From: Christopher Welty (welty@us.ibm.com)
Date: 01/18/05
[I tried using indentation for quoting, but I'm not sure it will come through correctly] Pat Hayes <phayes@ihmc.us> 01/18/2005 05:22 PM To "Wagner, G.R." <G.R.Wagner@tm.tue.nl> cc Christopher Welty/Watson/IBM@IBMUS, <guarino@loa-cnr.it>, "Mike Dean" <mdean@bbn.com>, <joint-committee@daml.org>, "Guizzardi, G. (Giancarlo)" <g.guizzardi@ewi.utwente.nl>, <herre@informatik.uni-leipzig.de> Subject RE: SWRL (FOL) n-ary relations [original qestion by MD] Can we come up with an n-ary representation that's significant simpler or otherwise better than the unary/binary SWRL representation? [GW] What do you mean with "significant simpler or otherwise better"? The issue here is simply that "objectifying" a relation may be unnatural and create some undesirable (and unnecessary) overhead in the language. [PH] What kind of overhead? Why would this create any overhead? [GW] If you don't see the overhead, this simply shows that you don't have much experience with coding practical appplications. The phrase could be referring to extra complexity in the logical encoding, or to computational overhead in any of various kinds of processing engine. These are not the same, and in some cases may be opposed to one another. In particular, a 'conceptual' overhead can in some cases yield a computational improvement (the restrictions needed for DL conformance are one example.) I would have liked to had the intended meaning clarified. I suspect what is meant by "overhead" here is simply that when relations are "reified" you end up with more tuples. As a simple example, if the extension of the (ternary) relation ChangePos is {<a,b,c>} then the standard kind of reification into binary relations would result in the extension of the (unary) relation ChangePos' being {C1} and introducing three binary relations, lets say Who, To, From whose extensions resp. are: {<C1,a>} {<C1,b>} and {<C1,c>} So this style of relation reification which is typically used when there is a limit to unary and binary predicates (I'm assuming that is what you are talking about, I don't know how I got into this discussion) results in "overhead" of three tuples, where a system that allows higher arity would have only 1 tuple. Is that clear? To make the particular point more forcibly, Common Logic allows one to write a relation name as an individual, and to quantify over names in relation position: the model theory objectifies all named relations for free, as it were. Now, what overhead do you see this as introducing? Indeed, this is a powerful facility, and would be extremely useful in specifying interoperability between languages like RDF & OWL (that are limited to binary relations and require some special handling for higher arity relations such as the style of reification exemplified above) and systems like relational DBs, KIF, etc. Or you may be in the position of an assembler programmer who doesn't want to see the unnatural overhead of coding a while loop with a jump/goto statement. I have been at various times at several different such positions. My general conclusion is that terms like 'unnatural' have no fixed or objective meaning, but simply indicate an implicit reference to some unspoken background bias or cultural assumptions made by the author. It is often useful to have these made explicit wherever possible. Agreed. [GW] In foundational ontology, one makes a distinction between formal and material relations (both of which would be represented with the help of predicates). [PH] ?Does one, indeed? That seems to depend a lot of which one one happens to be. Is there any philosophical, mathematical or practical reason for making such a distinction? [GW] Roughly, this distinction corresponds to the practical distinction between predefined and user-defined properties/functions/relations in computational formalisms. Wow. I really would like to see this analogy defended in a serious publication. For the present I will simply register my extreme cynicism regarding any such analogy, and a rejection of the 'formal/material' contrast. If this contrast really were basic or important, then formal relational logics would be surely have needed to have reinvent it: but they have not found any such need. There must have been parts of this exchange that were snipped before I was included, because I don't see the connection at all between relation reification and the formal/material "distinction". Anyway, this distinction, which is certainly debateable, is one which claims some relations are somehow more "foundational", let's call it, than others. THe distinction is the same as the "formal" vs. "material" ontology distinction. I think Barry would try to define it, or maybe he has published something that does, as relations that would exist even if people weren't there to record them. PartOf, for example, is often considered a formal relation, whereas "SpouseOf" is not. However I would be quite surprised to hear anyone claim the point is not debateable. There is certainly nothing at all special about formal relations that require special treatment in logic, from (my own) practical perspective