{"type":"ScholarlyArticle","title":"Formulas Free From Inconsistency: An Atom-Centric Characterization in Priest's Minimally Inconsistent LP (Extended Abstract)","authors":[{"name":"Kedian Mu","slug":"kedian-mu","given":"Kedian","family":"Mu","affiliation":"School of Mathematical Sciences , Peking University , P.R.China"}],"abstract":"As one of fundamental properties to characterize inconsistency measures for knowledge bases, the property of free formula independence  captures well the intuition that free formulas are independent of the amount of inconsistency in a knowledge base for cases where inconsistency is characterized in terms of minimal inconsistent subsets. But it has been argued that not all the  free formulas are  independent of inconsistency in some other contexts of inconsistency characterization.  In this paper, we propose a  notion of Bi-free formula to describe formulas  that are free from inconsistency in both syntactic characterization  and paraconsistent models in the framework of Priest's minimally inconsistent LP.  Then  we propose the  property of  Bi-free formula independence, which is more suitable for characterizing the role of formulas free from inconsistency in measuring inconsistency from both syntactic and semantic perspectives.","doi":"10.24963/ijcai.2020/713","url":"https://ijcai.org/proceedings/2020/713","pdf":"https://ijcai.org/proceedings/2020/0713.pdf","markdown":"https://ijcai.org/proceedings/2020/713.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/713","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":"Journal track","track":"Journal track","number":713,"pages":{"first":5090,"last":5094},"keywords":["Knowledge Representation and Reasoning: Logics for Knowledge Representation"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25038/file_25038.m3u8","length_sec":281,"provider":"hls"}],"references":[{"position":1,"raw":"[Arieli and Avron, 1998] Ofer Arieli and Arnon Avron. The value of the four values. Artif. Intell., 102(1):97-141, 1998.","title":"The value of the four values","authors":"Avron Arieli, Ofer Arieli, Arnon Avron","year":"1998","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Belnap, 1977] Nuel Belnap. A useful four-valued logic. In Modern Uses of Multiple-Valued Logic, pages 5-37, Dor- drecht, 1977. Springer Netherlands.","title":"A useful four-valued logic","authors":"Nuel Belnap","year":"1977","venue":"Modern Uses of Multiple-Valued Logic","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Besnard, 2014] Philippe Besnard. Revisiting postulates for inconsistency measures. In Logics in Artificial Intelli- gence -14th European Conference, JELIA 2014, Funchal, Madeira, Portugal, September 24-26, 2014. Proceedings, pages 383-396. Springer, 2014.","title":"Revisiting postulates for inconsistency measures","authors":"Philippe Besnard","year":"2014","venue":"Logics in Artificial Intelligence -14th European Conference, JELIA 2014","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Besnard, 2017] Philippe Besnard. Basic postulates for inconsistency measures. T. Large-Scale Data-and Knowledge-Centered Systems, 34:1-12, 2017.","title":"Basic postulates for inconsistency measures","authors":"Philippe Besnard","year":"2017","venue":"T. Large-Scale Data-and Knowledge-Centered Systems","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Grant and Hunter, 2011] John Grant and Anthony Hunter. Measuring the good and the bad in inconsistent informa- tion. In IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16-22, 2011, pages 2632-2637, 2011.","title":"Measuring the good and the bad in inconsistent information","authors":"Hunter ; Grant, John Grant, Anthony Hunter","year":"2011","venue":"Proceedings of the 22nd International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2011/438"},{"position":6,"raw":"[Hunter and Konieczny, 2006] Anthony Hunter and Sébastien Konieczny. Shapley inconsistency values. In Principles of knowledge representation and reasoning: Proceedings of the 10th international conference(KR06), pages 249-259. AAAI Press, 2006.","title":"Shapley inconsistency values","authors":"Anthony Hunter, Sébastien Konieczny","year":"2006","venue":"Principles of knowledge representation and reasoning: Proceedings of the 10th international conference(KR06)","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Hunter