Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T11:32:35.069Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abseher, M., Musliu, N. and Woltran, S. 2017. htd – A free, open-source framework for (customized) tree decompositions and beyond. In CPAIOR’17. LNCS, vol. 10335. Springer Verlag, 376–386.Google Scholar
Bichler, M., Morak, M. and Woltran, S. 2020. selp: A single-shot epistemic logic program solver. Theory and Practice of Logic Programming 20, 4, 435–455.CrossRefGoogle Scholar
Bliem, B., Ordyniak, S. and Woltran, S. 2016. Clique-width and directed width measures for answer-set programming. In Proc. ECAI. 1105–1113.Google Scholar
Bodlaender, H. L. and Kloks, T. 1996. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. Journal of Algorithms 21, 2, 358–402.CrossRefGoogle Scholar
Brewka, G., Eiter, T. and Truszczyński, M. 2011. Answer set programming at a glance. Communications of the ACM 54, 12, 92–103.CrossRefGoogle Scholar
Cabalar, P., Fandinno, J. and Fariñas del Cerro, L. 2019. Splitting epistemic logic programs. In LPNMR. 120–133.CrossRefGoogle Scholar
Cabalar, P., Fandinno, J., Garea, J., Romero, J. and Schaub, T. 2020. eclingo : A solver for epistemic logic programs. Theory and Practice of Logic Programming 20, 6, 834–847.CrossRefGoogle Scholar
Eiter, T. and Gottlob, G. 1995. On the computational cost of disjunctive logic programming: Propositional case. Annals of Mathematics and Artificial Intelligence 15, 3–4, 289–323.CrossRefGoogle Scholar
Fichte, J. K., Hecher, M. and Meier, A. 2021. Knowledge-base degrees of inconsistency: Complexity and counting. In AAAI. AAAI Press, 6349–6357.Google Scholar
Fichte, J. K., Hecher, M., and Pfandler, A. 2020. Lower bounds for QBFs of bounded treewidth. In LICS. ACM, 410–424.Google Scholar
Fichte, J. K., Kronegger, M. and Woltran, S. 2019. A multiparametric view on answer set programming. Annals of Mathematics and Artificial Intelligence 86, 1–3, 121–147.CrossRefGoogle Scholar
Fierens, D., den Broeck, G. V., Renkens, J., Shterionov, D. S., Gutmann, B., Thon, I., Janssens, G. and Raedt, L. D. 2015. Inference and learning in probabilistic logic programs using weighted Boolean formulas. Theory and Practice of Logic Programming 15, 3, 358–401.CrossRefGoogle Scholar
Ganian, R., Ramanujan, M. S., and Szeider, S. 2017. Combining treewidth and backdoors for CSP. In STACS’17. 36:1–36:17.Google Scholar
Gelfond, M. 1991. Strong introspection. In Proc. AAAI. AAAI Press/The MIT Press, 386–391.Google Scholar
Hanks, S. and Mcdermott, D. 1986. Default reasoning, nonmonotonic logics, and the frame problem. In AAAI’86: Proceedings of the Fifth AAAI National Conference on Artificial Intelligence, 328–333.Google Scholar
Hecher, M. 2020. Treewidth-aware reductions of normal ASP to SAT - is normal ASP harder than SAT after all? In KR 2020. 485–495.CrossRefGoogle Scholar
Hecher, M., Morak, M. and Woltran, S. 2020. Structural decompositions of epistemic logic programs. In AAAI 2020. AAAI Press, 2830–2837.Google Scholar
Hecher, M., Thier, P. and Woltran, S. 2020b. Taming high treewidth with abstraction, nested dynamic programming, and database technology. In SAT 2020. LNCS, vol. 12178. Springer, 343–360.Google Scholar
Jakl, M., Pichler, R. and Woltran, S. 2009. Answer-set programming with bounded treewidth. In IJCAI. 816–822.CrossRefGoogle Scholar
Kahl, P. T., Watson, R., Balai, E., Gelfond, M. and Zhang, Y. 2015. The language of epistemic specifications (refined) including a prototype solver. Journal of Logic and Computation 25. CrossRefGoogle Scholar
Lonc, Z. and Truszczynski, M. 2003. Fixed-parameter complexity of semantics for logic programs. ACM Trans. Comput. Log. 4, 1, 91–119.Google Scholar
Morak, M. 2019. Epistemic logic programs: A different world view. In Proc. ICLP, 52–64.Google Scholar
Shen, Y. and Eiter, T. 2016. Evaluating epistemic negation in answer set programming. Artificial Intelligence 237, 115–135.CrossRefGoogle Scholar
Son, T. C., Le, T., Kahl, P. T. and Leclerc, A. P. 2017. On computing world views of epistemic logic programs. In IJCAI, 1269–1275.Google Scholar
Truszczynski, M. 2011. Revisiting epistemic specifications. In Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning. LNCS, vol. 6565. Springer Verlag, 315–333.Google Scholar
Supplementary material: PDF

Besin et al.supplementary material

Besin et al.supplementary material 1

Download Besin et al.supplementary material(PDF)
PDF 187.4 KB