The deduction theorem for quantum logic--some negative results

Journal of Symbolic Logic 55 (2):615-625 (1990)
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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DOI 10.2307/2274651
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References found in this work BETA
Gudrun Kalmbach (1974). Orthomodular Logic. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 20 (25-27):395-406.
Gudrun Kalmbach (1974). Orthomodular Logic. Mathematical Logic Quarterly 20 (25‐27):395-406.

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Benjamin Eva (forthcoming). Topos Theoretic Quantum Realism. British Journal for the Philosophy of Science:axv057.

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