To: |
ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx> |
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Cc: |
Lucian_Russell/ESI/CSC@xxxxxxx |

From: |
Arun Majumdar <arun@xxxxxxxxxxxx> |

Date: |
Fri, 30 Dec 2005 13:11:21 -0500 |

Message-id: |
<43B57849.1060404@xxxxxxxxxxxx> |

Dear Lucian, (01) Very good points indeed. I would like to start off by straying off and then returning to the questions you posed by looking at how we might ontologically determine some simple phrases as acceptable or rejectable in the description of a conceptual idea: Let me draw attention to one of the examples provided in the WN papers in order to illustrate. Consider Miller's example: (02) Yet most people accept *Riding* is a *part* of *driving* and reject *Driving* is a *part * of *Riding* *... (from the Wordnet 5 papers). (03) *By consideration of the implied semantics of "part of" we might assume that "part-of" has an implied chronological or temporal substructure. Then, it makes sense that one would "Sit down in the car" (ie. "Ride") before "Drive". On the other hand, there is a connection between the two, and hence, if one looks at the topological connection without the assymetric temporal "arrow of time", we can accept that if one is driving, one is sitting in the vehicle, and hence, driving is necessarily connected to riding, though not in a passive sence. However, each of these substructures are relational or causal or dynamical schemas in the sense that one gives rise to the other through some action. Verb lexical semantics, as morphisms on one hand, and noun qualia semantics as objects on the other hand, may help us determine the basic underlying principles from a geometrical or topological representation as a function of *cultural semantics" (more morphisms!) which relates to the ontology of how one interpretation may dominate another. So we would have one ontology that accepts the first statement and rejects the second and a complementary ontology that rejects the first statement and accepts the second. (04) Between these two ontologies, the only reason I can find that I could use to explain the preferences is that the ontologies represent "theories" over a language (not just the associative elements in the language). A lattice of theories represents a lattice of ontologies inter-connected by the mophisms between their categories. (05) So, we could have a category for "Small" and one for "Large" and then relate them via theories ( ref: http://en.wikipedia.org/wiki/Object_(category_theory) ). Or, for "green theories" and one for "blue theories", and then relate them (as in QCD). (06) Hence, to answer the question you posed in (1): 1. Should a class name in an Ontology, especially an upper level class, be restricted to a word or phrase? (07) My suggestion is that the distinction be drawn on whether or not you are referring to the class name in terms of a "set", or in terms of a "category". If the category refers to a Locally Small Category, then I suggest that it does not belong in the top --- hence, my conjecture (as a heuristic) is that the more constraints you have, the "smaller" the category and the lower down it is pushed. Therefore, a single word like "Time" would be a "Large Category" (and here I suggest looking at Sowa's top ontology as well as others), since there is no way to describe Time because we get caught in Godels trap (ie. there is no way to talk about time without talking about "time" ... I can talk about Motion in terms of "time and distance" and hence, motion would not be at the top of the ontology) (08) Of course, my notions are suggestions and highly speculative, however, I wanted to introduce the idea of making distinctions from a CT perspective. The nice thing about the CT perspective is that it forms a lattice: A lattice of theories to be precise :) (09) You wrote also: "So for an Ontology a non-lexical class name is really a substitute for a mathematical description." I agree and suggest that the morphism from this to its lexicalization is an approximation to our current understanding, where the lexicalization is a richer understanding (at least, perhaps, in the mind of the reader), while the mathematical description be used in the computer. (010) Therefore, fundamentally, I agree with you on the issues and am biased towards having no top fixed lexicalized ontology but rather a lexical conceptualization with a mathematical foundation that provides a rapid means to extend, modify or inter-operate. Therefore, my viewpoint is dynamic, where I see the static elements as providing for constraints in the dynamism. I have much more to say about all this, but, I believe I have expressed some basic ideas for consideration although I wish I were more eloquent and able to choose optimal examples. (011) Cheers, (012) Arun (013) Lucian_Russell/ESI/CSC wrote: (014) > > |

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