > Before proceeding, please show us a sketch of this part of the basic FO, containing both kinds of entity. [PC] OK, first I will reproduce an email from PH dated March 20, 2008. Note the phrase [PH]: “This is a 'unified' ontology. But note, the result would not be acceptable to a confirmed 3D modeler; it is for example incompatible with the OBO foundational ontologies or DOLCE”
Exactly. So this whole included email isnt relevant to the discussion we are having. But see later comments anyway.
============ email from Pat Hayes 3-20-2008 ======================== At 3:35 PM -0400 3/20/08, Patrick Cassidy wrote: PatH,
There is an axiom provide by you during this thread which I would like to
clarify:
>> (forall (x (t Time) P)(iff (P x t)(P (x during t)) ))
[PC] >> I have not seen the two different syntactic expressions:
(P x t) and (P (x during t))
Used together before. The first suggests a 3D perspective, and the second
suggests a 4D perspective. Yes, exactly. Think of this as a 'bridging' axiom, part of a translation specification, if you like. OK, I'll come clean and tell you what I really think. There are a variety of notational options in combining a simple timeless assertion with a temporal parameter. One is to treat the time as a context, in effect attaching it to the entire sentence (or in IKL, proposition): (ist t (P x y)) (ist t (that (P x y))) another is as an extra relational argument, giving the 'fluent' style which goes naturally with continuants: (P x y t) and a third is to connect it to the object(s) being related, the relation then being naturally understood as a relation between time-slices: (P (x at t)(y at t)) But in fact, these are really all just notational variations on a single theme. They amount to choosing where in the parse tree of the simple _expression_ to attach the parameter, is all. If we simply FORGET the philosophy for a second, then we can treat this as an arbitrary conventional choice, and think of them as all meaning exactly the same thing, and therefore equivalent. Then it makes literally no difference if you say "At t, its true that P holds between x and y" or "P is true of x and y and t" or "P holds between the t-slices of x and y" , as these all mean the same. As to what exactly x and y are in this, I don't really care what your favorite philosophical answer is. Choose the philosophy you like best: but then be prepared to have your head exploded by some of the things that you might have to read. Maybe this is what you meant by 'dimension neutral', but I don't like that way of describing it, as I see them myself as inherently 4-D. Attaching the temporal parameter 'higher up' the tree is just a handy shorthand convention useful at times; but there are some things (Q (x at t)(y at t')) that just cannot be said any other way. So we have to have the 4D picture as a kind of base case; and once we have that, we really don't need the others (all of which are based on highly questionable philosophical foundations in any case. Trying to make actual physical sense of the notion of 'continuant' is just about impossible.) This is a 'unified' ontology. But note, the result would not be acceptable to a confirmed 3D modeler; it is for example incompatible with the OBO foundational ontologies or DOLCE. [PC] >> How would you describe the type that "x" belongs to? Type?? Do you mean, what kind of thing is it supposed to denote? Anything with an extension in space and time. This seems to me to be a basic ontological category. I'd say that if you are a 3D man, think of it as the union of continuants and occurrents; if a 4D man, think of it as a 4D 'worm' or history. [pc] >> The way it is used in those expressions, it looks a lot like the
"dimension neutral object" that I suggested as a way of providing both 3D
and 4D perspectives in the same ontology.
Possibly.
[PC] >> In my case, however, I did not
use the (x during t) _expression_, but created a type "TimeSlice" so that
time-slices (any temporal length) of 4D objects could be expressed in an OWL
formalism. Oh sure, any 2-argument function is basically trinary, so has to be re-manipulated to get it into a binary language like OWL. [PC] >> Is there a documentation somewhere that additionally explains the
intended meaning and use of that type (of which "x" is an instance)? See above. PatH -- ============================== end email from PatH ============================= A fragment of an ontology where 3D and 4D versions of entities live peacefully together: [[ notation: (iff {X rel Y @Z} (rel X Y @Z)) The notation (x during t), is introduced by PH (above) , and used here for further illustration: [PH] >> (forall (x (t Time) P)(iff (P x t)(P (x during t)) ))
My idea of a ‘unified’ 3D-4D ontology would permit (among other things) the assertions (I hope the meaning is clear from the labels): {PH isanInstanceOf Object} {PH4D isanInstanceOf Object4D}
Can you explain the difference between Object and Object4D? Intuitively, that is. What criteria are there for deciding whether a given thing is in one category or the other, that we can explain to knowledge modelers in the user handbook? Can there be one of these without the other also existing, such as a PH without a PH4D, or vice versa? (Why not?)
