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      Using the Set Equality Method (SEM) to Determine the Validity of Categorical Syllogisms

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            Abstract

            A description is provided of a method – the Set Equality Method (SEM) – to determine the validity, or lack of validity, of each categorical syllogism. A justification is given for the presentation of a new method to solve a problem which has already been solved using different approaches. First, the SEM assigns an equality of certain sets (or two of those equalities in specific cases as will be indicated) to each of the categorical propositions composing each syllogism considered – that is, to each of the two premises and to the conclusion. Each syllogism considered is valid if and only if a) it is possible to select one of those equalities corresponding to one of the premises such that one of its members is a certain set and the other of those equalities corresponding to the other premise such that one of its members is a subset of the set mentioned, and b) it is possible to deduce an equality corresponding to the conclusion of the two equalities corresponding to the premises. In some cases, as will be specified, it is possible to provide a second test for the validity of a syllogism whose validity was already proven, thus providing information about the logical form of categorical syllogisms.

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            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            9 February 2022
            Affiliations
            [1 ] Universidad Nacional, Costa Rica
            [2 ] Universidad Cenfotec, Costa Rica
            Author notes
            Article
            10.14293/S2199-1006.1.SOR-.PP8EZJC.v1
            2a1242cc-5c84-4c8e-abd8-0a8dd72c1921

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .


            All data generated or analysed during this study are included in this published article (and its supplementary information files).
            Artificial intelligence,Logic & Set theory
            categorical syllogisms,categorical propositions,set theory,set equalities

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