Eliminating Disjunction from Propositional Logic Programs under Stable Model Preservation

In general, disjunction is considered to add expressive power to propositional logic programs under stable model semantics, and to enlarge the range of problems which can be expressed. However, from a semantical point of view, disjunction is often not really needed, in that an equivalent program without disjunction can be given. We thus consider the question, given a disjunctive logic program , does there exist an equivalent normal (i.e., disjunction-free) logic program ? In fact, we consider this issue for different notions of equivalence, namely for ordinary equivalence (regarding the collections of all stable models of the programs) as well as for the more restrictive notions of strong and uniform equivalence. We resolve the issue for propositional programs, and present a simple, appealing semantic criterion for the programs from which all disjunctions can be eliminated under strong equivalence; testing this criterion is coNP-complete. We also show that under ordinary and uniform equivalence, this elimination is always possible. In all cases, there are constructive methods to achieve this. Our results extend and complement recent results on simplifying logic programs under different notions of equivalence, and add to the foundations of improving implementations of Answer Set Solvers.