Search results for "Algebraic logic"

showing 3 items of 3 documents

Lambda substitution algebras

1993

In the paper an algebraic metatheory of type-free λ-calculus is developed. Our version is based on lambda substitution algebras (λSAs), which are just SAs introduced by Feldman (for algebraizing equational logic) enriched with a countable family of unary operations of λ-abstraction and a binary operation of application. Two representation theorems, syntactical and semantic, are proved, what directly provides completeness theorems.

AlgebraDiscrete mathematicsUnary operationBinary operationComputer Science::Logic in Computer ScienceCompleteness (logic)Substitution (algebra)Countable setGödel's completeness theoremEquational logicAlgebraic logicMathematics
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Didactical note: probabilistic conditionality in a Boolean algebra

1996

This note deals with two logical topics and concerns Boolean Algebras from an elementary point of view. First we consider the class of operations on a Boolean Algebra that can be used for modelling ``If-then" propositions. These operations, or Conditionals, are characterized under the hypothesis that they only obey to the Modus Ponens-Inequality, and it is shown that only six of them are boolean two-place functions. Is the Conditional Probability the Probability of a Conditional? This problem will be only considered, with the Material Conditional Operation, on a Boolean Algebra endowed with a finite probability and in three different cases: with the Internal-Conditional Probability, with th…

Conditional operationsFinite probabilitiesProbability of a conditionLògica algebraicaboolean algebrasSettore INF/01 - InformaticaProbabilitatsÀlgebra booleana:03 Mathematical logic and foundations::03G Algebraic logic [Classificació AMS]Boolean algebrasConditional probabilities
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Leon Henkin the Reviewer

2014

In this chapter, we intend to look at Henkin’s reviews, a total of forty-six. The books and papers reviewed deal with a large variety of subjects that range from the algebraic treatment of logical systems to issues concerning the philosophy of mathematics and, not surprisingly—given his active work in mathematical education—one on the teaching of this subject. Most of them were published in The Journal of Symbolic Logic and only one in the Bulletin of the American Mathematical Society. We will start by sorting these works into subjects and continue by providing a brief summary of each of them in order to point out those aspects that are originally from Henkin, and what we take to be mistake…

Mathematical logicPhilosophy of mathematicsConsistency (negotiation)PhilosophyGödelFoundations of mathematicscomputerAlgebraic logicAxiomcomputer.programming_languageEpistemologyMetalogic
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