This paper introduces a new epistemic extension of answer set programming (ASP) called epistemic ASP (E-ASP). Then, it compares E-ASP with existing approaches, showing the advantages and the novelties of the new semantics and discusses which formalisms provide more intuitive results: compared to Gelfond's epistemic specifications (ES), E-ASP defines a simpler, but sufficiently strong language. Its epistemic view semantics is a natural and more standard generalisation of ASP's original answer set semantics, so it allows for ASP's previous language extensions. Moreover, compared to all semantics proposals in the literature, epistemic view semantics facilitates understanding of the intuitive meaning of epistemic logic programs and solves unintended results discussed in the literature, especially for epistemic logic programs including constraints.

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.

We extend the language of here-and-there logic by two kinds of atomic programs allowing to minimally update the truth value of a propositional variable here or there, if possible. These atomic programs are combined by the usual dynamic logic program connectives. We investigate the mathematical properties of the resulting extension of equilibrium logic: we prove that the problem of logical consequence in equilibrium models is EXPTIME complete by relating equilibrium logic to dynamic logic of propositional assignments.