Refining the Semantics of Epistemic Specifications

TL;DR

This paper critically examines existing semantics for epistemic ASP, proposes improvements, and introduces a new semantics to better formalize introspective reasoning in logic programming.

Contribution

It extends epistemic here-and-there logic and proposes a novel semantics for epistemic ASP, addressing unresolved issues and debates in the field.

Findings

Extended here-and-there logic to epistemic HT

Identified limitations of current epistemic ASP semantics

Proposed a reflexive extension of autoepistemic ASP

Abstract

Answer set programming (ASP) is an efficient problem-solving approach, which has been strongly supported both scientifically and technologically by several solvers, ongoing active research, and implementations in many different fields. However, although researchers acknowledged long ago the necessity of epistemic operators in the language of ASP for better introspective reasoning, this research venue did not attract much attention until recently. Moreover, the existing epistemic extensions of ASP in the literature are not widely approved either, due to the fact that some propose unintended results even for some simple acyclic epistemic programs, new unexpected results may possibly be found, and more importantly, researchers have different reasonings for some critical programs. To that end, Cabalar et al. have recently identified some structural properties of epistemic programs to formally support a possible semantics proposal of such programs and standardise their results. Nonetheless, the soundness of these properties is still under debate, and they are not widely accepted either by the ASP community. Thus, it seems that there is still time to really understand the paradigm, have a mature formalism, and determine the principles providing formal justification of their understandable models. In this paper, we mainly focus on the existing semantics approaches, the criteria that a satisfactory semantics is supposed to satisfy, and the ways to improve them. We also extend some well-known propositions of here-and-there logic (HT) into epistemic HT so as to reveal the real behaviour of programs. Finally, we propose a slightly novel semantics for epistemic ASP, which can be considered as a reflexive extension of Cabalar et al.'s recent formalism called autoepistemic ASP.