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Computation of Aristotle's and Gergonne's syllogisms

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Abstract

A connection between Aristotle's syllogistic and the calculus of relations is investigated. Aristotle's and Gergonne's syllogistics are considered as some algebraic structures. It is proved that Gergonne's syllogistic is isomorphic to closed elements algebra of a proper approximation relation algebra. This isomorphism permits to evaluate Gergonne's syllogisms and also Aristotle's syllogisms, laws of conversion and relations in the “square of oppositions” by means of regular computations with Boolean matrices.

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  1. Academy of Science of the BSSR Institute of Linguistics, Akademicheskaja str. 25, 220600, Minsk GSP, USSR

    S. N. Furs

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  1. S. N. Furs
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Furs, S.N. Computation of Aristotle's and Gergonne's syllogisms. Stud Logica 46, 209–225 (1987). https://doi.org/10.1007/BF00372546

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  • DOI: https://doi.org/10.1007/BF00372546

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