{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T04:44:33Z","timestamp":1773377073715,"version":"3.50.1"},"reference-count":52,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2018,5,19]],"date-time":"2018-05-19T00:00:00Z","timestamp":1526688000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/academic.oup.com\/journals\/pages\/about_us\/legal\/notices"}],"funder":[{"DOI":"10.13039\/501100003130","name":"Fonds Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,9,5]]},"DOI":"10.1093\/logcom\/exy015","type":"journal-article","created":{"date-parts":[[2018,4,30]],"date-time":"2018-04-30T12:00:29Z","timestamp":1525089629000},"page":"1323-1339","source":"Crossref","is-referenced-by-count":19,"title":["Computing the maximal Boolean complexity of families of Aristotelian diagrams"],"prefix":"10.1093","volume":"28","author":[{"given":"Lorenz","family":"Demey","sequence":"first","affiliation":[{"name":"Centre for Logic and Philosophy of Science KU Leuven, Leuven, Belgium"}]}],"member":"286","published-online":{"date-parts":[[2018,5,19]]},"reference":[{"key":"key\n\t\t\t\t20180903132126_C1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.4018\/jcini.2012070102","article-title":"Can AI models capture natural language argumentation?","volume":"6","author":"Amgoud","year":"2012","journal-title":"International Journal of Cognitive Informatics and Natural Intelligence"},{"key":"key\n\t\t\t\t20180903132126_C2","doi-asserted-by":"crossref","unstructured":"L. Amgoud and H.Prade. Towards a logic of argumentation. In Scalable Uncertainty Management 2012, E. H\u00fcllermeier et al., eds, pp. 558\u2013565. Vol. 7520 ofLecture Notes in Computer Science, Springer, Berlin, 2012.","DOI":"10.1007\/978-3-642-33362-0_43"},{"key":"key\n\t\t\t\t20180903132126_C3","unstructured":"L. Amgoud and H.Prade. A formal concept view of formal argumentation. In Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2013), L. C. van derGaag ed., pp.1\u201312. Vol. 7958 of Lecture Notes in Computer Science, Springer, Berlin, 2013."},{"key":"key\n\t\t\t\t20180903132126_C4","volume-title":"Prolog Programming for Artificial Intelligence","author":"Bratko","year":"2001"},{"key":"key\n\t\t\t\t20180903132126_C5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4020-8590-1","volume-title":"Modalities and Multimodalities","author":"Carnielli","year":"2008"},{"key":"key\n\t\t\t\t20180903132126_C6","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1007\/978-3-642-31900-6_62","article-title":"Oppositions in rough set theory","volume-title":"Rough Sets and Knowledge Technology","author":"Ciucci","year":"2012"},{"key":"key\n\t\t\t\t20180903132126_C7","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1007\/978-3-319-04939-7_7","article-title":"The structure of oppositions in rough set theory and formal concept analysis \u2013 toward a new bridge between the two settings","volume-title":"Foundations of Information and Knowledge Systems (FoIKS 2014)","author":"Ciucci","year":"2014"},{"key":"key\n\t\t\t\t20180903132126_C8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3233\/FI-2015-1282","article-title":"Structures of opposition in fuzzy rough sets","volume":"142","author":"Ciucci","year":"2015","journal-title":"Fundamenta Informaticae"},{"key":"key\n\t\t\t\t20180903132126_C9","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s10472-015-9480-8","article-title":"Structures of opposition induced by relations: The Boolean and the gradual cases","volume":"76","author":"Ciucci","year":"2016","journal-title":"Annals of Mathematics and Artificial Intelligence"},{"key":"key\n\t\t\t\t20180903132126_C10","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s10849-015-9215-6","article-title":"Not only Barbara","volume":"24","author":"Dekker","year":"2015","journal-title":"Journal of Logic, Language and Information"},{"key":"key\n\t\t\t\t20180903132126_C11","doi-asserted-by":"crossref","unstructured":"L. Demey . Structures of oppositions for public announcement logic. In Around and Beyond the Square of Opposition, J.