Semantics of structured normal logic programs

Abstract

In this paper we provide semantics for normal logic programs enriched with structuring mechanisms and scoping rules. Specifically, we consider constructive negation and expressions of the form Q⊃G in goals, where Q is a program unit, G is a goal and ⊃ stands for the so-called embedded implication. Allowing the use of these expressions can be seen as adding block structuring to logic programs. In this context, we consider static and dynamic rules for visibility in blocks. In particular, we provide new semantic definitions for the class of normal logic programs with both visibility rules. For the dynamic case we follow a standard approach. We first propose an operational semantics. Then, we define a model-theoretic semantics in terms of ordered structures which are a kind of intuitionistic Beth structures. Finally, an (effective) fixpoint semantics is provided and we prove the equivalence of these three definitions. In order to deal with the static case, we first define an operational semantics and then we present an alternative semantics in terms of a transformation of the given structured programs into flat ones. We finish by showing that this transformation preserves the computed answers of the given static program.