From: Wagner, G.R. <G.R.Wagner@tm.tue.nl>

Date: Wed, 19 Sep 2001 21:55:41 +0200

Message-ID: <511BB18E82E9D11188230008C724064602D9DDC6@tmex1.tm.tue.nl>

To: "'Pat Hayes'" <phayes@ai.uwf.edu>

Cc: www-rdf-rules@w3.org

Date: Wed, 19 Sep 2001 21:55:41 +0200

Message-ID: <511BB18E82E9D11188230008C724064602D9DDC6@tmex1.tm.tue.nl>

To: "'Pat Hayes'" <phayes@ai.uwf.edu>

Cc: www-rdf-rules@w3.org

> >Please notice that Prolog rules (as well as any other practical > >computational rule concept such as SQL views and OCL implications) > >are *not* Horn clauses! They are, for good reasons, more expressive, > >allowing for negation in their body/antecedent (and other things, > >such as quantifiers, as in the case of SQL views). > > Maybe Prolog has morphed into something else since the last time I > looked at it. Can you characterize what subset of logic *is* captured > by Prolog? I'm not sure what you mean by 'allowing for negation'. You probably know that Prolog, like SQL, applies a negation (in rule bodies only) under the closed-world assumption, often called negation-as-failure. A negation operator is essential for expressing queries that arise in practical applications. For being practically (and not just academically) relevant, rules for the SemanticWeb need negation! The model-theoretic semantics for logic programming rules with negation (also called "normal logic programs") is given by a certain definition of intended models (called "stable models"). There is an efficient inference operation, called "well-founded semantics" that is sound, but not complete, wrt stable models. > Ah, yes; SQL isnt what I would call a logical query language at all. But one may view SQL queries (without aggregates) as FOL formulas. E.g., "SELECT x,y,z FROM p WHERE x=y" corresponds to the formula "p(x,x,z)" which is answered by returning all bindings to x and z such that the corresponding instantiations are entailed by the current database state. > >We should consider the concept of a rule as a basic one that > >is not derived from that of a Horn clause (which happens to be > >a very restricted/simplified type of rule). The concept of a > >Horn clause is tight to classical (two-valued) logic. But rules > >play a role in all kinds of formalism with a non-classical > >logic semantics (such as intuitionistic, partial, temporal, > >inconsistency-tolerant logic, etc.). > > Hold on a minute there. There is no single notion of 'rule' that > plays a role in a variety of logics. Why not? For each logic (even if it does not have an implication) we can define the notion of a sequent F => G, where both F and G may be composite and have free variables, and using the logic's model theory, we can define when such a sequent is satisfied by a model. This seems to provide a generic concept of a rule. > BTW, the notion of Horn clause is not restricted to classical > two-valued logic. It applies to any logic which has conjunction, > disjunction and negation, which includes all those you mention here > and many others. I don't understand your remark. Isn't it essential for the concept of a Horn clause that -p v q is equivalent to p -> q? This equivalence does not hold, for instance, in intuitionistic or partial logic. -GerdReceived on Wednesday, 19 September 2001 15:55:45 GMT

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