{"type":"ScholarlyArticle","title":"Utilizing Treewidth for Quantitative Reasoning on Epistemic Logic Programs (Extended Abstract)","authors":[{"name":"Viktor Besin","slug":"viktor-besin","given":"Viktor","family":"Besin","affiliation":"TU Wien , Vienna , Austria"},{"name":"Markus Hecher","slug":"markus-hecher","given":"Markus","family":"Hecher","affiliation":"TU Wien , Vienna , Austria; University of Potsdam , Potsdam , Germany"},{"name":"Stefan Woltran","slug":"stefan-woltran","given":"Stefan","family":"Woltran","affiliation":"TU Wien , Vienna , Austria"}],"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 deci- sion problems (complexity analysis) and enumeration (development of systems) of world views. In this paper, we first 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 capable of efficiently solving the underlying counting problems required for quantitative reasoning. Our system exploits the graph-based measure treewidth by iteratively finding (graph) abstractions of ELPs.","doi":"10.24963/ijcai.2022/732","url":"https://ijcai.org/proceedings/2022/732","pdf":"https://ijcai.org/proceedings/2022/0732.pdf","markdown":"https://ijcai.org/proceedings/2022/732.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/732","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Sister Conferences Best Papers","track":"Sister Conferences Best Papers","number":732,"pages":{"first":5264,"last":5268},"keywords":["Artificial Intelligence: General"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38987255","length_sec":85,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985398","length_sec":719,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Abseher et al., 2017] Michael Abseher, Nysret Musliu, and Stefan Woltran. htd -a free, open-source framework for (customized) tree decompositions and beyond. In CPAIOR'17, volume 10335 of LNCS, pages 376-386. Springer Verlag, 2017.","title":"htd -a free, open-source framework for (customized) tree decompositions and beyond","authors":"Michael Abseher, Nysret Musliu, Stefan Woltran","year":"2017","venue":"CPAIOR'17","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Besin et al., 2021] Viktor Besin, Markus Hecher, and Stefan Woltran. Utilizing treewidth for quantitative reasoning on epis- temic logic programs. Theory Pract. Log. Program., 21(5):575- 592, 2021. Winner of the best paper award and best student paper award at ICLP'21.","title":"Utilizing treewidth for quantitative reasoning on epistemic logic programs","authors":"Besin","year":"2021","venue":"Theory Pract. Log. Program","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bichler et al., 2020] Manuel Bichler, Michael Morak, and Stefan Woltran. selp: A single-shot epistemic logic program solver. The- ory Pract. Log. Program., 20(4):435-455, 2020.","title":"selp: A single-shot epistemic logic program solver","authors":"Manuel Bichler, Michael Morak, Stefan Woltran","year":"2020","venue":"Theory Pract. Log. Program","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bliem et al., 2016] Bernhard Bliem, Sebastian Ordyniak, and Ste- fan Woltran. Clique-width and directed width measures for answer-set programming. In ECAI, pages 1105-1113, 2016.","title":"Clique-width and directed width measures for answer-set programming","authors":"Bernhard Bliem, Sebastian Ordyniak, Stefan Woltran","year":"2016","venue":"ECAI","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bodlaender and Kloks, 1996] Hans L. Bodlaender and Ton Kloks. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms, 21(2):358-402, 1996.","title":"Efficient and constructive algorithms for the pathwidth and treewidth of graphs","authors":"L Hans, Ton Bodlaender, Kloks","year":"1996","venue":"J. Algorithms","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Brewka et al., 2011] G. Brewka, T. Eiter, and M. Truszczyński. Answer set programming at a glance. Communications of the ACM, 54(12):92-103, 2011.","title":"Answer set programming at a glance","authors":"G Brewka, T Eiter, M Truszczyński","year":"2011","venue":"Communications of the ACM","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Cabalar et al., 2019] Pedro Cabalar, Jorge Fandinno, and Luis Fariñas del Cerro. Splitting epistemic logic programs. In LP- NMR, pages 120-133, 2019.","title":"Splitting epistemic logic programs","authors":"Pedro Cabalar, Jorge Fandinno, Luis Fariñas Del