-Y.B\u00e9ziau and D.Jacquette, eds, pp. 313\u2013339. Springer, Basel, 2012.","DOI":"10.1007\/978-3-0348-0379-3_22"},{"key":"key\n\t\t\t\t20180903132126_C12","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/978-3-319-25591-0_24","article-title":"Interactively illustrating the context-sensitivity of Aristotelian diagrams","volume-title":"Modeling and Using Context","author":"Demey","year":"2015"},{"key":"key\n\t\t\t\t20180903132126_C13","volume-title":"Logic-Sensitivity in Aristotelian Diagrams","author":"Demey","year":"2018"},{"key":"key\n\t\t\t\t20180903132126_C14","article-title":"The logical geometry of Russell\u2019s theory of definite descriptions","author":"Demey","year":"2018"},{"key":"key\n\t\t\t\t20180903132126_C15","doi-asserted-by":"crossref","DOI":"10.1007\/s11841-017-0632-7","article-title":"Aristotelian diagrams in the debate on future contingents","volume-title":"Sophia","author":"Demey"},{"key":"key\n\t\t\t\t20180903132126_C16","article-title":"Metalogic, metalanguage and logical geometry","volume-title":"Logique et Analyse","author":"Demey"},{"key":"key\n\t\t\t\t20180903132126_C17","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s11787-015-0136-6","article-title":"Metalogical decorations of logical diagrams","volume":"10","author":"Demey","year":"2016","journal-title":"Logica Universalis"},{"key":"key\n\t\t\t\t20180903132126_C18","doi-asserted-by":"crossref","first-page":"204","DOI":"10.3390\/sym9100204","article-title":"Logical and geometrical distance in polyhedral Aristotelian diagrams in knowledge representation","volume":"9","author":"Demey","year":"2017","journal-title":"Symmetry"},{"key":"key\n\t\t\t\t20180903132126_C19","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s10992-017-9430-5","article-title":"Combinatorial bitstring semantics for arbitrary logical fragments","volume":"47","author":"Demey","year":"2018","journal-title":"Journal of Philosophical Logic"},{"key":"key\n\t\t\t\t20180903132126_C20","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s11787-011-0039-0","article-title":"From Blanch\u00e9\u2019s hexagonal organization of concepts to formal concept analysis and possibility theory","volume":"6","author":"Dubois","year":"2012","journal-title":"Logica Universalis"},{"key":"key\n\t\t\t\t20180903132126_C21","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/978-3-319-19545-2_2","article-title":"Formal concept analysis from the standpoint of possibility theory","volume-title":"Formal Concept Analysis (ICFCA 2015)","author":"Dubois","year":"2015"},{"key":"key\n\t\t\t\t20180903132126_C22","doi-asserted-by":"crossref","unstructured":"D. Dubois and H.Prade. Gradual structures of oppositions. In Enric Trillas: A Passion for Fuzzy Sets, L.Magdalena, J. L.Verdegay and F.Esteva, eds, pp.79\u201391. Studies in Fuzziness and Soft Computing 322, Springer, Berlin, 2015.","DOI":"10.1007\/978-3-319-16235-5_7"},{"key":"key\n\t\t\t\t20180903132126_C23","first-page":"2933","article-title":"The cube of opposition \u2013 a structure underlying many knowledge representation formalisms","volume-title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence (IJCAI ) 2015","author":"Dubois","year":"2015"},{"key":"key\n\t\t\t\t20180903132126_C24","doi-asserted-by":"crossref","unstructured":"D. Dubois , H.Prade and A.Rico. The cube of opposition and the complete appraisal of situations by means of Sugeno integrals. In Foundations of Intelligent Systems (ISMIS 2015), F. Esposito et al., eds, pp.197\u2013207. Vol. 9384 of Lecture Notes in Computer Science, Springer, Berlin, 2015.","DOI":"10.1007\/978-3-319-25252-0_21"},{"key":"key\n\t\t\t\t20180903132126_C25","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.ijar.2017.02.006","article-title":"Graded cubes of opposition and possibility theory with fuzzy events","volume":"84","author":"Dubois","year":"2017","journal-title":"International Journal of Approximate Reasoning"},{"key":"key\n\t\t\t\t20180903132126_C26","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-5292-1","volume-title":"First-Order