formal relations are simply those with the highest degree of reusability across domains. So, yes there is a practical reason for making this conceptual distinction. There might be if that analogy made sense. A philosopher may claim that formal relations are the underlying threads that sew the universe together, so to speak; if you wanted to describe the universe you would need nothing else. Still, I don't see much practical value in making the distinction other than being able to judge which relations may be more reusable. A philosophical reason for it may be the desire to explain why some relations (such as those used in mathematics) have an extensional semantics and others have an intensional semantics. I do not know of any linguistic or philosophical justification for claiming that some relations are intensional while others are extensional. (Note, there are reasonable debates about whether relations should be construed as intensional or extensional: but those refer to relations in general. What I find implausible is the idea that both kinds are necessary.) I've never heard of this before either, it seems rather nonsensical. Intensional vs. extensional semantics seem like a completely different issue. What methodology or basic theory is used to justify making distinctions like this? And what does this particular distinction even mean? [Later. I have now read some papers on the subject. The definition appears to be purely circular: a relation is 'formal' if it is an extension which applies directly, and is 'material' if it is an individual with a relational extension. End of story. [GW] It's not quite that simple, unfortunately. Most people have some intuitive understanding of what is a formal relation because they know orderings and other relations from mathematics. Perhaps I did not make myself sufficiently clear. I do not accept any distinction between 'formal' relations and other kinds of relations (in fact between any kinds of relation) . Your discussion seems to presuppose this meaningless distinction. Well, I don't think your accepting it or not makes the idea go away. But the distinction certainly seems to me completely subjective. In fact, I can imagine building different theories (or logical descriptions) of the universe using different sets of assumptions as to what is "formal" and what is not. (between individuals that have a "history") is to point out that (instances of) these material relations hold between their relata because there is an individual (such as an event or a process) that affects the history of (and that existentially depends on) these relata. Again, I find this entire discussion to be profoundly confused. Me, too. Perhaps someone could clue me in as to the history and context. Of course there are material entities which have a history, and are distinct from nonmaterial entities such as numbers. However, none of that requires us to distinguish two kinds of relation. On the contrary, it seems to me that makes four kinds of relations: material x material, material x non-material, ... In fact, the contrary:if one makes the temporal structure and dependencies explicit, as will in fact be required in any practical ontology, then all relations become timeless. HERETIC!!!!! Thou hast been revealed!!! I am NOT A TEMPORAL PART! The resulting simplicity has been rediscovered many times: by McCarthy in the situation calculus, by Kripke in his possible-world modal semantics and the associated modal-to-FOL translation scheme, and by linguists studying tense and case grammars. It ought by now to be part of the standard stock-in-trade of any working ontologist. I think I agree with that, actually, however it (theories of temporal parts) should be a tool like anything else, not a religious conviction. There appear to be times when it is useful, and times when it is a royal pain. Much like its advocates. It can be summed up in a slogan: if you think that you need more than one kind of relation, look to the things that the relation holds between. Make distinctions there, and classify kinds of thing rather than kinds of relations. Err...are you saying you cannot have more than one kind of relation between the same kinds of things? A standard error is to think that because a word is used to refer in NL, that what it refers to must be a basic or primitive individual. For temporally embedded 'things', this is almost always a mistake. The logically primitive things in examples like yours are not people, but people-at-a-time. People last for a while and change their properties: they are complex entities. The 'conceptual' atoms suggested by informal usage are usually not the best logical atoms to try to build an ontology out of. That's one way to look at it. But it is not the only way. This is the case for relations such as "Person buys Product from Vendor" or "Person kisses Person", while it is not the case for relations such as "Point1 is between Point2 and Point3" How about if Point2 is defined in a spatial reference frame which is attached to a moving vehicle? Perhaps you do not accept such things as truly points; but they can be points in the topological sense. And