Invited Talk: Some Issues and Trends in the Semantics of Logic Programming

semantic properties is repeated here. Instead of mapping the intended domain on the Herbrand Universe and using specialized unification, programming is done directly in the intended domain using its natural constraints. We thus use an algebraic framework as well as a logic programming one. This revision of the scheme is called CLP which stands for Constraint Logic Programming. A CLP program consists of constrained rules which are of the form A ← c1, c2, ..., ck [] B1, B2, . . . , Bn where A,B1, B2, ..., Bn are atoms and c1, c2, ..., ck form a set of constraints. A goal is of the form ← c1, c2, ..., ck [] B1, B2, ..., Bn The interpreter of an instance of CLP consists of the standard goal reduction technique of logic programming and a constraint solver. Implementations of this model of computation can benefit from the wide literature on the problem of constraint solving. Allowing constraints in the goals and bodies considerably raises the expressive power. A comparison can be made with the introduction of negated atoms m the body of clauses of definite clause programs. It is well known (Clark [3], Shepherdson [38,39]) that the implementation of negation via variants of SLD resolution and negation as failure works only in restricted cases. Furthermore, the semantic properties of definite clauses that we have described no longer hold. It is therefore quite significant to note that CLP programs have least fixedpoint and least model semantics, and results of soundness and completeness that are similar to those of definite clause logic programs, despite the introduction of constraints. Furthermore, the algebraic and logical approaches also coincide for canonical programs. A formal presentation of these results is to be found in Jaffar and Lassez [12]. Colmerauer is now working on Prolog III and it seems that, as in the case of Prolog II and the scheme, we will be able to show that Prolog III can be viewed as an instance of CLP given the formal definition of Prolog