QUASI-DISTRIBUTIVE IMPLICATION GROUPOIDS

Petr Emanovsk´ y

Petr Emanovsk´ y

Keywords: Implication groupoid, ideal, deductive system, congruence kernel, quasidistributivity, quasi-exchange property

Abstract

Distributive implication groupoids as an essential generalization of the implication reduct of intuitionistic logic were introduced and studied by the second author and I. Chajda in [3]. It has been proved that for these algebras ideals, deductive systems and congruence kernels coincide. In the paper the same connection is shown even if the implication groupoid is quasi-distributive.