Implementing Default and Autoepistemic Logics via the Logic of GK

TL;DR

This paper demonstrates how the logic of GK can be embedded into disjunctive logic programming, enabling the computation of various nonmonotonic reasoning semantics using existing ASP solvers.

Contribution

It provides the first polynomial, non-modular embedding of GK into disjunctive logic programming, linking multiple nonmonotonic logics with practical solver implementations.

Findings

Embedding of GK into disjunctive logic programming is polynomial.

The approach enables computing semantics of default, autoepistemic, and universal causation logics.

Uses existing ASP solvers for practical reasoning tasks.

Abstract

The logic of knowledge and justified assumptions, also known as logic of grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for nonmonotonic reasoning. To date, it has been used to embed in it default logic (propositional case), autoepistemic logic, Turner's logic of universal causation, and general logic programming under stable model semantics. Besides showing the generality of GK as a logic for nonmonotonic reasoning, these embeddings shed light on the relationships among these other logics. In this paper, for the first time, we show how the logic of GK can be embedded into disjunctive logic programming in a polynomial but non-modular translation with new variables. The result can then be used to compute the extension/expansion semantics of default logic, autoepistemic logic and Turner's logic of universal causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.