The deduction theorem for quantum logic—some negative results

Journal of Symbolic Logic 55 (2):615-625 (1990)
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Abstract

We prove that no logic (i.e. consequence operation) determined by any class of orthomodular lattices admits the deduction theorem (Theorem 2.7). We extend those results to some broader class of logics determined by ortholattices (Corollary 2.6)

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Citations of this work

Topos Theoretic Quantum Realism.Benjamin Eva - 2017 - British Journal for the Philosophy of Science 68 (4):1149-1181.
Quantum logic in intuitionistic perspective.Bob Coecke - 2002 - Studia Logica 70 (3):411-440.
Some Properties of Orthologics.Yutaka Miyazaki - 2005 - Studia Logica 80 (1):75-93.

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References found in this work

Algebraic aspects of deduction theorems.Janusz Czelakowski - 1985 - Studia Logica 44 (4):369 - 387.
An axiom system for the modular logic.Jerzy Kotas - 1967 - Studia Logica 21 (1):17 - 38.
Orthomodular Logic.Gudrun Kalmbach - 1974 - Mathematical Logic Quarterly 20 (25‐27):395-406.

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