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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.
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