Stable models are generated by a stable chain

Abstract

We propose a general preference criterion selecting the “intended” models of generalized logic programs which: 1) is a conservative extension of the stable model semantics for normal logic programs of [2], 2) is very close to the answer set semantics of [4] for disjunctive logic programs, and 3) allows for arbitrary formulas in the body and in the head of a rule, i.e., does not depend on the presence of any specific connective, such as negation(-as-failure) or on any specific syntax of rules. Our preference criterion defines a model of a program as intended if it is generated by a stable chain. We show that stable models and answer sets are generated by a stable chain of length ≤ ω.