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Overlap Algebras: a Constructive Look at Complete Boolean Algebras [PDF]
Logical Methods in Computer Science, 2020 The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set.
Francesco Ciraulo, Michele Contente
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Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras.
Zdenka Riecanová
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Lattices of (Generalized) Fuzzy Ideals in Double Boolean Algebras [PDF]
Transactions on Fuzzy Sets and Systems, 2023 This paper develops the notion of fuzzy ideal and generalized fuzzy ideal on double Boolean algebra (dBa). According to Rudolf Wille, a double Boolean algebra $\underline{D}:=(D, \sqcap, \sqcup, \neg, \lrcorner, \bot, \top)$ is an algebra
Fernand Kuiebove Pefireko
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EPiC Series in Computing, 2013 Using Vaggione's concept of central element in a double pointed algebra, weintroduce the notion of Boolean like variety as a generalisation ofBoolean algebras to an arbitrary similarity type. Appropriately relaxing therequirement that every element be central in any member of the variety, weobtain the more general class of semi-Boolean like varieties ...
Salibra, A +3 more
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A Category of Ordered Algebras Equivalent to the Category of Multialgebras
Bulletin of the Section of Logic, 2023 It is well known that there is a correspondence between sets and complete, atomic Boolean algebras (\(\textit{CABA}\)s) taking a set to its power-set and, conversely, a complete, atomic Boolean algebra to its set of atomic elements.
Marcelo Esteban Coniglio +1 more
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Digital Circuit Design Utilizing Equation Solving over ‘Big’ Boolean Algebras [PDF]
International Journal of Mathematical, Engineering and Management Sciences, 2018 A task frequently encountered in digital circuit design is the solution of a two-valued Boolean equation of the form h(X,Y,Z)=1, where h: B_2^(k+m+n)→ B_2 and X,Y, and Z are binary vectors of lengths k, m, and n, representing inputs, intermediary values,
Ali Muhammad Ali Rushdi, Waleed Ahmad
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Fuzzy n-fold obstinate ideals in mv -algebras [PDF]
Journal of Hyperstructures, 2019 . In this paper, we introduce the notion of n-fold Boolean ideals of an MV -algebra and consider the quotient algebras induced by n-fold Boolean ideals. Also we prove that I is a n-fold Boolean ideal of an MV -algebra if and only if A/I is a n+1-bounded ...
Fereshteh Forouzesh
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The three types of normal sequential effect algebras [PDF]
Quantum, 2020 A sequential effect algebra (SEA) is an effect algebra equipped with a $\textit{sequential product}$ operation modeled after the Lüders product $(a,b)\mapsto \sqrt{a}b\sqrt{a}$ on C$^*$-algebras.
Abraham Westerbaan +2 more
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De Morgan Functions and Free De Morgan Algebras
Demonstratio Mathematica, 2014 It is commonly known that the free Boolean algebra on n free generators is isomorphic to the Boolean algebra of Boolean functions of n variables. The free bounded distributive lattice on n free generators is isomorphic to the bounded lattice of monotone ...
Movsisyan Yu. M. +2 more
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Mutually Exclusive Nuances of Truth in Moisil Logic [PDF]
Scientific Annals of Computer Science, 2015 Moisil logic, having as algebraic counterpart Łukasiewicz-Moisil algebras, provides an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events.
D. Diaconescu, I. Leuștean
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