{t1 isanInstanceOf TimePoint} {t2 isanInstanceOf TimePoint} {t1t2 isanInstanceOf TimeInterval} {t1t2 hasStartingTimePoint t1} {t1t2 hasEndingTimePoint t2} {PH4D isTheWholeLife4dVersionOf PH} {PHt1t2 isaTimeSliceOf PH4D from t1 to t2}
What relationship , if any, is there between PHt1t2 and PH?
If I included a ‘during’ similar to the one PH uses, it might look like: {(PH during t1t2) isIdenticalTo PHt1t2}
?? So (PH during BirthDeath) is identical to PH4D ?
{{PH isLocatedAt IHMC from t1 to t2} iff {PHt1t2 isLocatedAt IHMC}} And, redundantly, given the above: {{PH isLocatedAt IHMC from t1 to t2} iff {(PH during t1t2} isLocatedAt IHMC} The above explicitly has a 4D entity PH4D as TheWholeLife4dVersionOf the ‘dimension neutral’ object PH. The syntactic structures using an instance of ‘dimension neutral’ Object are identical to those of a 3D object. It just isn’t labeled as ‘3D’ – though the label shouldn’t matter. The way I use these, there cannot be a ‘disjoint’ axiom between the dimension-neutral ‘Object’ and ‘Object4D’ (instances of ‘Object’ can have time slices, in the OWL version, to allow time to be used in binary relations - a syntactic convenience).
If you are willing to allow dimension-neutral objects to have time-slices, you have completely abandoned the foundational ideas behind continuants. Whatever these PH things are, they aren't continuants. I therefore see no purpose in having them. Why not simply identify PH with PH4D?
. Although the ‘dimension-neutral’ Object is not explicitly 3D, it behaves syntactically like a 3D object. I think in this case there are actually two types of entities, not just syntactic variations on a single inherently 4D entity. Perhaps, if one wants to stick to solely 4D entities, it *might* be possible to equate PH with PH4D, and allow both syntactical forms (P x t1 t2) and (P xt1t2) but I haven’t tried to work through whether the domain restrictions would then become inconsistent (is this what you have already done?). I prefer to keep around something that looks like a 3D Object, not confused with the 4D, to make translation to pure 3D ontologies easier.
But it obviously cannot be 3D. It has to have a temporal extent, otherwise the construction (PH during t1t2) does not make sense. And if it has 3 spatial and 1 temporal extents, then it is 4D. That is exactly the intuition that led to the adoption of 4D in the first place: that is what 4D means. The 3D ‘Object’ behaves a lot like other 3D ontologies, except that it is not disjoint with Object4D.
Exactly, but this is the killer point. If one believes in the continuant/occurrent distinction, then the disjointness of these two categories (occurrents - in effect, 4D things - and continuants) is an absolute, foundational assumption. It would be impossible, in such an ontology, to allow something to be in both categories. I agree - not being one of the believers, myself - that to allow them to intersect is the simplest way to 'unify' the two conflicting points of view. But this is not acceptable to these guys (not surprisingly, as it amounts to a reduction of their language to 4D language): they prefer to keep the categories distinct, and 'unify' by treating the 4D ontology as claiming that everything is an occurrent. This is not a point on which happy agreement seems likely to emerge.
You say that the ‘unified ontology’ that uses such structures would be incompatible with OBO or DOLCE. I haven’t looked at them to check that. Could you cite specifically the axioms that would create that incompatibility if ‘Object’ was a subtype of ‘Continuant’ and ‘Object4D’ a subtype of Occurrent?
That alone would not be formally inconsistent, provided you keep continuants and occurrents disjoint. But now try to use this ontology to describe, say, me. If you respect the continuant idea, I have to be a continuant. OBO/DOLCE require me to therefore not be an occurrent, so not to be an Object4D, so not to have temporal parts. But this is anathema to a 4D ontologist: the whole point of using the 4D framework is to avoid the needless proliferation of entities which are distinguished only by these purely philosophical distinctions. In a 4D ontology, Pat Hayes really is a 4-D thing, because all spatiotemporal entities are 4D. What you have done here is to re-create the occurrent/continuant distinction in 4D language: and that satisfies nobody, since those who find the distinction useful (or even meaningful) do not accept the 4D framework in the first place, and those who wish to use 4D do not want to be forced to make the distinction. .
