1,720,970 research outputs found
Standard completeness of Hájek basic logic and decompositions of BL-chains
Get PDFThe aim of this paper is to survey the tools needed to prove the standard completeness of Hájek Basic Logic with respect to continuous t-norms. In particular, decompositions of totally ordered BL-algebras into simpler components are considered in some detail.Fil: Cignoli, Roberto Leonardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Torrens Torrell, Antoni. Universidad de Barcelona; Españ
Free Algebras in Varieties of Glivenko MTL-algebras Satisfying the Equation 2(x2) = (2x)2
Get PDFThe aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras.Fil: Cignoli, Roberto Leonardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Torrens Torrell, Antoni. Universidad de Barcelona; Españ
Decomposability of free Łukasiewicz implication algebras
Get PDFŁukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-Łukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127-133, 1978. The aim of this paper is to study the direct decomposability of free Łukasiewicz implication algebras. We show that freely generated algebras are directly indecomposable. We also study the direct decomposability in free algebras of all its proper subvarieties and show that infinitely freely generated algebras are indecomposable, while finitely free generated algebras can be only decomposed into a direct product of two factors, one of which is the two-element implication algebra.Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Torrens Torrell, Antoni. Universidad de Barcelona; Españ
Orthomodular logic. A proposal of a logic for quantum physics
No full textTreballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Antoni Torrens TorrellClassical physics are widely known to be closely related to classical propositional calculus, whereas there does not exist a strongly settled analogue for quantum physics. We will focus on orthomodular logic and, in particular, we will study two different sentential logics that have been purposed with this aim over othomodular lattices. Thus, we will introduce their semantics from the foundations of quantum mechanics and presenting them by means of two different approaches whose equivalence will be shown. Additionally, we will give an adequate syntax for each proposal, the first one due to M. L. dalla Chiara and R. Giuntini and the last one to G. Kalmbach. Finally, completeness theorems will be discussed as well as the results that have
been reached
Elements crisipians en àlgebres d-completes i àlgebres de Sales
No full textEl autor estudia los elementos de comportamiento clásico, o crisipianos, en álgebras d-completas (introducidas por él mismo como el sustrato algebraico de las lógicas completas) y en álgebras de Sales (sustrato algebraico de las lógicas multivaloradas). Da caracterizaciones de estos elementos en ambos casos. Estudia la relación de dichos elementos con los espectros irreducible, primo y completamente irreducible. Además obtiene que el conjunto de elementos crisipianos de un álgebra de Sales es una subálgebra y es un álgebra de Abbott (o de implicación)
W-algebras which are boolean products of members of SR[1] and CW-algebras
Get PDFPreprint enviat per a la seva publicació en una revista científica: Stud Logica 46, 265–274 (1987). [https://doi.org/10.1007/BF00372551]We show that the class of all isomorphic images of Booleans producís of members of SR[1] is the class of all Archimedean W-algebras. And the class of all isomorphic images of CW-lgebras is the class of all W-algebras such that the family of all minimal prime implicative filters is the family of all Stone ultrafilters
Cadenes de Sales discretes
No full textThe Sales algebras are the substract of some positive implicational calculi . As a first aproximation to their representation we study the Sales algebras that are discrete and linear . In this paper we present a caracteritzation of the finite Sales algebras and we give also an infinite discrete Sales algebra such that we can identify with it every linear infinite simple Sales algebra with a penultimate element . The most interes ting result is the first Theorem In it we show that certain elements of the Sales algebras generate finit linear subalgebras of them
Estudi i algebraització de certes lògiques: Àlgebres d-completes.
Get PDFEn aquesta tesi doctoral s'obtenen i estudien les àlgebres d-completes com les àlgebres implicatives associades a uns determinats càlculs proposicionals implicatius, que satisfan un teorema de la deducció feble i contenen als càlculs proposicionals multi-valorats donats per Lukasiewicz. Per altra banda, també s'estudien els sistemes deductius d'aquestes àlgebres
Elements crisipians en àlgebres d-completes i àlgebres de Sales
No full textEl autor estudia los elementos de comportamiento clásico, o crisipianos, en álgebras d-completas (introducidas por él mismo como el sustrato algebraico de las lógicas completas) y en álgebras de Sales (sustrato algebraico de las lógicas multivaloradas). Da caracterizaciones de estos elementos en ambos casos. Estudia la relación de dichos elementos con los espectros irreducible, primo y completamente irreducible. Además obtiene que el conjunto de elementos crisipianos de un álgebra de Sales es una subálgebra y es un álgebra de Abbott (o de implicación)
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