Syntactic and Semantic Inheritance in Logic Programming

Abstract

This paper aims at a deeper understanding of how inheritance can fit into a logic programming framework, by considering inheritance systems in terms of partially ordered sets of logic program units. We develop for such systems operational, declarative and fixed point semantics which are proven equivalent.

We begin by discussing, in logic programming terms, the basic types of inheritance that can be achieved. We identify two kinds, semantic and syntactic inheritance, which can occur in two modes, extension and overriding. We then present a (abstract) language for programming systems with combinations of these various types of inheritance. These combinations are obtained through a signature that assigns to each unit the sets of predicates for semantic and syntactic inheritance, extension and overriding becoming implicit. We define and characterize the operational, declarative, and fixed-point semantics, and we prove their equivalence. The equivalence between declarative and operational semantics is based on a two-step reduction of inheritance systems to non-inheritance systems, i.e. systems of standard logic programs, by eliminating first syntactic inheritance and then semantic inheritance. Through equivalence results along the way and using the well-known equivalence of semantics for standard logic programs we achieve the main result. Then we extend the language with inheritance control at the level of individual goal calls, using two new connectives super and self, and define the corresponding extension of the semantic definitions, showing that the equivalence is still preserved.

The semantics presented provide simple direct insights into inheritance phenomena. The reduction technique used in the main equivalence proof actually suggests that inheritance really adds no extra conceptual power to standard logic programs, although remaining a highly convenient structuring technique with implications for software engineering.