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Utilizing Treewidth for Quantitative Reasoning on Epistemic Logic Programs

Published online by Cambridge University Press:  05 November 2021

VIKTOR BESIN ,
MARKUS HECHER Open the ORCID record for MARKUS HECHER [Opens in a new window]  and
STEFAN WOLTRAN Open the ORCID record for STEFAN WOLTRAN [Opens in a new window]
VIKTOR BESIN
Affiliation:
TU Wien, Vienna, Austria (e-mail: vbesin@dbai.tuwien.ac.at)
MARKUS HECHER
Affiliation:
TU Wien, Vienna, Austria (e-mail: hecher@dbai.tuwien.ac.at)
STEFAN WOLTRAN
Affiliation:
TU Wien, Vienna, Austria (e-mail: woltran@dbai.tuwien.ac.at)
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Abstract

Extending the popular answer set programming 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, that is, 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.

Keywords

epistemic logic programmingtreewidthtree decompositionsabstractionshybrid solvingnested dynamic programming
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Issue 5: 37th International Conference on Logic Programming Special Issue I , September 2021 , pp. 575 - 592
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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