Pearce's Characterisation in an Epistemic Domain

TL;DR

This paper develops a comprehensive framework for epistemic answer-set programming, linking various existing semantics through Pearce's characterisation of answer-sets as equilibrium models, and extends foundational work to the epistemic domain.

Contribution

It introduces a unified framework for epistemic ASP, establishing correspondences with existing semantics and extending Ferraris' answer set theory to epistemic logic.

Findings

Established a correspondence between epistemic equilibrium logics and the new framework.

Extended Ferraris' work on answer sets to the epistemic case.

Revealed relationships among different ES-semantic proposals.

Abstract

Answer-set programming (ASP) is a successful problem-solving approach in logic-based AI. In ASP, problems are represented as declarative logic programs, and solutions are identified through their answer sets. Equilibrium logic (EL) is a general-purpose nonmonotonic reasoning formalism, based on a monotonic logic called here-and-there logic. EL was basically proposed by Pearce as a foundational framework of ASP. Epistemic specifications (ES) are extensions of ASP-programs with subjective literals. These new modal constructs in the ASP-language make it possible to check whether a regular literal of ASP is true in every (or some) answer-set of a program. ES-programs are interpreted by world-views, which are essentially collections of answer-sets. (Reflexive) autoepistemic logic is a nonmonotonic formalism, modeling self-belief (knowledge) of ideally rational agents. A relatively new semantics for ES is based on a combination of EL and (reflexive) autoepistemic logic. In this paper, we first propose an overarching framework in the epistemic ASP domain. We then establish a correspondence between existing (reflexive) (auto)epistemic equilibrium logics and our easily-adaptable comprehensive framework, building on Pearce's characterisation of answer-sets as equilibrium models. We achieve this by extending Ferraris' work on answer sets for propositional theories to the epistemic case and reveal the relationship between some ES-semantic proposals.