{"type":"ScholarlyArticle","title":"Inconsistency Measurement for Improving Logical Formula Clustering","authors":[{"name":"Yakoub Salhi","slug":"yakoub-salhi","given":"Yakoub","family":"Salhi","affiliation":"CRIL-CNRS , Université d'Artois , France"}],"abstract":"Formal logic can be used as a tool for representing complex and heterogeneous data such as beliefs, knowledge and preferences. This study proposes an approach for defining clustering methods that deal with bases of propositional formulas in classical logic, i.e., methods for dividing formula bases into meaningful groups. We first use a postulate-based approach for introducing an intuitive framework for formula clustering. Then, in order to characterize interesting clustering forms, we introduce additional properties that take into consideration different notions, such us logical consequence, overlapping, and consistent partition. Finally, we describe our approach that shows how the inconsistency\r\nmeasures can be involved in improving the task of formula clustering. The main idea consists in using the measures for quantifying the quality of the inconsistent clusters. In this context, we propose further properties that allow characterizing interesting aspects related to the amount of inconsistency.","doi":"10.24963/ijcai.2020/262","url":"https://ijcai.org/proceedings/2020/262","pdf":"https://ijcai.org/proceedings/2020/0262.pdf","markdown":"https://ijcai.org/proceedings/2020/262.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/262","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":262,"pages":{"first":1891,"last":1897},"keywords":["Machine Learning: Clustering","Knowledge Representation and Reasoning: Reasoning about Knowledge and Belief","Knowledge Representation and Reasoning: Logics for Knowledge Representation"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24280/file_24280.m3u8","length_sec":291,"provider":"hls"}],"references":[{"position":1,"raw":"[Aggarwal and Reddy, 2013] Charu C Aggarwal and Chan- dan K Reddy. Data clustering: algorithms and applica- tions. CRC Press, 2013.","title":"Data clustering: algorithms and applications","authors":"C Charu, Chandan K Aggarwal, Reddy","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Ammoura et al., 2017] Meriem Ammoura, Yakoub Salhi, Brahim Oukacha, and Badran Raddaoui. On an MCS- based inconsistency measure. International Journal of Ap- proximate Reasoning, 80:443-459, 2017.","title":"On an MCSbased inconsistency measure","authors":"Meriem Ammoura, Yakoub Salhi, Brahim Oukacha, Badran Raddaoui","year":"2017","venue":"International Journal of Approximate Reasoning","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Berkhin, 2006] Pavel Berkhin. A Survey of Clustering Data Mining Techniques. In Jacob Kogan, Charles K. Nicholas, and Marc Teboulle, editors, Grouping Multidi- mensional Data -Recent Advances in Clustering, pages 25-71. Springer, 2006.","title":"A Survey of Clustering Data Mining Techniques","authors":"Pavel Berkhin","year":"2006","venue":"Grouping Multidimensional Data -Recent Advances in Clustering","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Billard and Diday, 2012] Lynne Billard and Edwin Diday. Symbolic Data Analysis: Conceptual Statistics and Data Mining. John Wiley & Sons, 2012.","title":"Symbolic Data Analysis: Conceptual Statistics and Data Mining","authors":"Lynne Billard, Edwin Diday","year":"2012","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bock, 2000] Hans Hermann Bock. Analysis of Symbolic Data: Exploratory Methods for Extracting Statistical In- formation from Complex Data. Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2000.","title":"Analysis of Symbolic Data: Exploratory Methods for Extracting Statistical Information from Complex Data","authors":"Hans Hermann Bock, Bock","year":"2000","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bona et al., 2018] Glauber De Bona, John Grant, Anthony Hunter, and Sébastien Konieczny. Towards a Unified Framework for Syntactic Inconsistency Measures. In Pro- ceedings of the Thirty-Second AAAI Conference on Artifi- cial Intelligence, New Orleans, Louisiana, USA, 2018.","title":"Towards a Unified Framework for Syntactic Inconsistency Measures","authors":"Glauber De Bona, John Grant, Anthony Hunter, Sébastien Konieczny","year":"2018","venue":"Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Boudane et al., 2017] Abdelhamid Boudane, Saïd Jabbour, Lakhdar Sais, and Yakoub Salhi. Clustering Complex Data Represented as Propositional Formulas. In Advances in Knowledge Discovery and Data Mining -21st Pacific-Asia Conference, PAKDD 2017, Jeju, South Korea, Proceed- ings, Part II, volume 10235 of Lecture Notes in Computer Science, pages 441-452, 2017.","title":"Clustering Complex Data Represented as Propositional Formulas","authors":"Abdelhamid Boudane, Saïd Jabbour, Lakhdar Sais, Yakoub Salhi","year":"2017","venue":"Advances in Knowledge Discovery and Data Mining -21st Pacific-Asia Conference, PAKDD 2017","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[de Carvalho et al., 2009] Francisco de A.T. de Carvalho, Marc Csernel, and Yves Lechevallier. Clustering con- strained symbolic data. Pattern Recognition Letters, 30(11):1037-1045, 2009.","title":"Clustering constrained symbolic data","authors":"De Carvalho","year":"2009","venue":"Pattern Recognition Letters","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[de Souza and de Carvalho, 2004] Renata M.C.R. de Souza and Francisco de A.T. de Carvalho. Clustering of interval data based on city-block distances. Pattern Recognition Letters, 25(3):353-365, 