{"type":"ScholarlyArticle","title":"On Computational Aspects of Iterated Belief Change","authors":[{"name":"Nicolas Schwind","slug":"nicolas-schwind","given":"Nicolas","family":"Schwind","affiliation":"National Institute of Advanced Industrial Science and Technology , Tokyo , Japan"},{"name":"Sebastien Konieczny","slug":"sebastien-konieczny","given":"Sébastien","family":"Konieczny","affiliation":"CRIL -CNRS , Université d'Artois , Lens , France"},{"name":"Jean-Marie Lagniez","slug":"jean-marie-lagniez","given":"Jean-Marie","family":"Lagniez","affiliation":"Huawei Technologies Ltd , Boulogne-Billancourt , France"},{"name":"Pierre Marquis","slug":"pierre-marquis","given":"Pierre","family":"Marquis","affiliation":"CRIL -CNRS , Université d'Artois , Lens , France; Institut Universitaire de France"}],"abstract":"Iterated belief change aims to determine how the belief state of a rational agent evolves given a sequence of change formulae. Several families of iterated belief change operators (revision operators, improvement operators) have been pointed out so far, and characterized from an axiomatic point of view. This paper focuses on the inference problem for iterated belief change, when belief states are represented as a special kind of stratified belief bases. The computational complexity of the inference problem is identified and shown to be identical for all revision operators satisfying Darwiche and Pearl's (R*1-R*6) postulates. In addition, some complexity bounds for the inference problem are provided for the family of soft improvement operators. We also show that a revised belief state can be computed in a reasonable time for large-sized instances using SAT-based algorithms, and we report empirical results showing the feasibility of iterated belief change for bases of significant sizes.","doi":"10.24963/ijcai.2020/245","url":"https://ijcai.org/proceedings/2020/245","pdf":"https://ijcai.org/proceedings/2020/0245.pdf","markdown":"https://ijcai.org/proceedings/2020/245.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/245","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":245,"pages":{"first":1770,"last":1776},"keywords":["Knowledge Representation and Reasoning: Belief Change, Belief Merging","Knowledge Representation and Reasoning: Non-monotonic Reasoning, Common-Sense Reasoning"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24727/file_24727.m3u8","length_sec":291,"provider":"hls"}],"references":[{"position":1,"raw":"[Alchourrón et al., 1985] C. E. Alchourrón, P. Gärdenfors, and D. Makinson. On the logic of theory change: Par- tial meet contraction and revision functions. Journal of Symbolic Logic, 50:510-530, 1985.","title":"On the logic of theory change: Partial meet contraction and revision functions","authors":"C E Alchourrón, P Gärdenfors, D Makinson","year":"1985","venue":"Journal of Symbolic Logic","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Booth and Chandler, 2016] R. Booth and J. Chandler. Ex- tending the harper identity to iterated belief change. In IJCAI'16, pages 987-993, 2016.","title":"Extending the harper identity to iterated belief change","authors":"R Booth, J Chandler","year":"2016","venue":"IJCAI'16","doi":null,"url":null,"internal_url":"/proceedings/2016/144"},{"position":3,"raw":"[Booth and Meyer, 2006] R. Booth and T. A. Meyer. Admis- sible and restrained revision. Journal of Artificial Intelli- gence Research, 26:127-151, 2006.","title":"Admissible and restrained revision","authors":"R Booth, T A Meyer","year":"2006","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Boutilier, 1996] C. Boutilier. Iterated revision and minimal change of conditional beliefs. Journal of Philosophical Logic, 25(3):263-305, 1996.","title":"Iterated revision and minimal change of conditional beliefs","authors":"C Boutilier","year":"1996","venue":"Journal of Philosophical Logic","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Cai et al., 1988] J-Y. Cai, T. Gundermann, J. Hartmanis, L. A. