Comparing the expressive powers of some syntactically restricted classes of logic programs

Abstract

This paper studies the expressive powers of classes of logic programs that are obtained by restricting the number of positive literals (atoms) in the bodies of the rules. Three kinds of restrictions are considered, giving rise to the classes of atomic, unary and binary logic programs. The expressive powers of these classes of logic programs are compared by analyzing the existence of polynomial, faithful, and modular (PFM) translation functions between the classes. This analysis leads to a strict ordering of the classes of logic programs. The main result is that binary and unary rules are strictly more expressive than unary and atomic rules, respectively. This is the case even if we consider normal logic programs where negative literals may appear in the bodies of rules. Practical implications of the results are discussed in the context of a particular implementation technique for the stable model semantics of normal logic programs, namely contrapositive reasoning with rules.