On Jan 11, 2009, at 12:59 AM, Patrick Cassidy wrote: PatH, Just short responses to two points. I think we have almost bottomed out here on differences that can be fruitfully discussed further in anticipation of learning something.
I agree; but this conversation has been useful, in that it has revealed (for me) the key point of our disagreement.
(1) [PC] >> Is it possible that learning *some* new things always requires creating new primitives? Possibly, but that is the question that I have suggested can be investigated [PH ] To investigate that is the business of cognitive psychology, not ontology engineering. I'm just not interested in this question, and I don't think it is germane to this forum. I strongly disagree, and feel that the question of how many primitives are required to express the meanings of an unlimited number of domain terms is one of the most basic questions, beyond the definition of the basic logic, that can be asked about how an ontology can be structured so as to achieve broad interoperability, and I think it would be inherently interesting to anyone who deals in representation of concepts.
I think the question is unanswerable, if posed with precision (see below for exegesis) and therefore completely unimportant. But ‘de gustibus non disputandum’ and if this is not a matter of interest to you, your opinion is noted, and there is no point in discussing that further. It also has the very practical virtue of providing a tactic that can focus collaborative construction of a common foundation ontology on the minimum number of basic ontology elements that will serve the purpose of translating among multiple ontologies.
I think that to even discuss notions of 'primitiveness' is to divert useful effort into pointless and ultimately meaningless debate about nothing. If you don’t believe that there are such things as primitives, then I can see this point as being questionable to you, but I feel strongly that the linguistic evidence of the dictionary defining vocabularies is strongly suggestive of such primitives, and if you don’t think that linguistic descriptions are sufficiently related to ontological expressions, then again we just differ and this is still a question that has to be resolved by experiment. If you think it’s a waste of time, don’t participate.
Of course, I will not. But the point of the debate here is surely how the community should focus effort, not just you and I.
(2) [PC] >> Well, knowledge is certainly open-ended, but if new concepts (or terms labeling those concepts) are always composed from some combination of pre-existing concepts [PH] >> Again, what ARE you talking about? What is this 'composed from some combination'? What kind of composition operations do you have in mind here? How does these concept combinators relate to logical ontologies? None of this makes sense to me.
Every time you (a) create an element in an ontology (type or relation) and (b) the axioms expressing the intended meaning of that element (to a level of detail sufficient for your intended purpose) contain only terms already pre-existing in the ontology (no two or more newly created elements depend mutually one each other for their axiomatic description); and (c) one asserts that the intended meaning of that ontology element is adequately captured by the axioms, without appealing to known instances of the type, or to a linguistic description that is not also expressed by the axioms, then that type or relation is, in the sense I am discussing, “expressed by” or “described by” or “specified in terms of” the pre-existing ontology elements, i.e. it is not a “primitive” in the sense I am using it for an ontology element.
OK, though I would observe that to use language like 'combine' or 'construct' for this is misleading. But allow me to point out some problems with this. First, you have phrased it in terms of creating a new concept, so the distinction between new and old is a given; but in practice, things are not this simple. As others have pointed out, if we are simply presented with a complex logical theory, such as the equation F=M.A, one can decide that any one of these is less 'primitive' than the others, using the above criterion, just by re-ordering the set {F, M, A}. And this is typical: first-order theories don't typically have the onion-peel layered structure that your criteria relies upon. Second, your notion here is extremely fragile. For example, it can be changed simply by re-casting an ontology in slightly different terms, or by adding a single axiom. If one were to track the development history of an ontology, even in its initial informal stages, the classification of concepts as primitive or non-primitive would be varying wildly as new facts were noted by the participants. Third, it begs the central issue which is illustrated by the time catalog: there isn't a single ontology to create new elements into. Right from the start, even for the most 'basic' concepts such as space, time and objecthood, there are alternatives, all equally valid and all having their active proponents and devotees, and all mutually incompatible. Your criteria, as stated here, simply cannot deal with this basic fact. And fourth, its too weak. For example, if I take the OWL wine ontology and add a single new wine to it, asserting only that it is a member of the class RhoneValleyWhiteWines and different from all the previously described members of this class, then according to the above, I have not added a new primitive. Which seems to me to be simply wrong, a clear bug in the criterion as given. In the case of relations, a proper description requires that every newly created relation have some logical inference as part of its description.
As stated, that does not make sense, but I think I see what you mean. . Relations that inherit logical inferences from parent relations do not require additional inferences specified. This operation of ontological description does not, in my view, require a “necessary and sufficient” definition in order to qualify as “non-primitive” .
As 'primitive' is a term of art which you have introduced, and has no established psychological or ontological or logical meaning, you are free to define it any way you like. We are not here talking about matters of fact. It only has to express the intended meaning axiomatically so that a person who understands the axioms can understand the intended meaning without a textual gloss, and without pointing to instances of a type or instances of usage of a relation – and the axiomatic specification should be sufficiently detailed so that ambiguities that might occur to another ontologist as being relevant to the same application are absent. This may still leave, in some sense. some “primitive” component unspecified logically (as with a natural kinds), but if the axiomatic description is sufficient to distinguish each element from all the others, and is useful for the intended purpose of the domain ontology, then it can be said, in the sense I am using, to be “described by” or “specified by” or “expressed by” a combination of pre-existing ontology elements – it is not a “primitive” element. When you say “Those various temporal theories can all be expressed in terms of three concepts: time-point, time-interval and duration.” , what do you mean by that? Is being “expressed in terms of” used only for necessary and sufficient definitions?