and Konieczny, 2008] Anthony Hunter and Sébastien Konieczny. Measuring inconsistency through minimal inconsistent sets. In Principles of knowledge representation and reasoning: Proceedings of the eleventh international conference(KR08), pages 358-366. AAAI Press, 2008.","title":"Measuring inconsistency through minimal inconsistent sets","authors":"Anthony Hunter, Sébastien Konieczny","year":"2008","venue":"Principles of knowledge representation and reasoning: Proceedings of the eleventh international conference(KR08)","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Hunter and Konieczny, 2010] Anthony Hunter and Sébastien Konieczny. On the measure of conflicts: Shapley inconsistency values. Artificial Intelligence, 174(14):1007-1026, 2010.","title":"On the measure of conflicts: Shapley inconsistency values","authors":"Anthony Hunter, Sébastien Konieczny","year":"2010","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Hunter, 2006] Anthony Hunter. How to act on inconsis- tent news: Ignore, resolve, or reject. Data Knowl. Eng., 57(3):221-239, 2006.","title":"How to act on inconsistent news: Ignore, resolve, or reject","authors":"Anthony Hunter","year":"2006","venue":"Data Knowl. Eng","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Jabbour et al., 2014] Saïd Jabbour, Yue Ma, and Badran Raddaoui. Inconsistency measurement thanks to mus de- composition. In International conference on Autonomous Agents and Multi-Agent Systems, AAMAS '14, pages 877- 884. IFAAMAS/ACM, 2014.","title":"Inconsistency measurement thanks to mus decomposition","authors":"Saïd Jabbour, Yue Ma, Badran Raddaoui","year":"2014","venue":"International conference on Autonomous Agents and Multi-Agent Systems, AAMAS '14","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Jabbour et al., 2016] Saïd Jabbour, Yue Ma, Badran Rad- daoui, Lakhdar Sais, and Yakoub Salhi. A MIS parti- tion based framework for measuring inconsistency. In Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, pages 84-93. AAAI Press, 2016.","title":"A MIS partition based framework for measuring inconsistency","authors":"Saïd Jabbour, Yue Ma, Badran Raddaoui, Lakhdar Sais, Yakoub Salhi","year":"2016","venue":"Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Konieczny et al., 2003] Sébastien Konieczny, Jérôme Lang, and Pierre Marquis. Quantifying information and contra- diction in propositional logic through epistemic actions. In Proceedings of the 18th International Joint Conference on Artificial Intellignce (IJCAI2003), pages 106-111, 2003.","title":"Quantifying information and contradiction in propositional logic through epistemic actions","authors":"Sébastien Konieczny, Jérôme Lang, Pierre Marquis","year":"2003","venue":"Proceedings of the 18th International Joint Conference on Artificial Intellignce (IJCAI2003)","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Liu and Mu, 2017] Weiru Liu and Kedian Mu. Introduction to the special issue on theories of inconsistency measures and their applications. Int. J. Approx. Reasoning, 89:1-2, 2017.","title":"Introduction to the special issue on theories of inconsistency measures and their applications","authors":"Mu Liu, Weiru Liu, Kedian Mu","year":"2017","venue":"Int. J. Approx. Reasoning","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Ma et al., 2011] Yue Ma, Guilin Qi, and Pascal Hitzler. Computing inconsistency measure based on paraconsis- tent semantics. Journal of Logic and Computation., 21(6):1257-1281, 2011.","title":"Computing inconsistency measure based on paraconsistent semantics","authors":"Yue Ma, Guilin Qi, Pascal Hitzler","year":"2011","venue":"Journal of Logic and Computation","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[McAreavey et al., 2011] Kevin McAreavey, Weiru Liu, Paul Miller, and Kedian Mu. Measuring inconsistency in a network intrusion detection rule set based on snort. Inter- national Journal of Semantic Computing, 5(3):281-322, 2011.","title":"Measuring inconsistency in a network intrusion detection rule set based on snort","authors":"Kevin Mcareavey, Weiru Liu, Paul Miller, Kedian Mu","year":"2011","venue":"International Journal of Semantic Computing","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Mu et al., 2011] Kedian Mu, Weiru Liu, Zhi Jin, and David Bell. A syntax-based approach to measuring the