Search results for "consequence relation"

showing 2 items of 2 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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Modal Consequence Relations Extending S4.3: An Application of Projective Unification

2016

We characterize all finitary consequence relations over $\mathbf{S4.3}$ , both syntactically, by exhibiting so-called (admissible) passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic $L$ extending $\mathbf{S4}$ has projective unification if and only if $L$ contains $\mathbf{S4.3}$ . In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the known results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relation…

projective unificationPure mathematicsUnificationLogicFinite model property02 engineering and technology68T15Lattice (discrete subgroup)01 natural sciencesadmissible rulesComputer Science::Logic in Computer Science0202 electrical engineering electronic engineering information engineeringCountable setFinitaryHeyting algebra08C150101 mathematics03B45MathematicsDiscrete mathematics010102 general mathematicsquasivarietiesModal logicstructural completenessconsequence relations03B35Distributive property06E25$\mathbf{S4.3}$S4.3020201 artificial intelligence & image processingNotre Dame Journal of Formal Logic
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