Expressiveness of stable model semantics for disjunctive logic programs with functions

Abstract

In this paper, we study the expressive power and recursion-theoretic complexity of disjunctive logic programs with functions symbols over Herbrand models. In particular, we consider the disjunctive stable model semantics, and show that a relation R is definable over the Herbrand universe of a disjunctive logic program if and only if R is Π 1 1 definable. Thus, disjunctive logic programming under the stable model semantics expresses exactly Π 1 1, and is thus Π 1 1 complete over the integers. This result is surprising because it shows that disjunctive logic programming is not more expressive than normal logic programming under the stable or well-founded semantics. This sharply contrasts with the function-free case.