2004.","title":"Clustering of interval data based on city-block distances","authors":"M C R Renata, Francisco Souza, A T De, De Carvalho","year":"2004","venue":"Pattern Recognition Letters","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Diday and Esposito, 2003] Edwin Diday and Floriana Es- posito. An introduction to symbolic data analysis and the SODAS software. Intelligent Data Analysis, 7(6):583- 601, 2003.","title":"Edwin Diday and Floriana Esposito. An introduction to symbolic data analysis and the SODAS software","authors":"Esposito Diday","year":"2003","venue":"Intelligent Data Analysis","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Gowda and Diday, 1994] K. Chidananda Gowda and Edwin Diday. New Approaches in Classification and Data Anal- ysis, chapter Symbolic Clustering Algorithms using Simi- larity and Dissimilarity Measures. Springer Berlin Heidel- berg, 1994.","title":"New Approaches in Classification and Data Analysis, chapter Symbolic Clustering Algorithms using Similarity and Dissimilarity Measures","authors":"K, Chidananda Gowda, Edwin Diday","year":"1994","venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"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, pages 2632-2637. IJCAI/AAAI, 2011.","title":"Measuring the Good and the Bad in Inconsistent Information","authors":"Hunter ; Grant, John Grant, Anthony Hunter","year":"2011","venue":"IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2011/438"},{"position":13,"raw":"[Grant and Hunter, 2013] John Grant and Anthony Hunter. Distance-Based Measures of Inconsistency. In Symbolic and Quantitative Approaches to Reasoning with Uncer- tainty -12th European Conference, ECSQARU 2013, Utrecht, The Netherlands, pages 230-241. Springer, 2013.","title":"Distance-Based Measures of Inconsistency","authors":"Hunter ; Grant, John Grant, Anthony Hunter","year":"2013","venue":"Symbolic and Quantitative Approaches to Reasoning with Uncertainty -12th European Conference, ECSQARU 2013","doi":null,"url":null,"internal_url":null},{"position":14,"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, KR 2008, Sydney, Australia, 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, KR 2008","doi":null,"url":null,"internal_url":null},{"position":15,"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":16,"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, Cape Town, South Africa, 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, KR 2016","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Konieczny et al., 2003] Sébastien Konieczny, Jérôme Lang, and Pierre Marquis. Quantifying information and con- tradiction in propositional logic through test actions. In IJCAI-03, Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence, Acapulco, Mexico, pages 106-111.","title":"Quantifying information and contradiction in propositional logic through test actions","authors":"Sébastien Konieczny, Jérôme Lang, Pierre Marquis","year":null,"venue":"Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2003/15"},{"position":18,"raw":"Morgan Kaufmann, 2003.","title":null,"authors":"Morgan Kaufmann","year":"2003","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Lozinskii, 1994] Eliezer L. Lozinskii. Information and evi- dence in logic systems. Journal of Experimental & Theo- retical Artificial Intelligence, 6(2):163-193, 1994.","title":"Information and evidence in logic systems","authors":"L Eliezer, Lozinskii","year":"1994","venue":"Journal of Experimental & Theoretical Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Marques-Silva and Lynce, 2007] João P. Marques-Silva and Inês Lynce. Towards Robust CNF Encodings of Cardinal- ity Constraints. In Principles and Practice of Constraint Programming, 13th International Conference, CP 2007, Providence, RI, USA, pages 483-497, 2007.","title":"Towards Robust CNF Encodings of Cardinality Constraints","authors":"P João, Inês Marques-Silva, Lynce","year":"2007","venue":"Principles and Practice of Constraint Programming, 13th International Conference, CP 2007","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Michalski, 1980] Ryszard Stanislaw Michalski. Knowledge Acquisition Through Conceptual Clustering: A Theoreti- cal Framework and an Algorithm for Partitioning Data into Conjunctive Concepts. Journal of Policy Analysis and In- formation Systems, 4(3):219-244, 1980.","title":"Knowledge Acquisition Through Conceptual Clustering: A Theoretical Framework and an Algorithm for Partitioning Data into Conjunctive Concepts","authors":"Ryszard Stanislaw, Michalski","year":"1980","venue":"Journal of Policy Analysis and Information Systems","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Sinz, 2005] Carsten Sinz. Towards an Optimal CNF Encod- ing of Boolean Cardinality Constraints. In Principles and Practice of Constraint Programming, 11th International Conference, CP 2005, Sitges, Spain, pages 827-831, 2005.","title":"Towards an Optimal CNF Encoding of Boolean Cardinality Constraints","authors":"Carsten Sinz","year":"2005","venue":"Principles and Practice of Constraint Programming, 11th International Conference, CP 2005","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Thimm, 2016] Matthias Thimm. On the expressivity of in- consistency measures. Artificial Intelligence, 234:120- 151, 2016.","title":"On the expressivity of inconsistency measures","authors":"Matthias Thimm","year":"2016","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":24,"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, volume 73 of Studies in Logic. College Publications, February 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."}