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To: "'Pat Hayes'" <phayes@xxxxxxx>, "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Chris Partridge" <mail@xxxxxxxxxxxxxxxxxx>
Date: Thu, 12 Feb 2009 10:35:01 -0000
Message-id: <00b701c98cfd$8f848110$ae8d8330$@net>



Many thanks for taking the trouble to make such a full answer.


Like and agree with much of what you say, but a few points


Can I start with your last comment.

PH> Priority??  And aren't we, in this forum, talking about logics (in a broad sense, ie formalisms for description) and KR, rather than statistics or metaphysics?


I appreciate that this is your (and others) view.

However, there is another view (and another view of logic) which I think John was espousing in an earlier set of emails (in relation to Aristotelian syllogisms), which is that logic is a formalism for describing the way the world is – or more grandly, what exists. And that in some way the form of the logic reflects the structure/nature of the world.

A colleague pointed out to me something you may be familiar with, “ARISTOTLE'S LOGIC: A COMPARISON OF LUKASIEWICZ'S AND CORCORAN-SMILEY'S RECONSTRUCTIONS”


Though this is not exactly the point we are discussing, it illustrates the kinds of tensions that can arise between the ‘formalisms for description’ and ‘formalism for describing the way the world is’.


However, I expect we will just have to agree to disagree.


With respect to the intended meaning of individual (a point you raised), we were trying to find out what the OWL sense was. It is explicitly mentioned several times in the specification. See some extracts below. We definitely were not using it in its metaphysical sense.



1. Introduction (Informative)

This document contains two formal semantics for OWL. One of these semantics, defined in Section 3, is a direct, standard model-theoretic semantics for OWL ontologies written in the abstract syntax. The other, defined in Section 5, is a vocabulary extension of the RDF semantics [RDF Semantics] that provides semantics for OWL ontologies in the form of RDF graphs. Two versions of this second semantics are provided, one that corresponds more closely to the direct semantics (and is thus a semantics for OWL DL) and one that can be used in cases where classes need to be treated as individuals or other situations that cannot be handled in the abstract syntax (and is thus a semantics for OWL Full). These two versions are actually very close, only differing in how they divide up the domain of discourse.

Appendix A contains a proof that the direct and RDFS-compatible semantics have the same consequences on OWL ontologies that correspond to abstract OWL ontologies that separate OWL individuals, OWL classes, OWL properties, and the RDF, RDFS, and OWL structural vocabulary. Appendix A also contains the sketch of a proof that the entailments in the RDFS-compatible semantics for OWL Full include all the entailments in the RDFS-compatible semantics for OWL DL. Finally a few examples of the various concepts defined in the document are presented in Appendix B.


I agree that a logician may not like the term individual – I prefer element – but in it what is intended in the ordinary language sense. You may prefer ur-element.


PH> It is not a metaphysical classification: it does not separate the ontic universe into two kinds of thing, one kind more 'individuated' than the other. (Speaking personally, now, I have never understood what such a distinction could possibly mean.)


I think, in logic, it may be the distinction between ur-elements and sets.


One of the things that continues to surprise me it that the current ZF contain only sets. This seems to be the outcome of mathematicians desire to avoid any contact with the real world at the beginning og the last century.  But “The Zermelo set theory of 1908 included urelements. It was soon realized that in the context of this and closely related axiomatic set theories, the urelements were not needed because they can easily be modeled in a set theory without urelements. Thus standard expositions of the canonical axiomatic set theories ZF and ZFC do not mention urelements.” http://en.wikipedia.org/wiki/Urelement


Have you come across NFU? http://en.wikipedia.org/wiki/New_Foundations  http://plato.stanford.edu/entries/quine-nf/ Intriguingly, NFU has ur-elements and a universal set – which, from what you say, you approve of.


Could you live with an urelement / set distinction?



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