Epistemic Equilibrium Logic

Abstract

We add epistemic modal operators to the language of here-and-there logic and define epistemic here-and-there models.We then successively define epistemic equilibrium models and autoepistemic equilibrium models. The former are obtained from here-and-there models by the standard minimisation of truth of Pearce’s equilibrium logic; they provide an epistemic extension of that logic. The latter are obtained from the former by maximising the set of epistemic possibilities; they provide a new semantics for Gelfond’s epistemic specifications. For both definitions we characterise strong equivalence by means of logical equivalence in epistemic here-and-there logic.