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An axiom system for orthomodular quantum logic

Gary M. Hardegree

Studia Logica 40 (1):1 - 12 (1981)

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Probabilistic logic of quantum observations.A. Sernadas, J. Rasga, C. Sernadas, L. Alcácer & A. B. Henriques - 2019 - Logic Journal of the IGPL 27 (3):328-370.details A probabilistic propositional logic, endowed with a constructor for asserting compatibility of diagonalisable and bounded observables, is presented and illustrated for reasoning about the random results of projective measurements made on a given quantum state. Simultaneous measurements are assumed to imply that the underlying observables are compatible. A sound and weakly complete axiomatisation is provided relying on the decidable first-order theory of real closed ordered fields. The proposed logic is proved to be a conservative extension of classical propositional logic. Download Export citation Bookmark
Unified quantum logic.Mladen Pavičić - 1989 - Foundations of Physics 19 (8):999-1016.details Unified quantum logic based on unified operations of implication is formulated as an axiomatic calculus. Soundness and completeness are demonstrated using standard algebraic techniques. An embedding of quantum logic into a new modal system is carried out and discussed. Download Export citation Bookmark
The Birth of quantum logic.Miklós Rédei - 2007 - History and Philosophy of Logic 28 (2):107-122.details By quoting extensively from unpublished letters written by John von Neumann to Garret Birkhoff during the preparatory phase (in 1935) of their ground-breaking 1936 paper that established quantum logic, the main steps in the thought process leading to the 1936 Birkhoff–von Neumann paper are reconstructed. The reconstruction makes it clear why Birkhoff and von Neumann rejected the notion of quantum logic as the projection lattice of an infinite dimensional complex Hilbert space and why they postulated in their 1936 paper that (...) Download Export citation Bookmark 4 citations
A Natural Deduction System for Orthomodular Logic.Andre Kornell - 2024 - Review of Symbolic Logic 17 (3):910-949.details Orthomodular logic is a weakening of quantum logic in the sense of Birkhoff and von Neumann. Orthomodular logic is shown to be a nonlinear noncommutative logic. Sequents are given a physically motivated semantics that is consistent with exactly one semantics for propositional formulas that use negation, conjunction, and implication. In particular, implication must be interpreted as the Sasaki arrow, which satisfies the deduction theorem in this logic. As an application, this deductive system is extended to two systems of predicate logic: (...) Download Export citation Bookmark 1 citation
Pluralists about Pluralism? Versions of Explanatory Pluralism in Psychiatry.Jeroen Van Bouwel - 2014 - In Thomas Uebel (ed.), New Directions in the Philosophy of Science. Cham: Springer. pp. 105-119.details In this contribution, I comment on Raffaella Campaner’s defense of explanatory pluralism in psychiatry (in this volume). In her paper, Campaner focuses primarily on explanatory pluralism in contrast to explanatory reductionism. Furthermore, she distinguishes between pluralists who consider pluralism to be a temporary state on the one hand and pluralists who consider it to be a persisting state on the other hand. I suggest that it would be helpful to distinguish more than those two versions of pluralism – different understandings (...) Download Export citation Bookmark 5 citations

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