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Loyer Y., Straccia U. An Epistemic Foundation of Stable Model Semantics. The document will be submitted to Journal of ACM, Technical report, 2003.
 
 
Abstract
(English)
Stable model semantics have become a dominating approach for the management of negation in logic programming and close relationships to important non-monotonic formalisms for knowledge representation has been established. It relies mainly on the closed world assumption to complete the available knowledge. Its formulation has its founding root in the so-called Gelfond-Lifschitz transform. The primary goal of this work is to present an intuitive and epistemic based characterisation of the stable model semantics, as an alternative 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, does rely on the classical management of negation and 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. It is based on monotone operators (under the knowledge order) over bilattices only and, thus, has a wide range of applicability.
Subject Bilattices
Fixed-point semantics
Logic programs
Stable model
F.4.1:Mathematical Logic and Formal Languages: Mathematical Logic: Logic
I.2.3:Artificial Intelligence: Deduction and Theorem Proving: Logic


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