Displaying similar documents to “On an algebraic and Kripke semantics for intermediate logics”

On the Leibniz congruences

Josep Font (1993)

Banach Center Publications

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The aim of this paper is to discuss the motivation for a new general algebraic semantics for deductive systems, to introduce it, and to present an outline of its main features. Some tools from the theory of abstract logics are also introduced, and two classifications of deductive systems are analysed: one is based on the behaviour of the Leibniz congruence (the maximum congruence of a logical matrix) and the other on the behaviour of the Frege operator (which associates to every theory...

Algebraic Approach to Algorithmic Logic

Grzegorz Bancerek (2014)

Formalized Mathematics

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We introduce algorithmic logic - an algebraic approach according to [25]. It is done in three stages: propositional calculus, quantifier calculus with equality, and finally proper algorithmic logic. For each stage appropriate signature and theory are defined. Propositional calculus and quantifier calculus with equality are explored according to [24]. A language is introduced with language signature including free variables, substitution, and equality. Algorithmic logic requires a bialgebra...

Polyadic algebras over nonclassical logics

Don Pigozzi, Antonino Salibra (1993)

Banach Center Publications

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The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.

An algebraic and Kripke-style approach to a certain extension of intuitionistic logic

Cecylia Rauszer

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CONTENTSIntroduction............................................................................... 5Chapter I. Semi-Boolean algebras 1. Semi-Boolean algebras....................................... 8 2. Q-filters in semi-Boolean algebras............................ 11 3. Extensions of semi-Boolean algebras...................... 15Chapter II. Algebraic and semantic modelsfor Heyting-Brouwer logic 1. Preliminaries.......................................................... 17 2. Algebraic...

From two- to four-valued logic

Chris Brink (1993)

Banach Center Publications

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The purpose of this note is to show that a known and natural four-valued logic co-exists with classical two-valued logic in the familiar context of truth tables. The tool required is the power construction.