A study of algebraic logic from the point of view of category theory.
Luis M. Laita · Notre Dame Journal of Formal Logic · 1976
In this paper a model is provided for the bivalued propositional calculus and for Halmos' monadic and polyadic logics, by means of a preorder category which has unions, intersections, nul and conul objects, and a contravariant functor defined on it.The set of propositions and of propositional functions are structured as categories the arrows of which are the implication functors.Quantifiers and logical constants are shown to be special functors.Implications, implications among implications and so on, are described respectively as arrows, functors, natural transformations, etc., so that logical formuli are studied as constructs of the theory of categories.An extension to the study of cylindric algebras is suggested at the end.The paper is an extract of the more important points of a Ph.D.