Algebraic methods in the compositional analysis of logic programs

Abstract

The compositionality of the semantics of logic programs with respect to (different varieties of) program union has been studied recently by a number of researchers. The approaches used can be considered quite ad-hoc in the sense that they provide, from scratch, the semantic constructions needed to ensure compositionality and, in some cases, full abstraction in the given framework. In this paper, we study the application of general algebraic methods for obtaining, systematically, this kind of results. In particular, the method proposed consists in defining the adequate institution for describing the given class of logic programs and, then, in using general institution-independent results to prove compositionality and full abstraction. This is done in detail for the class of definite logic programs, where the associated institution is defined in such a way that initial algebra semantics is equivalent to computed answer substitution semantics. Then a similar solution is sketched for definite logic programs with constraints and equality and for normal logic programs with constructive negation.