Autoepistemic equilibrium logic and epistemic specifications

Ezgi Iraz Su (1, 2) , Luis Fariñas del Cerro (1, 3) , Andreas Herzig (1, 3)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 ULISBOA - Universidade de Lisboa = University of Lisbon
3 CNRS - Centre National de la Recherche Scientifique

Epistemic specifications extend disjunctive answer-set programs by an epistemic modal operator that may occur in the body of rules. Their semantics is in terms of world views, which are sets of answer sets, and the idea is that the epistemic modal operator quantifies over these answer sets. Several such semantics were proposed in the literature. We here propose a new semantics that is based on the logic of here-and-there: we add epistemic modal operators to its language and define epistemic here-and-there models. We then successively define epistemic equilibrium models and autoepistemic equilibrium models. The former are obtained from epistemic here-and-there models in exactly the same way as Pearce's equilibrium models are obtained from here-and-there models, viz. by minimising truth; they provide an epistemic extension of equilibrium logic. The latter are obtained from the former by maximising the set of epistemic possibilities, and they provide a new semantics for Gelfond's epistemic specifications. For both semantics we establish a strong equivalence result: we characterise strong equivalence of two epistemic programs by means of logical equivalence in epistemic here-and-there logic. We finally compare our approach to the existing semantics of epistemic specifications and discuss which formalisms provide more intuitive results by pointing out some formal properties a semantics proposal should satisfy.

Mots clés: Answer set programming; Epistemic specifications; Epistemic logic programs; Here-and-there logic Equilibrium logic; Modal logic

Domaines: Intelligence artificielle [cs.AI]; Informatique et langage [cs.CL]; Théorie et langage formel [cs.FL]

Ezgi Iraz Su, Luis Fariñas del Cerro, Andreas Herzig. Autoepistemic equilibrium logic and epistemic specifications. Artificial Intelligence, 2020, 282, pp.103249. ⟨10.1016/j.artint.2020.103249⟩. ⟨hal-02945872⟩