An axiom system for orthomodular quantum logic

Studia Logica 40 (1):1 - 12 (1981)
Abstract
Logical matrices for orthomodular logic are introduced. The underlying algebraic structures are orthomodular lattices, where the conditional connective is the Sasaki arrow. An axiomatic calculusOMC is proposed for the orthomodular-valid formulas.OMC is based on two primitive connectives — the conditional, and the falsity constant. Of the five axiom schemata and two rules, only one pertains to the falsity constant. Soundness is routine. Completeness is demonstrated using standard algebraic techniques. The Lindenbaum-Tarski algebra ofOMC is constructed, and it is shown to be an orthomodular lattice whose unit element is the equivalence class of theses ofOMC.
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DOI 10.1007/BF01837551
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References found in this work BETA
Semantic Analysis of Orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.
The Conditional in Quantum Logic.Gary M. Hardegree - 1974 - Synthese 29 (1-4):63 - 80.
Modal Propositional Logic on an Orthomodular Basis. I.L. Herman & R. Piziak - 1974 - Journal of Symbolic Logic 39 (3):478-488.
Orthomodular Lattices as Implication Algebras.Robert Piziak - 1974 - Journal of Philosophical Logic 3 (4):413 - 418.
Orthoimplication Algebras.J. C. Abbott - 1976 - Studia Logica 35 (2):173 - 177.

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