Search results for "Łukasiewicz logic"

showing 3 items of 3 documents

The Infinite-Valued Łukasiewicz Logic and Probability

2017

The paper concerns the algebraic structure of the set of cumulative distribution functions as well as the relationship between the resulting algebra and the infinite-valued Łukasiewicz algebra. The paper also discusses interrelations holding between the logical systems determined by the above algebras. Zadanie „ Wdrożenie platformy Open Journal System dla czasopisma „ Bulletin of the Section of Logic” finansowane w ramach umowy 948/P-DUN/2016 ze środków Ministra Nauki i Szkolnictwa Wyższego przeznaczonych na działalność upowszechniającą naukę.

Discrete mathematicsLogicprobabilityconsequence relationCumulative distribution functionPhilosophy03G20the infinite-valued standard Łukasiewicz algebracumulative distribution functionŁukasiewicz logic06D3060A05MathematicsBulletin of the Section of Logic
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Probabilistic Interpretations of Predicates

2016

In classical logic, any m-ary predicate is interpreted as an m-argument two-valued relation defined on a non-empty universe. In probability theory, m-ary predicates are interpreted as probability measures on the mth power of a probability space. m-ary probabilistic predicates are equivalently semantically characterized as m-dimensional cumulative distribution functions defined on \(\mathbb {R}^m\). The paper is mainly concerned with probabilistic interpretations of unary predicates in the algebra of cumulative distribution functions defined on \(\mathbb {R}\). This algebra, enriched with two constants, forms a bounded De Morgan algebra. Two logical systems based on the algebra of cumulative…

Discrete mathematicsUnary operationComputer Science::Logic in Computer ScienceCumulative distribution functionClassical logicProbabilistic logicRandom variableŁukasiewicz logicDe Morgan algebraMathematicsProbability measure
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Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras

2013

AbstractWe prove that the unification type of Łukasiewicz (infinite-valued propositional) logic and of its equivalent algebraic semantics, the variety of MV-algebras, is nullary. The proof rests upon Ghilardiʼs algebraic characterisation of unification types in terms of projective objects, recent progress by Cabrer and Mundici in the investigation of projective MV-algebras, the categorical duality between finitely presented MV-algebras and rational polyhedra, and, finally, a homotopy-theoretic argument that exploits lifts of continuous maps to the universal covering space of the circle. We discuss the background to such diverse tools. In particular, we offer a detailed proof of the duality …

Fundamental groupPure mathematicsUnificationŁukasiewicz logic; Unification; Projective MV-algebras; Rational polyhedra; Fundamental group; Covering spaceLogicCovering spaceDuality (mathematics)Projective MV-algebrasMV-algebraCovering spaceŁukasiewicz logicRational polyhedraAlgebraAlgebraic semanticsUnificationVariety (universal algebra)Algebraic numberŁukasiewicz logicMathematicsAnnals of Pure and Applied Logic
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