Natural Deduction for Quantum Logic

Logica Universalis 16 (3):469-497 (2022)
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Abstract

This paper presents a natural deduction system for orthomodular quantum logic. The system is shown to be provably equivalent to Nishimura’s quantum sequent calculus. Through the Curry–Howard isomorphism, quantum $$\lambda $$ -calculus is also introduced for which strong normalization property is established.

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10.1007/s11787-022-00307-7

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The conditional in quantum logic.Gary M. Hardegree - 1974 - Synthese 29 (1-4):63 - 80.
Implication connectives in orthomodular lattices.L. Herman, E. L. Marsden & R. Piziak - 1975 - Notre Dame Journal of Formal Logic 16 (3):305-328.

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