Utilizing Treewidth for Quantitative Reasoning on Epistemic Logic Programs

TL;DR

This paper introduces a new approach to quantitative reasoning in epistemic logic programs by leveraging treewidth-based graph abstractions and dynamic programming to efficiently solve counting problems related to world views.

Contribution

It extends epistemic logic programming by enabling quantitative reasoning and presents a novel system that exploits treewidth and dynamic programming for efficient problem solving.

Findings

The system effectively solves counting problems in ELPs.

It is competitive with recent existing systems.

The approach improves reasoning efficiency in epistemic logic programs.

Abstract

Extending the popular Answer Set Programming (ASP) paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs) where standard rules are equipped with modal operators which allow to express conditions on literals for being known or possible, i.e., contained in all or some answer sets, respectively. ELPs thus deliver multiple collections of answer sets, known as world views. Employing ELPs for reasoning problems so far has mainly been restricted to standard decision problems (complexity analysis) and enumeration (development of systems) of world views. In this paper, we take a next step and contribute to epistemic logic programming in two ways: First, we establish quantitative reasoning for ELPs, where the acceptance of a certain set of literals depends on the number (proportion) of world views that are compatible with the set. Second, we present a novel system that is capable of efficiently solving the underlying counting problems required to answer such quantitative reasoning problems. Our system exploits the graph-based measure treewidth and works by iteratively finding and refining (graph) abstractions of an ELP program. On top of these abstractions, we apply dynamic programming that is combined with utilizing existing search-based solvers like (e)clingo for hard combinatorial subproblems that appear during solving. It turns out that our approach is competitive with existing systems that were introduced recently. This work is under consideration for acceptance in TPLP.