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Re: RDF Abstract Syntax: a strawman

From: Bill Andersen <andersen@ontologyworks.com>
Date: Wed, 30 May 2001 16:27:26 -0500
To: pat hayes <phayes@ai.uwf.edu>, "Je'ro^me Euzenat" <Jerome.Euzenat@inrialpes.fr>
CC: RDF Logic <www-rdf-logic@w3.org>
Message-ID: <B73ACFEE.ED6%andersen@ontologyworks.com>
On 5/30/01 10:26, "pat hayes" <phayes@ai.uwf.edu> wrote:

> OK. In brief: FOL model theory says that the universe of
> quantification is a set. It does not say that the set cannot contain
> relations. So quantifying over relations is not ruled out by FOL.
> What makes a language higher-order is when its relational quantifiers
> are required to range over a rather large set of relations (exactly
> how large depends on the logic, eg classical HOL= *all* relations, ie
> the set 2|(D|n) where D is the base domain of individuals; Henkin
> logic = all lambda-definable relations.) If one does not impose any
> requirement on the size of the relational universe (other than it
> provide a denotation for every relational term) then there is nothing
> higher-order in the semantics and it is easy to allow quantification
> over relations and still be first-order. Those quantifiers have only
> a first-order kind of 'bite', of course, and the language has no
> rules of lambda-conversion.

For those of you interested in a reference, what Pat mentions is described
in Enderton's "Mathematical Introduction to Logic", Ch. 4.  See "General
Models of Second Order Logic"...


Bill Andersen
Chief Scientist, Ontology Works
1132 Annapolis Road, Suite 104
Odenton, Maryland, 21113
Mobile 443-858-6444
Office 410-674-7600
Received on Wednesday, 30 May 2001 17:28:05 UTC

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