Providing Declarative Semantics for HH Extended Constraint Logic Programs

摘要

This paper is focused on a double extension of traditional Logic Programming which enhances it following two different approaches. On one hand, extending Horn logic to hereditary Harrop formulas (HH), in order to improve the expressive power; on the other, incorporating constraints, in order to increase the efficiency. For this combination, called HH(C), an operational semantics exists, but no declarative semantic for it has been defined so far. One of the main features of (Constraint) Logic Programming is that the algorithmic behavior of (constraint) logic programs and its mathematical interpretations agree with each other, in the sense that the declarative meaning of a program can be interpreted operationally as a goal-oriented search for solutions. Both operational (algorithmic) and declarative (mathematical) semantics for programs are useful and widely developed in the frame of Logic Programming as well as in its extension, Constraint Logic Programming. For these reasons, HH(C) was in need of a more mathematical interpretation of programs. In this paper some fixed point semantics for HH(C) are presented. Taking as a starting point the techniques used by Miller to interpret the fragment of HH that incorporates intuitionistic implication in goals, we have formulated two novel extensions capable of dealing with the whole HH logic, including universal quantifiers, as well as with the presence of constraints. Those semantics are proved to be sound and complete w.r.t. the operational semantics of HH(C).