Cerro","year":"2019","venue":"LP-NMR","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Cabalar et al., 2020] Pedro Cabalar, Jorge Fandinno, Javier Garea, Javier Romero, and Torsten Schaub. eclingo : A solver for epis- temic logic programs. Theory Pract. Log. Program., 20(6):834- 847, 2020.","title":"eclingo : A solver for epistemic logic programs","authors":"Pedro Cabalar, Jorge Fandinno, Javier Garea, Javier Romero, Torsten Schaub","year":"2020","venue":"Theory Pract. Log. Program","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Diestel, 2012] Reinhard Diestel. Graph Theory, 4th Edition, vol- ume 173 of Graduate Texts in Mathematics. Springer Verlag, 2012.","title":"Graph Theory, 4th Edition","authors":"Reinhard Diestel","year":"2012","venue":null,"doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Eiter and Gottlob, 1995] Thomas Eiter and Georg Gottlob. On the computational cost of disjunctive logic programming: Proposi- tional case. Ann. Math. Artif. Intell., 15(3-4):289-323, 1995.","title":"On the computational cost of disjunctive logic programming: Propositional case","authors":"Thomas Eiter, Georg Gottlob","year":"1995","venue":"Ann. Math. Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Fandinno and Hecher, 2021] Jorge Fandinno and Markus Hecher. Treewidth-Aware Complexity in ASP: Not all Positive Cycles are Equally Hard. In AAAI, pages 6312-6320. AAAI Press, 2021.","title":"Treewidth-Aware Complexity in ASP: Not all Positive Cycles are Equally Hard","authors":"Jorge Fandinno, Markus Hecher","year":"2021","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Fichte et al., 2019] Johannes Klaus Fichte, Martin Kronegger, and Stefan Woltran. A multiparametric view on answer set program- ming. Ann. Math. Artif. Intell., 86(1-3):121-147, 2019.","title":"A multiparametric view on answer set programming","authors":"Fichte","year":"2019","venue":"Ann. Math. Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Fichte et al., 2020] Johannes Klaus Fichte, Markus Hecher, and Andreas Pfandler. Lower bounds for QBFs of bounded treewidth. In LICS, pages 410-424. ACM, 2020.","title":"Lower bounds for QBFs of bounded treewidth","authors":"Fichte","year":"2020","venue":"LICS","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Fichte et al., 2021a] Johannes K. Fichte, Markus Hecher, and Florim Hamiti. The Model Counting Competition 2020. ACM Journal of Experimental Algorithmics, 26, 2021.","title":"The Model Counting Competition","authors":"Fichte","year":"2020","venue":"ACM Journal of Experimental Algorithmics","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Fichte et al., 2021b] Johannes Klaus Fichte, Markus Hecher, and Arne Meier. Knowledge-base degrees of inconsistency: Com- plexity and counting. In AAAI, pages 6349-6357. AAAI Press, 2021.","title":"Knowledge-base degrees of inconsistency: Complexity and counting","authors":"Fichte","year":"2021","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Fierens et al., 2015] Daan Fierens, Guy Van den Broeck, Joris Renkens, Dimitar Sht. Shterionov, Bernd Gutmann, Ingo Thon, Gerda Janssens, and Luc De Raedt. Inference and learning in probabilistic logic programs using weighted Boolean formulas. Theory Pract. Log. Program., 15(3):358-401, 2015.","title":"Inference and learning in probabilistic logic programs using weighted Boolean formulas","authors":"Daan Fierens, Guy Van Den, Joris Broeck, Dimitar Renkens, Sht, Bernd Shterionov, Ingo Gutmann, Gerda Thon, Luc Janssens, Raedt De","year":"2015","venue":"Theory Pract. Log. Program","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Ganian et al., 2017] Robert Ganian, M. S. Ramanujan, and Stefan Szeider. Combining treewidth and backdoors for CSP. In STACS, pages 36:1-36:17, 2017.","title":"Combining treewidth and backdoors for CSP","authors":"M S Robert Ganian, Stefan Ramanujan, Szeider","year":"2017","venue":"STACS","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Gelfond, 1991] Michael Gelfond. Strong introspection. In Proc. AAAI, pages 386-391. AAAI Press / The MIT Press, 1991.","title":"Strong introspection","authors":"Michael Gelfond","year":"1991","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Hanks and Mcdermott, 1986] Steve Hanks and Drew Mcdermott. Default reasoning, nonmonotonic logics, and the frame problem. In AAAI, pages 328-333.","title":"Default reasoning, nonmonotonic logics, and the frame