if you reject these as points then you seem to be assuming a global spatial reference frame, which has been known to be physically meaningless since Einstein stated special relativity. Yes, indeed. The distinction is entirely subjective. or "Person is taller than Person" (the latter is a relation between the individual heights of two persons, being qualities in the underlying "conceptual space" according to the theory of Peter Gärdenfors presented in his book "Conceptual Spaces: the Geometry of Thought", 2000). Regarding the last example, I think you are confusing 'person is taller than person' (where the 'person's refer to continuants) with 'the height of person is greater than the height of person', interpreted at a moment in time. However, thanks for clarifying which of the various possible philosophical theories you are taking for granted. I take it then that you are proposing to base the world's ontology standards on the work of Gardenfors? The idea of ontological "features" or "moments" was something that you, Fritz, and I discussed all night once in Maine. And I don't think you ever got it. It would be difficult to explain how Gaardenfors stuff fits into that picture if you can't see the picture. However it is certainly not the case that anyone I know proposes to "base" any ontology on it, it is simply used in places in several ontological theories. What would be the basis for rejecting a claim that *any* relation defines a relator universal? [GW] A relator universal is an intensional concept, while formal/mathematical relations are extensional. First, I do not accept that this is meaningful; but even if it were, it does not answer the question: for I could rationally claim that any relation, even a merely extensional relation, defined an intensional relation (of which it was the extension). This would be consistent with a philosophical position to the effect that all relations ultimately resided in thoughts, for example, along with a rejection of simple mathematical Platonism. It is also the position built into the Common Logic and RDF formal semantics, by the way. I agree with Pat. This holds no meaning to me, I really can't fathom what is being referred to. ... you have no right to prevent me treating your 'formal' relations as 'material' relations: unless, that is, you want to claim that this is a *logical* distinction. [GW] No, of course, the distinction between formal and material relations is not a logical one. Most of the conceptual distinctions we make in order to understand the real world and to construct working computational systems are not logical! Quite. And since they are not, there is reasonable scope for rational people to disagree about them. Let's get some of them involved in the discussion, then. Which is why any generally acceptable ontological framework cannot be based on any of them. Certainly I personally will resist any attempt to impose the GFO ideas on any reasoner that I have anything to do with. (BTW, there are good engineering reasons for this declaration, not just philosophical distaste. Though in fact I also believe that philosophical distaste is quite a sufficient reason in itself.) Is that being proposed? Hmmm...I think this could be an interesting discussion, but I'm skeptical, too. I can imagine special-purpose reasoners that assume some ontological position in order to gain some efficiency advantage, but in general it seems best to stick to logic. PS sorry if you are wondering why a casual remark has stirred up such a hornets nest. I do have have rather strong feelings about attempts to impose a 'correct' ontological framework, and react rather strongly to assumptions that any such 'basic' framework should be accepted, particularly on any kind of philosophical authority. If there ever were a profession which is least likely to understand the way that world is actually constructed - which , after all, is the original meaning of 'ontology' - then philosopher would be a good candidate. Having been a philosopher (for a while), I am left with a deep-seated, almost religious, conviction that almost all philosophy is either in fact logic, or else is bad philosophy. Certainly I will claim it as an objective, verifiable fact that any nontrivial philosophical claim has been disputed by some other philosopher, and that nothing is ever settled. Philosophy, unlike science, does not make progress: it does not accrue knowledge, but simply invents new arguments. Excepting someone who is brilliant beyond the degree of anyone I've ever met, like Shelock Holmes maybe, it is only through argumentation that we truly come to understand what we really mean by our convictions and beliefs. It is a complete mistake to say that Philosophy does not make progress, unless you think having a better understanding of what it really means to believe something is not progress. -Gerd -- --------------------------------------------------------------------- IHMC (850)434 8903 or (650)494 3973 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32502 (850)291 0667 cell phayes@ihmc.us http://www.ihmc.us/users/phayes
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