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A glimpse of deductive systems in algebra

Dumitru Buşneag, Sergiu Rudeanu (2010)

Open Mathematics

The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.

A short note on lattices allowing disjunctive reasoning.

Enric Trillas, Eloy Renedo, Claudi Alsina (2006)

Mathware and Soft Computing

This short note shows that the scheme of disjunctive reasoning, a or b, not b : a, does not hold neither in proper ortholattices nor in proper de Morgan algebras. In both cases the scheme, once translated into the inequality b' · (a+b) ≤ a, forces the structure to be a boolean algebra.

Alcune proprietà delle algebre di Boole principali

Francesco Lacava (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper some properties of principal Boolean algebras are studied.

Boolean differential operators

Jorge Catumba, Rafael Díaz (2014)

Commentationes Mathematicae Universitatis Carolinae

We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.

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