No, I mean only that each theory uses only those three terms, or can be reformulated using only those (or in some cases only two of them.) Of course, since the theories have different axioms, they assign somewhat different meanings to them.
PatH
PatC Patrick Cassidy MICRA, Inc. 908-561-3416 cell: 908-565-4053
On Jan 10, 2009, at 12:40 AM, Patrick Cassidy wrote:
... I confess it has been an assumption of mine that, from the point of view of a “primitive” concept being indivisible into smaller primitive concepts (crudely analogous to an atom, in its role as a component of molecules), that a finite inventory of such primitive-atoms (if such exists) would be unique. Ignoring the finer to-and-fro points of the argument for a moment, this seems to capture the basic place where we differ. You have a central vision - I can't use a more precise term - of concepts being 'formed' out of other concepts. by some process of combination, a kind of conceptual chemistry; and then there must be a collection of elements, a kind of concept periodic table. This analogy seems to drive a lot of your intuitions in this debate. But I don't share this intuition, and indeed I can't make philosophical sense of it: it seems to me to simply rest on a mistake, one that Fodor has also critiqued very acutely. Concepts simply aren't made up of combinations of other concepts in this way. They are all "atomic". (Well, virtually all: all the 'natural kind' concepts, as opposed to artificial combinations such as "French women between the ages of 25 and 50".) Just look at a first-order theory: all the names in it are on an equal footing; none are more 'primitive' than another, and they have no internal conceptual structure which would permit their being decomposed into something simpler or more elemental. The chemistry atom/molecule analogy is just misleading. Peirce made the same mistake, and others since then (mostly psychologists) have done so, but it seems to me that its long past time to bury this idea of concepts having 'structure'. They don't divide into smaller things, so they are all "primitive"; which is just another way of saying that "primitive" isn't a useful notion here.
I have never seen this point raised, and it may be significant, but right now I can’t think of any way a set of indivisible primitives could be anything but unique. But surely the time catalog is a clear case of this non-uniqueness. I fail to understand how you cannot see this, it seems so obvious. What would you reduce all of it to?
Limited imagination, perhaps. Now I have noticed that there are mathematical objects that have very non-intuitive properties, and perhaps a mathematician can provide some examples of how a set of primitive concepts (not divisible into component primitive concepts) might be able to be formulated in more than one way. I am genuinely curious about this suggestion. There are many, many ways to model space, for example, all of them different and none of them reducible to the others.
(2) are primitives finite in number? [PC] >> , 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. [PH] > 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? Well, knowledge is certainly open-ended, but if new concepts (or terms labeling those concepts) are always composed from some combination of pre-existing concepts Again, what ARE you talking about? What is this 'composed from some combination'? What kind of composition operations do you have in mind here? How does these concept combinators relate to logical ontologies? None of this makes sense to me.
, then the number of primitives need not increase as knowledge increases. This may depend on what you mean by ‘knowledge’. With a set of basic concepts we can predict an infinite number of things that *might* exist in the real world, but I think of knowledge as knowing what actually does exist and what doesn’t. Learning about the laws of physics (and chemistry and biology) that exist in our real world allows us to know some of the things that can’t exist. That’s knowledge, in my lexicon, but it doesn’t necessarily require new primitives. ?? Really? So when you first learned about, say, the distinction between temperature and heat (an example I recall especially vividly from my own education), you already had all the necessary mental apparatus to describe thermodynamics? The learning was just juggling the same basic stock of ideas in a new way? It sure didn't feel like that to me: it felt like learning something entirely new, something I had never previously thought. Similarly the first time I came across the notion of entropy, it was a wholly new idea, not reducible to anything previously known. I was able to use it to understand things that had been previously mysterious. My inventory of mental concepts had grown. It continues to grow. Not long ago I learned the idea of "duende", a word that cannot be translated into English.
Is it possible that learning *some* new things always requires creating new primitives? Possibly, but that is the question that I have suggested can be investigated
To investigate that is the business of cognitive psychology, not ontology engineering. I'm just not interested in this question, and I don't think it is germane to this forum.
by the process of creating a plausible set of ontology elements based on primitives (as best we can discern them) and then seeing how quickly that inventory in the FO must increase to allow the elements in each new additional domain ontology to be expressed in terms of the primitive set. If there is a finite set, then from the increase in required primitives for each new block of domain concepts, it will be possible to assign a probability that the total inventory will reach an asymptote at infinity. The alternative is that no limit is indicated, and the number of primitives behaves, say, like the number of prime numbers as the number of integers increase. I do not know for sure which is more ‘realistic’, but my suspicion lies with the finite number, based on evidence from linguistic usage, such as the Longman defining vocabulary and the relatively small number (2000 – 5000) in AMESLAN sign language dictionaries. There are other suggestive kinds of evidence from language, but what needs to be determined experimentally is whether the finite defining vocabularies in languages are in fact analogous (at least on the point of the number of primitives) to the task of creating ontology elements as combinations of other ontology elements. Again: what do you mean here? What kind of combinations are you talking about? How are they expressed? _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxxShared Files: http://ontolog.cim3.net/file/Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1JTo Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
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