I am assuming that the syntax of OBO or DOLCE might require some translation of axioms to achieve logical consistency, and it is logical consistency after/modulo translation that I am concerned about. Final question: I interpreted your comment that the axioms you gave are part of a ‘unified’ ontology – which I took to mean, containing 3D-like and 4D-like entities.
These labels are misleading. All 4D ontologies contain 3D entities. What they don't contain are continuants, which are 3D but also extended in time. The axioms seemed to be consistent with that, though the (x during t) structure was not repeated in the later axiom set. Perhaps you meant something else by ‘unified’?
I was using the term optimistically, but subsequent discussions have made me less optimistic than I had become.
PatH
PatC Patrick Cassidy MICRA, Inc. 908-561-3416 cell: 908-565-4053 ======================= original note from PH Thursday, January 08, 2009 ========================== On Jan 8, 2009, at 4:02 PM, Patrick Cassidy wrote:
A few points are selected that seem most productive: (1) [pc] >> Alternative theories can be represented in extensions to the
>> foundation ontology [PH] > That is extremely unlikely, for two reasons. First, no such foundation is likely to exist; second, even if it did, the extensions to it would be mutually inconsistent with one another, so would not all together form a coherent single ontology. We may be using “extension” in a different sense. Extensions in the sense I intend do not have to be logically consistent with each other. Hmm. OK, then, in what sense is this resulting, er, structure of extensions an ontology? And why are you not just being vacuous here, and urging that there should be many alternative, mutually inconsistent, ontologies? We can arrange for that with a very low cost to the government. [[PC]] The base FO plus extensions would form a hierarchy of possible ontologies and ontology modules from which parts could be taken for specific applications. Each extension would have to be logically consistent with the sum of modules of which it is a submodule. It will be essential to specify which branches of the hierarchy are logically inconsistent with which others. Having done that, it will be possible to take and combine modules with some confidence that the whole will be logically consistent. Proving consistency among specific modules may well be intractable, but some degree of certainty may be derived by running a consistency checker for some time (or, being open-source, having everyone interested run a consistency checker on the parts of interest to them, perhaps using SETI-like system for distribution of tasks and receipt of results) . Such a hierarchy will allow a much higher level of confidence in the consistency of any given collection of modules than an unregulated collection. Any two collections of modules known to be consistent, or not proven to be inconsistent, should then be able to be automatically merged into a common ontology that should also be consistent, and able to produce the same inferences form the same data as the individual collections used locally. Using this hierarchy (and creating any local extensions desired, based on the terms in the extracted modules) would provide what I would consider a higher level of interoperability than any I have seen suggested by any technique other than everyone using the same ontology. Not every ontology describable using the terms of the FO would necessarily be consistent with the FO (one only has to assert (not P) for some P in the FO), and therefore would not be part of this hierarchy. Ontologies described in terms of, but inconsistent with, the base FO might be maintained in a separate registry. That will be an issue for decision by the committee maintaining the FO. Well, now, this is certainly a reasonable grand vision to guide future effort and research. What you describe here is very similar to what John Sowa has described as a lattice of theories, and what Cyc has implemented using its 'micro-theory' context mechanism. (Cyc actually has the choice of modules semi-automated, as part of the overall Cyc ontology is a fairly comprehensive ontology of contexts themselves, allowing the inference engine to reason about what assemblages of micro-theories are most suitable for various reasoning tasks or topic areas.) But allow me to suggest one small amendment. Given the notions of being able to combine mutually consistent modules, why do we need to have a single 'basic' FO at all? This combining-module idea does not depend on there being a single central 'basic' module somewhere in the lattice, or on all concepts being reducible to a smallish set of 'primitives'. It can be a true catalog of various alternatives, with no single 'root', and still provide the interoperability advantages. I have no problem with the lattice of theories notion: it is this mythical single primitive core that is so unconvincing: but your vision here does not seem to depend on that. For example, for some purposes, a discrete time and a continuous space ontology seems useful; for others, it is important to allow temporal limit points, but spatial references can be minimal, and so on. Why do we need to decide which combinations are more 'basic' than others, when it seems that all such decisions will be largely matters of taste, and likely fraught with endless controversy?