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The Boolean hierarchy I: Structural proper- ties. SIAM Journal of Computing, 17(6):1232-1252, 1988.","title":"The Boolean hierarchy I: Structural properties","authors":"J-Y Cai, T Gundermann, J Hartmanis, L A Hemachandra, V Sewelson, K Wagner, G Wechsung","year":"1988","venue":"SIAM Journal of Computing","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Chou and Winslett, 1991] S-C. T. Chou and M. Winslett. The implementation of a model-based belief revision sys- tem. SIGART Bulletin, 2(3):28-34, 1991.","title":"The implementation of a model-based belief revision system","authors":"S-C T Chou, M Winslett","year":"1991","venue":"SIGART Bulletin","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Darwiche and Pearl, 1997] A. Darwiche and J. Pearl. On the logic of iterated belief revision. Artificial Intelligence, 89(1-2):1-29, 1997.","title":"On the logic of iterated belief revision","authors":"A Darwiche, J Pearl","year":"1997","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Delgrande et al., 2007] J. P. Delgrande, D. H. Liu, T. Schaub, and S. Thiele. COBA 2.0: A consistency-based belief change system. In ECSQARU'07, pages 78-90, 2007.","title":"COBA 2.0: A consistency-based belief change system","authors":"J P Delgrande, D H Liu, T Schaub, S Thiele","year":"2007","venue":"ECSQARU'07","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Dixon and Wobcke, 1993] S. Dixon and W. Wobcke. The implementation of a first-order logic AGM belief revision system. In ICTAI'93, pages 40-47, 1993.","title":"The implementation of a first-order logic AGM belief revision system","authors":"S Dixon, W Wobcke","year":"1993","venue":"ICTAI'93","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Eén and Sörensson, 2003] N. Eén and N. Sörensson. An ex- tensible SAT-solver. In SAT'03, pages 502-518, 2003.","title":"An extensible SAT-solver","authors":"N Eén, N Sörensson","year":"2003","venue":"SAT'03","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Eiter and Gottlob, 1997] T. Eiter and G. Gottlob. The com- plexity class θ p 2 : Recent results and applications in AI and modal logic. In FCT'97, pages 1-18, 1997.","title":"The complexity class θ p 2 : Recent results and applications in AI and modal logic","authors":"T Eiter, G Gottlob","year":"1997","venue":"FCT'97","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Fermé and Hansson, 2011] E. Fermé and S. O. Hansson. AGM 25 years: Twenty-five years of research in belief change. Journal of Philosophical Logic, 40(2):295-331, 2011.","title":"AGM 25 years: Twenty-five years of research in belief change","authors":"Fermé, ] E Hansson, S O Fermé, Hansson","year":"2011","venue":"Journal of Philosophical Logic","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Gärdenfors, 1988] P. Gärdenfors. Knowledge in flux. MIT Press, 1988.","title":"Knowledge in flux","authors":"P Gärdenfors","year":"1988","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Giráldez-Cru and Levy, 2015] J. Giráldez-Cru and J. Levy. A modularity-based random SAT instances generator. In IJCAI'15, pages 1952-1958, 2015.","title":"A modularity-based random SAT instances generator","authors":"Giráldez-Cru And Levy, ; ] J Giráldez-Cru, J Levy","year":"2015","venue":"IJCAI'15","doi":null,"url":null,"internal_url":"/proceedings/2015/277"},{"position":15,"raw":"[Gorogiannis and Ryan, 2002] N. Gorogiannis and M. Ryan. Implementation of belief change operators using BDDs. Studia Logica, 70(1):131-156, 2002.","title":"Implementation of belief change operators using BDDs","authors":"N Gorogiannis, M Ryan","year":"2002","venue":"Studia Logica","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Hansson, 1999] S. O. Hansson. A Textbook of Belief Dy- namics. Theory Change and Database Updating. Kluwer, 1999.","title":"A Textbook of Belief Dynamics. Theory Change and Database Updating","authors":"S O Hansson","year":"1999","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Jin and Thielscher, 2007] Y. Jin and M. Thielscher. Iterated belief revision, revised. Artificial Intelligence, 171(1):1- 18, 2007.","title":"Iterated belief revision, revised","authors":"Y Jin, M Thielscher","year":"2007","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Konieczny and Pino Pérez, 2008] S. Konieczny and R. Pino Pérez. Improvement operators. In KR'08, pages 177-187, 2008.","title":"Improvement operators","authors":"Pino Konieczny, ; Pérez, S Konieczny, R Pino Pérez","year":"2008","venue":"KR'08","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Konieczny and Pino Pérez, 2017] S. Konieczny and R. Pino Pérez. On iterated contraction: Syntactic charac- terization, representation theorem and limitations of the levi identity. In SUM'17, pages 348-362, 2017.","title":"On iterated contraction: Syntactic characterization, representation theorem and limitations of the levi identity","authors":"Pino Konieczny, ; Pérez, S Konieczny, R Pino Pérez","year":"2017","venue":"SUM'","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Konieczny et al., 2010] S. Konieczny, M. M. Grespan, and R. Pino Pérez. Taxonomy of improvement operators and the problem of minimal change. In KR'10, pages 161-170, 2010.","title":"Taxonomy of improvement operators and the problem of minimal change","authors":"S Konieczny, M