{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T06:36:49Z","timestamp":1719988609563},"reference-count":15,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,9,4]],"date-time":"2019-09-04T00:00:00Z","timestamp":1567555200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"In this paper, we give a mathematical model of the logic of determination of objects (LDO) based on preordered sets, and a mathematical model of the logic of typical and atypical instances (LTA). We prove that LTA is an extension of LDO. It can manipulate several types of \u201cexceptions\u201d. Finally, we show that the structural part of LTA can be modeled by a quasi topology structure (QTS).<\/jats:p>","DOI":"10.3390\/axioms8030104","type":"journal-article","created":{"date-parts":[[2019,9,5]],"date-time":"2019-09-05T07:22:36Z","timestamp":1567668156000},"page":"104","source":"Crossref","is-referenced-by-count":1,"title":["Logic of Typical and Atypical Instances of a Concept\u2014A Mathematical Model"],"prefix":"10.3390","volume":"8","author":[{"given":"Jean-Pierre","family":"Descl\u00e9s","sequence":"first","affiliation":[{"name":"Sens, Texte, Informatique, Histoire (STIH), Universit\u00e9 de Paris Sorbonne, 75005 Paris, France"}]},{"given":"Anca Christine","family":"Pascu","sequence":"additional","affiliation":[{"name":"Laboratoire des Sciences et Techniques de l\u2019Information, de la Communication et de la Connaissance (Lab-STICC), Universit\u00e9 de Brest, 29200 Brest, France"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Rosch, E.H. (1976). Classification d\u2019objets du monde r\u00e9el: Origine et repr\u00e9sentations dans la cognition. Bull. Psychol. Num\u00e9ro Sp\u00e9cial La M\u00e9moire S\u00e9mantique, 246\u2013250.","DOI":"10.3406\/bupsy.1976.10814"},{"key":"ref_2","unstructured":"Le Ny, J.-F. (2005). Comment L\u2019esprit Produit du Sens, Odile Jacob."},{"key":"ref_3","unstructured":"Descl\u00e9s, J.-P., Pascu, A.C., and Jouis, C. (2013, January 22\u201324). The Logic of Typical and Atypical Instances (LTA). Proceedings of the Twenty-Sixth International Florida Artificial Intelligence Research Society Conference, FLAIRS13, Miami, FL, USA."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s11787-011-0024-7","article-title":"Logic of Determination of Objects (LDO): How to Articulate \u201cExtension\u201d with \u201cIntension\u201d and \u201cObjects\u201d with \u201cConcepts\u201d","volume":"5","author":"Pascu","year":"2011","journal-title":"Log. Univers."},{"key":"ref_5","unstructured":"Descl\u00e9s, J.-P., Pascu, A.C., and Biskri, I. (2019). A topological approach for the notion of quasi topology structure. Int. South Am. J. Log., submitted."},{"key":"ref_6","unstructured":"Descl\u00e9s, J.-P., Pascu, A.C., and Biskri, I. (2018, January 21\u201323). A Quasi-Topologic Structure of Extensions in the Logic of Typical and Atypical Objects (LTA) and Logic of Determination of Objects (LDO). Proceedings of the 31th FLAIRS Conference, Melbourne, FL, USA."},{"key":"ref_7","unstructured":"Descl\u00e9s, J.-P., and Pascu, A.C. (2016, January 13\u201314). Logique de la D\u00e9termination des Objets (LDO): Structuration topologique et quasi-topologique des extensions. Proceedings of the Conference La logique en question\/Locic in Question, Paris-Sorbonne, Paris, France."},{"key":"ref_8","first-page":"85","article-title":"Categorization: A logical approach to a cognitive problem","volume":"3","year":"2002","journal-title":"J. Cogn. Sci."},{"key":"ref_9","unstructured":"Curry, H.B., and Feys, R. (1958). Combinatory Logic, North Holland Publishing, Co."},{"key":"ref_10","unstructured":"Descl\u00e9s, J.P., Guibert, G., and Sauzay, B. (2016). Logique Combinatoire et \u03bb-Calcul: Des Logiques D\u2019op\u00e9rateurs, C\u00e9padu\u00e8s."},{"key":"ref_11","unstructured":"Descl\u00e9s, J.-P., and Pascu, A.C. (2013). The Logic of Determination of Objects (LDO)\u2014A Paraconsistenr Logic, UNILOG."},{"key":"ref_12","unstructured":"Da Costa, N.C.A. (1997). Logique Classiques et non Classiques\u2014Essai sur les Fondements de la Logique, Traduit du Portugais et Compl\u00e9t\u00e9 par Jean-Yves B\u00e9ziau; Masson."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ganter, B., and Wille, R. (1999). Formam Concept Analysis, Mathematical Foundations, Springer.","DOI":"10.1007\/978-3-642-59830-2"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough Sets","volume":"11","author":"Pawlak","year":"1982","journal-title":"Int. J. Comput. Inf. Sci."},{"key":"ref_15","unstructured":"Descl\u00e9s, J.-P., Pascu, A.C., and Biskri, I. A Rough Sets Approach for defining the Notion of Quasi Topology Structure. to be submitted."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/3\/104\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T08:45:11Z","timestamp":1718873111000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/3\/104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,4]]},"references-count":15,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["axioms8030104"],"URL":"https:\/\/doi.org\/10.3390\/axioms8030104","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,9,4]]}}}