Modal Logic","author":"Fitting","year":"1998"},{"key":"key\n\t\t\t\t20180903132126_C27","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.jal.2015.09.012","article-title":"Transitivity in coherence-based probability logic","volume":"14","author":"Gilio","year":"2016","journal-title":"Journal of Applied Logic"},{"key":"key\n\t\t\t\t20180903132126_C28","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-32503-4","volume-title":"Fuzzy Quantifiers","author":"Gl\u00f6ckner","year":"2006"},{"key":"key\n\t\t\t\t20180903132126_C29","volume-title":"A Natural History of Negation","author":"Horn","year":"1989"},{"key":"key\n\t\t\t\t20180903132126_C30","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s11098-015-0509-y","article-title":"Lie-toe-tease: double negatives and unexcluded middles","volume":"174","author":"Horn","year":"2017","journal-title":"Philosophical Studies"},{"key":"key\n\t\t\t\t20180903132126_C31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10988-013-9130-8","article-title":"Constraints on the lexicalization of logical operators","volume":"36","author":"Katzir","year":"2013","journal-title":"Linguistics and Philosophy"},{"key":"key\n\t\t\t\t20180903132126_C32","doi-asserted-by":"crossref","unstructured":"W. Lenzen . How to square knowledge and belief. In Around and Beyond the Square of Opposition, J. -Y.B\u00e9ziau and D.Jacquette, eds, pp.305\u2013311. Springer, Basel, 2012.","DOI":"10.1007\/978-3-0348-0379-3_21"},{"key":"key\n\t\t\t\t20180903132126_C33","doi-asserted-by":"crossref","unstructured":"B. MacCartney and C.Manning. Modeling semantic containment and exclusion in natural language inference. In Proceedings of the 22nd International Conference on Computational Linguistics, D.Scott and H.Uszkoreit, eds, pp.521\u2013528. Coling2008, Manchester, 2008.","DOI":"10.3115\/1599081.1599147"},{"key":"key\n\t\t\t\t20180903132126_C34","doi-asserted-by":"crossref","unstructured":"B. MacCartney and C.Manning. Natural logic and natural language inference. In Computing Meaning, H. Bunt, J. Bos and S. Pulman, eds, pp.129\u2013147. Springer, Dordrecht, 2014.","DOI":"10.1007\/978-94-007-7284-7_8"},{"key":"key\n\t\t\t\t20180903132126_C35","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.fss.2013.05.006","article-title":"Analysis of generalized square of opposition with intermediate quantifiers","volume":"242","author":"Murinov\u00e1","year":"2014","journal-title":"Fuzzy Sets and Systems"},{"key":"key\n\t\t\t\t20180903132126_C36","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s11787-016-0146-z","article-title":"Syllogisms and 5-square of opposition with intermediate quantifiers in fuzzy natural logic","volume":"10","author":"Murinov\u00e1","year":"2016","journal-title":"Logica Universalis"},{"key":"key\n\t\t\t\t20180903132126_C37","doi-asserted-by":"crossref","first-page":"269","DOI":"10.5840\/monist193242243","article-title":"The square of opposition","volume":"42","author":"Nelson","year":"1932","journal-title":"The Monist"},{"key":"key\n\t\t\t\t20180903132126_C38","article-title":"The traditional square of opposition","volume-title":"Stanford Encyclopedia of Philosophy","author":"Parsons","year":"2012"},{"key":"key\n\t\t\t\t20180903132126_C39","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s11787-008-0038-y","article-title":"Setting n-opposition","volume":"2","author":"Pellissier","year":"2008","journal-title":"Logica Universalis"},{"key":"key\n\t\t\t\t20180903132126_C40","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.ijar.2017.05.014","article-title":"Probabilistic squares and hexagons of opposition under coherence","volume":"88","author":"Pfeifer","year":"2017","journal-title":"International Journal of Approximate Reasoning"},{"key":"key\n\t\t\t\t20180903132126_C41","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s11787-016-0142-3","article-title":"Generalization and composition of modal squares of opposition","volume":"10","author":"Pizzi","year":"2016","journal-title":"Logica