M Grespan, R Pino Pérez","year":"2010","venue":"KR'10","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Konieczny et al., 2017] S. Konieczny, J-M. Lagniez, and P. Marquis. Boosting distance-based revision using SAT encodings. In LORI'17, pages 480-496, 2017.","title":"Boosting distance-based revision using SAT encodings","authors":"S Konieczny, J-M Lagniez, P Marquis","year":"2017","venue":"LORI'","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Lehmann, 1995] D. Lehmann. Belief revision, revised. In IJCAI'95, pages 1534-1540, 1995.","title":"Belief revision, revised","authors":"D Lehmann","year":"1995","venue":"IJCAI'95","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Liberatore, 1997] P. Liberatore. The complexity of iterated belief revision. In ICDT'97, pages 276-290, 1997.","title":"The complexity of iterated belief revision","authors":"P Liberatore","year":"1997","venue":"ICDT'97","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Liberatore, 1999] P. Liberatore. BReLS: a system for revis- ing, updating, and merging knowledge bases. In NRAC'99, 1999.","title":"BReLS: a system for revising, updating, and merging knowledge bases","authors":"P Liberatore","year":"1999","venue":"NRAC'99","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Nayak et al., 2003] A. C. Nayak, M. Pagnucco, and P. Pep- pas. Dynamic belief revision operators. Artificial Intelli- gence, 146(2):193-228, 2003.","title":"Dynamic belief revision operators","authors":"A C Nayak, M Pagnucco, P","year":"2003","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Nebel, 1998] B. Nebel. How Hard is it to Revise a Belief Base?, pages 77-145. Springer Netherlands, Dordrecht, 1998.","title":"How Hard is it to Revise a Belief Base?","authors":"B Nebel","year":"1998","venue":null,"doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Plaisted and Greenbaum, 1986] D. A. Plaisted and S. Greenbaum. A structure-preserving clause form translation. Journal of Symbolic Computation, 2(3):293- 304, 1986.","title":"A structure-preserving clause form translation","authors":"D A Plaisted, S Greenbaum","year":"1986","venue":"Journal of Symbolic Computation","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Rott, 2006] H. Rott. Revision by comparison as a unify- ing framework: Severe withdrawal, irrevocable revision and irrefutable revision. Theoretical Computer Science, 355(2):228-242, 2006.","title":"Revision by comparison as a unifying framework: Severe withdrawal, irrevocable revision and irrefutable revision","authors":"H Rott","year":"2006","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Rott, 2009] H. Rott. Shifting priorities: Simple represen- tations for twenty-seven iterated theory change operators.","title":"Shifting priorities: Simple representations for twenty-seven iterated theory change operators","authors":"H Rott","year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":30,"raw":"In D. Makinson, J. Malinowski, and H. Wansing, edi- tors, Towards Mathematical Philosophy, pages 269-296. Springer, 2009.","title":"Towards Mathematical Philosophy","authors":"D Makinson, J Malinowski, H Wansing","year":"2009","venue":null,"doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Thimm, 2014] M. Thimm. Tweety: A comprehensive col- lection of java libraries for logical aspects of artificial in- telligence and knowledge representation. In KR'14, 2014.","title":"Tweety: A comprehensive collection of java libraries for logical aspects of artificial intelligence and knowledge representation","authors":"M Thimm","year":"2014","venue":"KR'","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Wagner, 1987] K. W. Wagner. More complicated questions about maxima and minima, and some closures of NP. The- oretical Computer Science, 51:53-80, 1987.","title":"More complicated questions about maxima and minima, and some closures of NP","authors":"K W Wagner","year":"1987","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Williams and Sims, 2000] M-A. Williams and A. Sims. SATEN: an object-oriented web-based revision and extrac- tion engine. CoRR, cs.AI/0003059, 2000.","title":"SATEN: an object-oriented web-based revision and extraction engine","authors":"M-A Williams, A Sims","year":"2000","venue":null,"doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Zhuang et al., 2007] Z. Q. Zhuang, M. Pagnucco, and T. Meyer. Implementing iterated belief change via prime implicates. In AI'07, pages 507-518, 2007.","title":"Implementing iterated belief change via prime implicates","authors":"Z Q Zhuang, M Pagnucco, T Meyer","year":"2007","venue":"AI'07","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}