From: Pat Hayes (phayes@ihmc.us)
Date: 01/18/05
>[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. 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? >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. >[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. >So, yes there is a practical reason for making >this conceptual distinction. There might be if that analogy made sense. >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.) >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. >An attempt to characterize the difference between >those formal relations and other relations There are no such differences. > (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. 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. 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. 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. 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. 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. >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. >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? >...; and the elaborate but misguided ideas >emerging from the Leipzig institute do >not stand up to even a moment's close analysis; ... > >[GW] Note that there are two "Leipzig >institutes" (that have arised from a schism) >and that I was referring to the work of Heinrich Herre and others on what they >call "General Formal Ontology (GFO)" and "General Ontological Language (GOL)". >Please don't confuse this with "BFO" as proposed by others and Smith, whose >work is less profound. Thanks for clarifying that interesting piece of academic politics: I had wondered why Barry had left the place so soon after going there with such fanfare (I was visiting Buffalo when he was shortly to depart for Leipzig). However, it was the GFO and GOL that I was referring to, in fact. I have separate disagreements with Barry's ontological views, and you and I may well agree on those. >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. >... 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. 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.) Pat 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. > >-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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