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The paper introduces the concept of B-Almost distributive fuzzy lattice (BADFL) in terms of its principal ideal fuzzy lattice. Necessary and sufficient conditions for an ADFL to become a B-ADFL are investigated. We also prove the equivalency of B-algebra and B-fuzzy algebra. In addition, we extend PSADL to PSADFL and prove that B-ADFL implies PSADFL.
This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view...
This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the Grzegorczyk’s system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to dissimilarities,...
One of the logic defined by Richard Epstein in a context of an analysis of subject matter relationship is Symmetric Relatedness Logic S. In the monograph [2] we can find some open problems concerning relatedness logic, a Post-style completeness theorem for logic S is one of them. Our paper introduces a solution of this metalogical issue.
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