Implicative Quasi-Semi-Lattices

Abstract

In this paper, we introduce implicative quasi-semi-lattices as a generalization of implicative semi-lattices. We give the definition of implicative quasi-semi-lattices and present the related properties of an implicative quasi-semi-lattice. Moreover, we show that there exists an isomorphism between the lattice of filters of an implicative quasi-semi-lattice and the lattice of filter congruences on an implicative quasi-semi-lattice.