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Some Properties of Orthologics

Studia Logica 80 (1):75-93 (2005)

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  1. The deduction theorem for quantum logic—some negative results.Jacek Malinowski - 1990 - Journal of Symbolic Logic 55 (2):615-625.
    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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  • Semantic analysis of orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.
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  • The Super-amalgamation Property Of The Variety Of Ortholattices.Yutaka Miyazaki - 1999 - Reports on Mathematical Logic:45-63.
    It is shown that the variety of ortholattices is super-amalgamable. From this fact, it is proved, by an algebraic argument, that the minimum orthologic and its first order predicate extension have the Craig's interpolation property.
     
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