Universalis"},{"key":"key\n\t\t\t\t20180903132126_C42","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s11787-013-0089-6","article-title":"From analogical proportion to logical proportions","volume":"7","author":"Prade","year":"2013","journal-title":"Logica Universalis"},{"key":"key\n\t\t\t\t20180903132126_C43","doi-asserted-by":"crossref","unstructured":"H. Prade and G.Richard. On different ways to be (dis)similar to elements in a set. Boolean analysis and graded extension. In Information Processing and Management of Uncertainty in Knowledge-Based Systems 2016, Part II, J. P. Carvalho et al., eds, pp.605\u2013618. Communications in Computer and Information Science 611. Springer, Berlin, 2016.","DOI":"10.1007\/978-3-319-40581-0_49"},{"key":"key\n\t\t\t\t20180903132126_C44","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s10579-009-9089-9","article-title":"FactBank: a corpus annotated with event factuality","volume":"43","author":"Saur\u00ed","year":"2009","journal-title":"Language Resources and Evaluation"},{"key":"key\n\t\t\t\t20180903132126_C45","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1162\/COLI_a_00096","article-title":"Are you sure that this happened? Assessing the factuality degree of events in text","volume":"38","author":"Saur\u00ed","year":"2012","journal-title":"Computational Linguistics"},{"key":"key\n\t\t\t\t20180903132126_C46","first-page":"275","article-title":"Back to Aristotle!","volume":"21","author":"Slater","year":"2011","journal-title":"Logic and Logical Philosophy"},{"key":"key\n\t\t\t\t20180903132126_C47","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s10849-014-9207-y","article-title":"Logical geometries and information in the square of opposition","volume":"23","author":"Smessaert","year":"2014","journal-title":"Journal of Logic, Language and Information"},{"key":"key\n\t\t\t\t20180903132126_C48","doi-asserted-by":"crossref","unstructured":"H. Smessaert and L.Demey. B\u00e9ziau\u2019s contributions to the logical geometry of modalities and quantifiers. In The Road to Universal Logic, A.Koslow and A.Buchsbaum, eds, pp.475\u2013493. Springer, Basel, 2015.","DOI":"10.1007\/978-3-319-10193-4_23"},{"key":"key\n\t\t\t\t20180903132126_C49","doi-asserted-by":"crossref","unstructured":"H. Smessaert and L.Demey. The unreasonable effectiveness of bitstrings in logical geometry. In The Square of Opposition: A Cornerstone of Thought, J.-Y.B\u00e9ziau and G.Basti, eds, pp.197\u2013214. Springer, Basel, 2017.","DOI":"10.1007\/978-3-319-45062-9_12"},{"key":"key\n\t\t\t\t20180903132126_C50","doi-asserted-by":"crossref","DOI":"10.1515\/9783110896619","volume-title":"Die gute Samariterin. Zur Struktur der Supererogation","author":"Wessels","year":"2002"},{"key":"key\n\t\t\t\t20180903132126_C51","doi-asserted-by":"crossref","first-page":"49","DOI":"10.3233\/FI-2013-895","article-title":"Duality in rough set theory based on the square of opposition","volume":"127","author":"Yao","year":"2013","journal-title":"Fundamenta Informaticae"},{"key":"key\n\t\t\t\t20180903132126_C52","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.pragma.2017.03.008","article-title":"On the empty O-corner of the Aristotelian square: A view from Singapore English","volume":"115","author":"Ziegeler","year":"2017","journal-title":"Journal of Pragmatics"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/logcom\/article-pdf\/28\/6\/1323\/25677644\/exy015.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,2]],"date-time":"2023-09-02T10:15:39Z","timestamp":1693649739000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/28\/6\/1323\/4999161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,19]]},"references-count":52,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,5,19]]},"published-print":{"date-parts":[[2018,9,5]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exy015","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"value":"0955-792X","type":"print"},{"value":"1465-363X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2018,9]]},"published":{"date-parts":[[2018,5,19]]}}}