Epistemic Foundation of Stable Model Semantics

TL;DR

This paper offers an epistemic, algebraic characterization of stable model semantics in logic programming, extending Kripke-Kleene semantics with a cumulative closed world assumption, providing a formal foundation alternative to Gelfond-Lifschitz transformation.

Contribution

It introduces an epistemic-based, algebraic framework for stable model semantics, independent of specific formalisms, based on monotone operators over bilattices.

Findings

Stable model semantics can be derived from Kripke-Kleene semantics with added falsehood.

The approach is purely algebraic and formalizes the closed world assumption as an extension.

Provides an alternative foundation for stable model semantics beyond Gelfond-Lifschitz transformation.

Abstract

Stable model semantics has become a very popular approach for the management of negation in logic programming. This approach relies mainly on the closed world assumption to complete the available knowledge and its formulation has its basis in the so-called Gelfond-Lifschitz transformation. The primary goal of this work is to present an alternative and epistemic-based characterization of stable model semantics, to the Gelfond-Lifschitz transformation. In particular, we show that stable model semantics can be defined entirely as an extension of the Kripke-Kleene semantics. Indeed, we show that the closed world assumption can be seen as an additional source of `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.