(3) [PH]> >> This seems vanishingly unlikely. This first requirement forces this common theory >> to be as small as possible, but you believe that it will be as large as any theory >> every conceived by the human mind.
[PC] >> No, the theory encoded by the FO is only as large as the number of primitives and their deductive closure. But extensions can be infinitely large, since there is no limit to the number of complex concept representations that can be constructed as combinations of the primitive concept representations.
[PH] > Since these complex concepts are all defined, they are all eliminable. The extensions have the same expressive power as the FO. So the FO itself already has the expressive power of every other theory. [[PC]] Well, if “largeness” is the same as “expressive power” in your terminology, then, yes. I am accustomed to thinking of size as something different. The point is that this single theory has to be both small, and expressive enough to define all concepts adequate for human thought. There is no reason to suppose that such a theory exists, and many reasons to suggest otherwise. And, perhaps more to the current point, its not even clear that it would be very much use even if it did exist, cf. above.
(4) [PC] >> I recall that PH and I had a long exchange last year or so at the end of which I thought that we agreed that 4D and 3D assertions could be translated into each other. Did I get a wrong impression, or is PH misinterpreting what I am saying?
[PH] > You got a wrong impression. But the point is not just about translation. I recently had a discussion with Barry Smith about this. Barry's view of the way to reconcile 3-D with 4-D (apologies for the terminology) is that the 4D perspective simply classifies everything as an occurrent. That is the most natural way to express it from his perspective, and it is in a sense accurate. For Barry, people are continuants, and the 4D-ers say they are occurrents: a simple difference of ontological opinion, like me saying I'm Irish and Barry saying I'm American. > That would be one way to reconcile the two point of view, but it has the demerit that if the basic ontology accepts the distinction, there have to be two 'me's: the occurrent and the continuant. And this is a problem for the 4Ders such as myself, because from our point of view, this bifurcation of entities into two halves is an ontological mistake. From this point of view, there simply is no meaningful distinction to be made between continuants and occurrents; that all the so-called continuants are in fact occurrents. From this point of view, there is no disagreement between Barry saying I am a continuant and me saying I am an occurrent; we aren't disagreeing about any matter of fact, or indeed about anything. > The problem lies higher up the classification chain: it is the notion, fundamental to Barry, that the occurrent/continuant distinction is basic ("upper") and also sharply dichotomous, so that nothing can possibly be in both categories. To me, in contrast, the distinction is vacuous or, at most, amounts merely to a syntactic preference for writing certain time-dependent facts in one style rather than another. > Now, it is possible to translate between these points of view, but not to reduce them to a single one. They are not two branches extending from a common trunk: they are more like two completely separate plants which are about the same height. They give different accounts of Pat Hayes the person: in one viewpoint, there are two of me: me the continuant and me (my lifespan) the occurrent, and all the vocabulary for talking about me has to be duplicated. One cannot simply say that the 4D perspective is got by equating these (though that would be intuitively correct) as the ontology itself would prohibit this equation. [PC] >> If some person PH is classified in one ontology as 4D and in another as 3D, clearly the ontologies cannot be combined under the assumption that the label PH applies to the same thing in the two cases. It isn’t. [PH] > Ah, but you see, it IS. That is the critical point. Lets agree that I am what I am, the facts of my life are what they are, and so on. Nobody will dispute any of this, let’s suppose. Still, two philosophers can disagree about how all this stuff should be encoded in an ontology. But they are both talking about the same person, the actual Pat Hayes in the actual world. (If they aren't, there is something badly wrong with their ontologies.) The two ontologies conceptualize me differently, but it is simply factually wrong to claim that I am two persons, just because two philosophers disagree about how best to describe me. Everyone agrees that I last for a time and occupy space and have properties which vary with time, and so on. They just disagree about how to formulate this in a logic. But neither of them thinks that there are two Pat Hayeses, and any ontology which says there are is just flat wrong. http://www.ihmc.us/users/phayes/PatHayes denotes me, the actual me, here in the actual world. [PC] >> In one case, it is a 4D entity whose lifetime is PH4D and in the other case it is a 4D entity whose lifetime is PH4D, where the ‘lifetime’ is in the FO even if that concept is not in the 3D ontology (actually, I use a “dimension-neutral object” to relate the two). When