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Re: The Mel99 semantics for RDF

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Fri, 18 May 2001 11:11:41 -0400
To: connolly@w3.org
Cc: www-rdf-logic@w3.org
Message-Id: <20010518111141N.pfps@research.bell-labs.com>
I have a number of problems with your summarization of Melnik's interesting
algebraic specification for RDF.  

I think that your summarization has a lot more in it that Melnik's
specification does.  Melnik does not mention URI's at all.  Melnik does not
talk about variables, existentially quantified or otherwise.

Melnik's algebraic structure is, in essence, a set of statements, and is
not a graph of any shape or form.

Melnik distinguishes between resources and literals in many places.  The
distinction forms a major portion of his algebraic specification.

Melnik has a PARTIAL map from statements to their reification, not a total
map.

Melnik's specification is an algebraic specification.  In general this
implies that a KB (or whatever you want to call it) maps to a specific
structure, namely the one that has the statements from the KB.  On the
other hand, model theoretic semantics generally have a many-to-many
satisfaction relationship between KBs and semantic structures.  It makes
sense in model-theoretic semantics to talk about interpretations satisfying
different KBS, and thus makes sense to talk about the ``principle of
erasure'' or monotonicity.  Such notions are harder to define in algebraic
specifications---you have to talk about an algebraic structure having more
information than another.


In general, algebraic specification can be used to provide meaning for
logics.  However, for logics that have non-trivial inference, algebraic
specification begins to look a lot like axiomatic specification.  (You need
to talk about something like saturated sets of statements, i.e., sets of
statements that contain all their conclusions.)  For this, and other,
reasons I prefer model-theoretic semantics.


Peter Patel-Schneider
Bell Labs Research
Received on Friday, 18 May 2001 11:11:50 UTC

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