A CONSTRUCTION OF HEYTING ALGEBRA ON CATEGORICAL SYLLOGISMS

Abstract

The main purpose of this paper is to define a Heyting algebra on categorical syllogisms. For this aim, we explain categorical syllogisms by the diagrammatic method, which gives us a suitable treatment to logical reasoning with Caroll’s diagrams. In this regard, we represent the quantitative relations between syllogisms’ terms by means of bilateral diagrams. Finally, we construct a system, which is a Heyting algebra, for examining categorical syllogisms by using sets.