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>

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 ResearchReceived on Friday, 18 May 2001 11:11:50 UTC

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