Epistemic Foundation of the Stable Model Semantics

The stable model semantics has become a dominating approach for the management of negation in logic programming. It relies mainly on the closed world assumption to complete the available knowledge and its formulation has its founding root in the so-called Gelfond-Lifschitz transform. The primary goal of this work is to present an alternative and epistemic based characterization of the stable model semantics, to the Gelfond-Lifschitz transform. In particular, we show that the stable model semantics can be defined entirely as an extension of the Kripke-Kleene semantics and, thus, (i) does rely on the classical management of negation; and (ii) does not require any program transformation. Indeed, we show that the closed world assumption can be seen as an additional source for ‘falsehood’ to be added cumulatively to the Kripke-Kleene semantics. Our approach is purely algebraic and can abstract from the particular formalism of choice as it is based on monotone operators (under the knowledge order) over bilattices only.