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Maps on a quantum logic

Soft Computing, 2009
Let \(L\) be an orthomodular lattice. The author introduces a class \(\Gamma\) of functions \(G: L \times L \to L\) and studies their properties. \(\Gamma\) splits into eight subclasses \(\Gamma_i\) according to the values of each \(G\) in the points \((O,O)\), \((O,I)\) and \((I,I)\).
Olga Nánásiová, Lubica Valásková
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Concrete Quantum Logics

International Journal of Theoretical Physics, 2000
The paper is a remarkable survey of recent results on concrete (set-representable) quantum logics, which seem to be significant within quantum axiomatics and also other areas of mathematics. Especially various results and open problems concerning compact-like concrete logics (with a natural generalization of compatibility) and measure theory on ...
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Unified quantum logic

Foundations of Physics, 1989
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.
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Quantum Logics and Instruments

International Journal of Theoretical Physics, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Conditional in Quantum Logic

Synthese, 1974
Besides the physicomathematical controversy concerning the ‘phenomenological justification’ and the specific formal structure of the calculus known as quantum logic (QL), there is a philosophical controversy concerning whether this ‘calculus of experimental propositions’ is properly speaking a logic rather than simply an algebraic structure only ...
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Quantum Logic and Decoherence

International Journal of Theoretical Physics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Logic and Quantum Logic

1976
Strict analysis of quantum theory has shown that for certain propositions about quantum-mechanical systems some laws of logic lose their validity. This assertion is justified by pointing out that quantum mechanics is an empirically verified theory.
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Regularity in Quantum Logic

International Journal of Theoretical Physics, 1998
A quantum mechanical system is said to be regular if every pairwise compatible set of questions of it is compatible. In the paper, the author shows that this property is a consequence of associating questions of the system with direct product decompositions of its state space if one assumes that the true and false questions correspond to the binary ...
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Quantum Computational Logic

International Journal of Theoretical Physics, 2003
In [\textit{G. Cattaneo, M. Dalla Chiara, R. Giuntini} and \textit{R. Leporini}, An unsharp logic from quantum computation. Int. J. Theor. Phys. (in press)], the authors developed a new form of quantum logic (called \textit{quantum computational logic}) based on the theory of quantum computation.
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Typed Quantum Logic

International Journal of Theoretical Physics, 2003
This paper develops a higher-order version of orthomodular logic in terms of type theory. The soundness and completeness theorems are established.
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