degree of inconsistency for belief bases. International Journal of Approximate Reasoning, 52(7):978-999, 2011.","title":"A syntax-based approach to measuring the degree of inconsistency for belief bases","authors":"Mu","year":"2011","venue":"International Journal of Approximate Reasoning","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Mu et al., 2013a] Kedian Mu, Jun Hong, Zhi Jin, and Weiru Liu. From inconsistency handling to non-canonical re- quirements management: A logical perspective. Interna- tional Journal of Approximate Reasoning, 54(1):109-131, 2013.","title":"From inconsistency handling to non-canonical requirements management: A logical perspective","authors":"Mu","year":"2013","venue":"International Journal of Approximate Reasoning","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Mu et al., 2013b] Kedian Mu, Zhi Jin, Weiru Liu, Didar Zowghi, and Bo Wei. Measuring the significance of in- consistency in the viewpoints framework. Science of Com- puter Programming, 78(9):1572-1599, 2013.","title":"Measuring the significance of inconsistency in the viewpoints framework","authors":"Mu","year":"2013","venue":"Science of Computer Programming","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Mu, 2015] Kedian Mu. Responsibility for inconsistency. In- ternational Journal of Approximate Reasoning, 61:43-60, 2015.","title":"Kedian Mu. Responsibility for inconsistency","authors":"Mu","year":"2015","venue":"ternational Journal of Approximate Reasoning","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Mu, 2018] Kedian Mu. Measuring inconsistency with con- straints for propositional knowledge bases. Artificial Intel- ligence, 259:52-90, 2018.","title":"Kedian Mu. Measuring inconsistency with constraints for propositional knowledge bases","authors":"Mu","year":"2018","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Mu, 2019] Kedian Mu. Formulas free from inconsistency: An atom-centric characterization in priest's minimally in- consistent LP. J. Artif. Intell. Res., 66:279-296, 2019.","title":"Kedian Mu. Formulas free from inconsistency: An atom-centric characterization in priest's minimally inconsistent LP","authors":"Mu","year":"2019","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Picado-Muiño, 2011] David Picado-Muiño. Measuring and repairing inconsistency in probabilistic knowledge bases. International Journal of Approximate Reasoning, 52(6):828-840, 2011.","title":"Measuring and repairing inconsistency in probabilistic knowledge bases","authors":"David Picado-Muiño","year":"2011","venue":"International Journal of Approximate Reasoning","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Priest, 1979] Graham Priest. The logic of paradox. J. Philo- sophical Logic, 8(1):219-241, 1979.","title":"The logic of paradox","authors":"Graham Priest","year":"1979","venue":"J. Philosophical Logic","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Priest, 1991] Graham Priest. Minimally inconsistent LP. Studia Logica, 50(1):321-331, 1991.","title":"Minimally inconsistent LP","authors":"Graham Priest","year":"1991","venue":"Studia Logica","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Thimm, 2009] Matthias Thimm. Measuring inconsistency in probabilistic knowledge bases. In Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence (UAI'09),Montreal, Canada, June 2009, pages 530-537. AUAI Press, 2009.","title":"Measuring inconsistency in probabilistic knowledge bases","authors":"Matthias Thimm","year":"2009","venue":"Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence (UAI'09)","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Thimm, 2017] Matthias Thimm. Measuring inconsistency with many-valued logics. Int. J. Approx. Reasoning, 86:1- 23, 2017.","title":"Measuring inconsistency with many-valued logics","authors":"Matthias Thimm","year":"2017","venue":"Int. J. Approx. Reasoning","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Thimm, 2018] Matthias Thimm. On the evaluation of in- consistency measures. In John Grant and Maria Vanina Martinez, editors, Measuring Inconsistency in Informa- tion, pages 19-60. College Publications, 2018.","title":"On the evaluation of inconsistency measures","authors":"Matthias Thimm","year":"2018","venue":"Measuring Inconsistency in Information","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}