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Re: [ontolog-forum] Logic, Datalog and SQL

To: Christopher Menzel <cmenzel@xxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 11 Feb 2007 18:57:33 -0500
Message-id: <45CFAD6D.4000102@xxxxxxxxxxx>
Chris,    (01)

Yes, I agree:    (02)

 > First, you say that T is stated in terms of a nonempty
 > vocabulary V; then you suggest that V is only a subset
 > of the type and relation names in T.    (03)

I was a bit hasty when I sent off that note on Jan 30th,
and I had some second thoughts about it.  But when I
copied it today, I had forgotten my earlier second thoughts.    (04)

In programming languages, they distinguish variables that
are imported by a procedure, those that are defined in a
procedure and exported to other procedures, and those that
are purely internal to a given procedure.  I think that
we should make some such distinction for ontologies.    (05)

Following is a revised version:    (06)

    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:    (07)

    1. Names defined elsewhere, which are used in one
       or more axioms of T.    (08)

    2. Names defined in T, which may be used in other
       theories.    (09)

    3. Names that are never used in any other theories.    (010)

    To be considered an ontology, the set of names in
    subset #2 must be nonempty; i.e., the theory T
    must define one or more types or relations, whose
    names may be used in statements other than T.    (011)

John    (012)

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