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Re: Reification -> Higher Order Logic question

From: Adrian Walker <adrianw@snet.net>
Date: Mon, 27 Sep 2004 22:17:14 -0400
Message-Id: <>
To: Harry Halpin <hhalpin@ibiblio.org>
Cc: "Spork, Murray" <murray.spork@sap.com>, www-rdf-logic@w3.org

Harry --

A possible solution to the difficulties you describe lies in keeping 
everything first order, while appearing to do second order reasoning.

A couple of executable examples of this, in a notation that is hopefully 
friendly to non-logicians:



If you have examples in mind in which this approach may break down, please 
let me know.

                         Thanks in advance,    -- Adrian

At 06:40 PM 9/27/04 -0400, you wrote:

>Apologies for introducing myself with what may be another obvious
>question, but at a recent XML conference I was at the one continual
>complaint was that "reification" seems to lead to misleading inferences
>and is generally hard to fit computationally within an implementation.
>I thought about the problem briefly, and it appears that this is similar
>to the classic higher-order problem of logic, i.e. when one makes
>quantified predicates about predicates one leaves normal predicate logic 
>and enters
>higher-order logic. It appears that while higher-order logics are more
>expressive, but their properties make them more difficult, i.e.
>intractable and harder to make statements about, i.e. in  lower-order
>logic (My FOL->DL question revisited).
>Does anyone have a good logical story for how RDF reification replicates
>or has similar behavior? It would seem that this would be one method
>to attempt to state useful things about RDF reified statements, even
>if those inferences were not really DL.
>Note the RDF Semantics states this problem clearly:  "Since an assertion
>of a reification of a triple does not implicitly assert the triple itself, 
>this means that there are no
>entailment relationships which hold between a triple and a reification of
>it. Thus the reification vocabulary has no effective semantic constraints
>on it, other than those that apply to an rdf-interpretation.
>A reification of a triple does not entail the triple, and is not entailed
>by it. (The reification only says that the triple token exists and what it
>is about, not that it is true. The second non-entailment is a consequence
>of the fact that asserting a triple does not automatically assert that any
>triple tokens exist in the universe being described by the triple. For
>example, the triple might be part of an ontology describing animals, which
>could be satisfied by an interpretation in which the universe contained
>only animals, and in which a reification of it was therefore false.)"
>Ahhh....which I could see could lead to some non-intuitive reasoning
>and difficulties with implementation. The named graph approach attempts
>to solve this issue, correct?
>                                 --harry
>         Harry Halpin
>         Informatics, University of Edinburgh
>         http://www.ibiblio.org/hhalpin
Received on Tuesday, 28 September 2004 02:13:25 UTC

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