An axiom system for orthomodular quantum logic

Studia Logica 40 (1):1 - 12 (1981)
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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References found in this work BETA
R. I. Goldblatt (1974). Semantic Analysis of Orthologic. Journal of Philosophical Logic 3 (1/2):19 - 35.
Robert Piziak (1974). Orthomodular Lattices as Implication Algebras. Journal of Philosophical Logic 3 (4):413 - 418.

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