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Orthoimplication algebras
Studia Logica 35 (2):173 - 177 (1976)
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.Other Versions
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Citations of this work
An axiom system for orthomodular quantum logic.Gary M. Hardegree - 1981 - Studia Logica 40 (1):1 - 12.
Deduction, Ordering, and Operations in Quantum Logic.Normal D. Megill & Mladen Pavičić - 2002 - Foundations of Physics 32 (3):357-378.
Sequent Calculi for Orthologic with Strict Implication.Tomoaki Kawano - 2022 - Bulletin of the Section of Logic 51 (1):73-89.
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.
Rasiowa Helena. An algebraic approach to non-classical logics. Studies in logic and the foundations of mathematics, vol. 78. North-Holland Publishing Company, Amsterdam and London, and American Elsevier Publishing Company, Inc., New York, 1974, xv + 403 pp. [REVIEW]Anne Preller - 1977 - Journal of Symbolic Logic 42 (3):432-432.
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