The Expressive Powers of Stable Models for Bound and Unbound DATALOG Queries

Abstract

Various types of stable models are known in the literature:T-stable(total stable),P-stable(partial stable, also calledthree-valued stable),M-stable(maximal stable, also known under various different names), andL-stable(least undefined stable). For each type of stable model, the paper analyzes two versions of deterministic semantics:possiblesemantics, which is based on the union of all stable models of the given type, anddefinitesemantics, which is instead based on their intersection and is like classicalcertainsemantics except that it makes no inference if no model exists. For total stable models, which are the only type of stable models whose existence is not guaranteed for every program, certain semantics is taken into account as well. The expressive powers of each type of stable model under the above versions of semantics are investigated for bothbound(i.e., ground) andunboundqueries on DATALOG programs with negation. As deterministic semantics is argued to be inappropriate for unbound queries, a non-deterministic semantics is also proposed for them and its expressive power is fully characterized as well.