Epistemic Equilibrium Logic

International audienceWe 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

Revisiting Explicit Negation in Answer Set Programming

[Abstract] A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson’s strong negation.Ministerio de Economía y Competitividad; TIC2017-84453-PXunta de Galicia; GPC ED431B 2019/03Xunta de Galicia; 2016-2019 ED431G/01, CITICCentre International de Math´ematiques et d’Informatique de Toulouse; ANR-11-LABEX-004

Fast Prototyping of a Solver for Reduct-based ELP Semantics

Several semantic approaches have been proposed over time for Epistemic Logic Programs (ELPs), which is an extension to Answer Set Programming (ASP) with epistemic operators. ELP semantics has been defined, in various ways, in terms of world views, which are sets whose elements are sets of atoms. Several semantic approaches are Reduct-based, i.e., extend to ELPs what done for ASP, in the sense that in order to find the world views of a given program they propose to: start with a candidate world view; build the reduct of the program with respect to this candidate world view, according to some specific definition of such reduct; compute the set of stable models of the reduct; check whether the candidate world view is indeed a world view, which is the case if it coincides with the set of stable models of the reduct. Solvers have been developed for some of these approaches, but new semantics/variations have been introduced, and are likely to be introduced in the future, as there is no consensus yet on the “right” semantics. We propose a fast-prototyping approach to obtain a solver for any reduct-based semantics, with the advantage to be able to experiment the approach on small/medium programs, and not only on very small programs as done so far, prior to undertaking the costly process of developing a dedicated solver

Epistemic Logic Programs: an Approach to Semantic Comparison

Epistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic operators. The semantics of such programs is provided in terms of world views, which are sets of belief sets. Several semantic approaches have been proposed over time to characterize world views. Recent work has introduced semantic properties that should be met by any semantics for ELPs. We propose a new method, easy but, we believe, effective, to compare the different semantic approaches

Epistemic Logic Programs with World View Constraints

An epistemic logic program is a set of rules written in the language of Epistemic Specifications, an extension of the language of answer set programming that provides for more powerful introspective reasoning through the use of modal operators K and M. We propose adding a new construct to Epistemic Specifications called a world view constraint that provides a universal device for expressing global constraints in the various versions of the language. We further propose the use of subjective literals (literals preceded by K or M) in rule heads as syntactic sugar for world view constraints. Additionally, we provide an algorithm for finding the world views of such programs

Epistemic Logic Programs: a Novel Perspective and Some Extensions

Epistemic Logic Programs (ELPs), which propose an extension to Answer Set Programming (ASP) with epistemic operators, have their semantic defined, in various ways, in terms of world views, which are sets of belief sets. Several semantic approaches have in fact been proposed over time to characterize world views, and, recently, to also characterize semantic properties that should be met by any semantics for ELPs. We propose a new semantics, easy also from the computational point of view, but effective, also in order to compare the different semantic approaches. We also propose a significant extension to the ELP approach, by allowing epistemic atoms in rule heads