Natural Deduction for Quantum Logic

Tokuo, Kenji

doi:10.1007/s11787-022-00307-7

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Results 5 (Commutator) the Following Rules Of Inference Are ...1

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2022

2023

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Cited by 2 publications

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“…The development of SOM coincided with development of several other deductive systems that incorporate the Sasaki adjunction. In the Implicational Quantum Logic of Tokuo [84], the Sasaki projection is a primitive logical connective. Furthermore, in the Orthomodular Groupoid Calculus of Fazio, Ledda, Paoli and St. John [14] and the Projective Linear Logic of Lehmann [50], the Sasaki projection is a structural connective, as it is in SOM .…”

Section: Results 5 (Commutator) the Following Rules Of Inference Are ...mentioning

confidence: 99%

A Natural Deduction System for Orthomodular Logic

Kornell¹

2023

The Review of Symbolic Logic

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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: the first is sound for Takeuti’s quantum set theory, and the second is sound for a variant of Weaver’s quantum logic.

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Section: Results 5 (Commutator) the Following Rules Of Inference Are ...mentioning

confidence: 99%