Compositional Semantics for the Procedural Interpretation of Logic

The composition of logic programs out of clauses has been studied semantically, but not the composition of a single clause out of its components. Structurally, a logic program can be regarded as a sentence in clausal form. In his procedural interpretation of logic programs, Kowalski has shown that a positive Horn clause can be viewed as a procedure in the programming sense. This interpretation suggests a composition operator for logic programs, the one where a clause results from composing a head with a body. In this paper we give more detail to the procedural interpretation by giving an algebraic characterization of Kowalski’s composition. In addition, we give algebraic characterizations of the composition of goals in a procedure body and for the composition of the predicate symbol with the argument tuple within a goal. A starting point for the semantic operator corresponding to composition of goals is provided by Tarski’s cylindric algebra semantics for first-order predicate logic. Tarski’s construction is briefly reviewed and suitably modified. The additional semantic operators are shown to be correct with respect to the fixpoint semantics of the logic program as a whole.