Computation of Aristotle's and gergonne's syllogisms

Studia Logica 46 (3):209 - 225 (1987)
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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DOI 10.1007/BF00372546
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On the Calculus of Relations.Alfred Tarski - 1941 - Journal of Symbolic Logic 6 (3):73-89.
The Gergonne Relations.J. A. Faris - 1955 - Journal of Symbolic Logic 20 (3):207-231.

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