the ontologies are translated or merged [PH] > If you merge them, they will be inconsistent. I agree that in many cases one can translate between the two points of view, but its not easy and not always possible at all. I've never seen a program that can do it. [PC] >> , the different entities PH3D and PH4D are both present, and assertions about the properties of one in 3D-speak can be translated into assertions about the properties of the other in 4D-speak. [PH] > Yes, though not always in the other direction. [PC] >> The problem here again appears (from the description) to be an attempt to use the same term to refer to 2 different entities –a terminology clash. [PC] well, my point is that a 3D entity and it corresponding 4D entity are truly different though intimately related things, though they are labeled by the same term by different people. The problem goes deeper than this. The things which some philosophers call 'continuants' are not either 3-d or 4-d when viewed from a 4-d perspective; they are simply impossible. They have to be 3-dimensional but also persist through time, which is logically incoherent in a 4-d ontological perspective. (Continuants aren't the 3-d slices of the 4-d thing; those are different at different times, but continuants retain their identity through time.) Its not just a matter of terminology. One perspective insists that things exist which are provably impossible when seen from the other perspective. It is possible for a broad-minded 4-d thinker to take what the other guys say and make a kind of sense of it (I speak here from personal experience) but only by 'translating' it a way that the other guys insist isn't acceptable, by denying a basic assumption of their universe.
One philosopher may insist that only 4D entities exist, and another philosopher may insist that only 3D entities exist. These are different **belief systems** about their real world. As far as an ontological engineer should be concerned, what “exists” is only what is or can be represented in an ontology, and ontologically speaking, both 3D and 4D entities exist in that sense. But not in the same ontology. There is no single consistent ontology that admits both continuants and 4-d histories.
We can model the belief systems of those ontologists, by asserting the “non-existence” in the sense that the philosophers are using, and since both of those belief systems assert the non-existence of something that is in the ontology, then whether these belief systems are or are not inconsistent with the base FO (which has both kinds of entities) Before proceeding, please show us a sketch of this part of the basic FO, containing both kinds of entity.
depends on how one interprets the philosophers’ view of “exist”. If it is identical to the logical “exists’ applying to axioms in the ontology, there would be an inconsistency, and both belief systems would be inconsistent – moved into a module in the “inconsistent” set. The ontology would still be able to express assertions about the 3D and 4D entities. IF the ontologists’ “exists” is something different – existence in the real world, or in some ideal world, then both theories individually would be consistent with the base FO, though inconsistent with each other. Then they could be put into different logically inconsistent extensions of the FO. It all sounds very nice, but it doesn't actually work out this way. Just try it and you will find out why.
[PH] > But my point is that there is only one entity, in fact. And it is important for an ontology to be able to say this, and clearly draw appropriate conclusions. If I am in a room and nobody else is in it, there is one person in the room. Not two people, one of them 4-d and one of them 3-d. From an ontological point of view, I would say there are at least two entities: a PH3D and a time-slice of PH4D. And how do they differ? Which of them has my social security number? Can one of them be hungry and the other not, a the same time? (Why not?)
In fact, there are an infinite number of time slices of PH4D, though one is likely to be concerned only with one of them. (5) [PC] >> , The FO needs to be permissive to serve its purpose of translation. Where there are logical inconsistencies, one or both of the candidate entities needs to be moved to an extension (which can be logically incompatible with other extensions). This decision would be taken by a vote of the executive committee for the FO project. [PH] > I cant help expressing my amusement at the naiveity of this casual remark. Patrick, have you ever been on a standards working group? I have attended meetings of some groups, and am aware of the difficulty of finding consensus. But a practical project of this kind cannot depend on consensus, there has to be a simple majority up-or-down vote on issues of controversy, and very quickly. Anyone who cannot bear to participate under such conditions doesn’t have to – that will be clear before any organization work gets under way. I expect there will be enough people oriented toward a practical solution to form the large community that is required for this project. If not, the project will never start – no harm done. This isn’t naïve, it’s practical and realistic. I hope you will agree to be the chairman.
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