Orthoimplication algebras

Studia Logica 35 (2):173 - 177 (1976)
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Abstract

Orthologic is defined by weakening the axioms and rules of inference of the classical propositional calculus. The resulting Lindenbaum-Tarski quotient algebra is an orthoimplication algebra which generalizes the author's implication algebra. The associated order structure is a semi-orthomodular lattice. The theory of orthomodular lattices is obtained by adjoining a falsity symbol to the underlying orthologic or a least element to the orthoimplication algebra.

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10.1007/bf02120879

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Citations of this work

Sequent Calculi for Orthologic with Strict Implication.Tomoaki Kawano - 2022 - Bulletin of the Section of Logic 51 (1):73-89.
Unified quantum logic.Mladen Pavičić - 1989 - Foundations of Physics 19 (8):999-1016.

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References found in this work

An algebraic approach to non-classical logics.Helena Rasiowa - 1974 - Warszawa,: PWN - Polish Scientific Publishers.
The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
The Mathematics of Metamathematics.Donald Monk - 1963 - Journal of Symbolic Logic 32 (2):274-275.
An Algebraic Approach to Non-Classical Logics.Anne Preller - 1977 - Journal of Symbolic Logic 42 (3):432-432.

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