Let R be a quasi-order on a compact Hausdorff topological space X. We prove that if X is scattered, then R satisfies the Priestley separation axiom if and only if R is closed in the product space X × X. Furthermore, if X is not scattered, then we show that there is a quasi-order on X that is closed in X × X but does not satisfy the Priestley separation axiom. As a result, we obtain a new charac...

In this paper, we extend some results obtained by A. Amroune and B. Davvaz in [1]. More precisely, we will develop a representation theory of intuitionistic fuzzy perfect distributive lattices in the finite case. To that end, we introduce the notion of intuitionistic fuzzy perfect distributive lattices and the one of fuzzy perfect Priestley spaces. In this way, the results of A. Amroune and B. ...

In this note we introduce and study algebras ( L , V, A, 1, 0,l) of type (2,2,1,1,1) such that ( L , V, A, 0 , l ) is a bounded distributive lattice and -,is an operator that satisfies the conditions -,(a V b ) = -,a A -,b and -0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras o...

Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of Abstract Algebraic Logic. In [4], a Priestley-style duality is established between the category of positive modal alg...

A rescaling of variables changes the Priestley-Taylor parameter value in complementary relationship evaporation for optimal performance.