problem","authors":"Mcdermott Hanks","year":"1986","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"Morgan Kaufmann, 1986.","title":null,"authors":"Morgan Kaufmann","year":"1986","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Hecher et al., 2020a] Markus Hecher, Michael Morak, and Stefan Woltran. Structural decompositions of epistemic logic programs. In AAAI, pages 2830-2837. AAAI Press, 2020.","title":"Structural decompositions of epistemic logic programs","authors":"Hecher","year":"2020","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Hecher et al., 2020b] Markus Hecher, Patrick Thier, and Stefan Woltran. Taming high treewidth with abstraction, nested dynamic programming, and database technology. In SAT 2020, volume 12178 of LNCS, pages 343-360. Springer, 2020.","title":"Taming high treewidth with abstraction, nested dynamic programming, and database technology","authors":"Hecher","year":"2020","venue":"SAT 2020","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Hecher, 2022] Markus Hecher. Treewidth-aware reductions of nor- mal ASP to SAT -Is normal ASP harder than SAT after all? Artif. Intell., 304:103651, 2022.","title":"Treewidth-aware reductions of normal ASP to SAT -Is normal ASP harder than SAT after all?","authors":"Markus Hecher","year":"2022","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Jakl et al., 2009] Michael Jakl, Reinhard Pichler, and Stefan Woltran. Answer-set programming with bounded treewidth. In IJCAI, pages 816-822, 2009.","title":"Answer-set programming with bounded treewidth","authors":"Michael Jakl, Reinhard Pichler, Stefan Woltran","year":"2009","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2009/140"},{"position":25,"raw":"[Kahl et al., 2015] Patrick Thor Kahl, Richard Watson, Evgenii Balai, Michael Gelfond, and Yuanlin Zhang. The language of epistemic specifications (refined) including a prototype solver. J. Log. Comput., 25, 2015.","title":"The language of epistemic specifications (refined) including a prototype solver","authors":"Thor Patrick, Richard Kahl, Evgenii Watson, Michael Balai, Yuanlin Gelfond, Zhang","year":"2015","venue":"J. Log. Comput","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Lonc and Truszczynski, 2003] Zbigniew Lonc and Miroslaw Truszczynski. Fixed-parameter complexity of semantics for logic programs. ACM Trans. Comput. Log., 4(1):91-119, 2003.","title":"Zbigniew Lonc and Miroslaw Truszczynski. Fixed-parameter complexity of semantics for logic programs","authors":"Truszczynski Lonc","year":"2003","venue":"ACM Trans. Comput. Log","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Morak, 2019] Michael Morak. Epistemic logic programs: A dif- ferent world view. In ICLP, pages 52-64, 2019.","title":"Epistemic logic programs: A different world view","authors":"Michael Morak","year":"2019","venue":"ICLP","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Saribatur and Eiter, 2021] Zeynep Gözen Saribatur and Thomas Eiter. Omission-based abstraction for answer set programs. The- ory Pract. Log. Program., 21(2):145-195, 2021.","title":"Omission-based abstraction for answer set programs","authors":"Eiter ; Saribatur, Gözen Zeynep, Thomas Saribatur, Eiter","year":"2021","venue":"Theory Pract. Log. Program","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Shen and Eiter, 2016] Yi-Dong Shen and Thomas Eiter. Evaluat- ing epistemic negation in answer set programming. Artif. Intell., 237:115-135, 2016.","title":"Evaluating epistemic negation in answer set programming","authors":"Yi-Dong Shen, Thomas Eiter","year":"2016","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Son et al., 2017] Tran Cao Son, Tiep Le, Patrick Thor Kahl, and Anthony P. Leclerc. On computing world views of epistemic logic programs. In IJCAI, pages 1269-1275, 2017.","title":"On computing world views of epistemic logic programs","authors":"Tran Cao, Son, Tiep Le, Patrick, Thor Kahl, Anthony P Leclerc","year":"2017","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2017/176"},{"position":31,"raw":"[Truszczynski, 2011] Miroslaw Truszczynski. Revisiting epistemic specifications. In Logic Programming, Knowledge Represen- tation, and Nonmonotonic Reasoning, volume 6565 of LNCS, pages 315-333. Springer Verlag, 2011.","title":"Revisiting epistemic specifications","authors":"Miroslaw Truszczynski","year":"2011","venue":"Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}