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Open AccessArticle

Logic of Typical and Atypical Instances of a Concept—A Mathematical Model

1
Sens, Texte, Informatique, Histoire (STIH), Université de Paris Sorbonne, 75005 Paris, France
2
Laboratoire des Sciences et Techniques de l’Information, de la Communication et de la Connaissance (Lab-STICC), Université de Brest, 29200 Brest, France
*
Authors to whom correspondence should be addressed.
Axioms 2019, 8(3), 104; https://doi.org/10.3390/axioms8030104
Received: 10 July 2019 / Revised: 18 August 2019 / Accepted: 21 August 2019 / Published: 4 September 2019
(This article belongs to the Special Issue Deductive Systems)
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 “exceptions”. Finally, we show that the structural part of LTA can be modeled by a quasi topology structure (QTS). View Full-Text
Keywords: logic of typical and atypical instances (LTA); logic of determination of objects (LDO); quasi topology structure (QTS); concept; object; typical object; atypical object; lattice; filter; ideal logic of typical and atypical instances (LTA); logic of determination of objects (LDO); quasi topology structure (QTS); concept; object; typical object; atypical object; lattice; filter; ideal
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Desclés, J.-P.; Pascu, A.C. Logic of Typical and Atypical Instances of a Concept—A Mathematical Model. Axioms 2019, 8, 104.

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