On Feb 12, 2007, at 11:53 AM, Pat Hayes wrote:
> [John wrote:]
>> ...
>> Following is a revised version:
>>
>> A formal ontology consists of a theory T stated in
>> some version of logic and a nonempty vocabulary V
>> of types and relations. The names in V are divided
>> in three disjoint subsets:
>>
>> 1. Names defined elsewhere, which are used in one
>> or more axioms of T.
>>
>> 2. Names defined in T, which may be used in other
>> theories.
>
> I would prefer that we don't say that names are "defined". Very few
> ontology languages provide for actual definitions of names, and
> several that once did (notably KIF) no longer do. Explicit
> definitions are semantically troublesome, practically of no actual
> use, create paradoxes, and generally have negative utility. The
> entire SWeb apparatus has no definitions in it anywhere, nor is it
> likely to in the future. It is very hard to even see what it would
> mean to define a globally useable name. Let us just say that names
> occur in ontologies, and ontologies constrain the meaning of names. (01)
Strictly speaking, a definition in a theory T just *is* an axiom in a
conservative extension of T (hence an axiom that constrains the
meaning of the name so defined) that satisfies certain criteria. I
can imagine it being useful in some contexts to be able to say that a
certain axiom counts as a definition, but the concept of definition
is so often abused and ill-understood that it is probably best
overall to avoid it, as you suggest. (02)
-chris (03)
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