Capturing equilibrium models in modal logic

Abstract

Here-and-there models and equilibrium models were investigated as a semantical framework for answer-set programming by Pearce, Valverde, Cabalar, Lifschitz, Ferraris and others. The semantics of equilibrium logic is given in an indirect way: the notion of satisfiability is defined in terms of satisfiability in propositional logic and in the logic of here-and-there. We here give a direct semantics of equilibrium logic, stated in terms of a modal language embedding the language of equilibrium logic.