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Natural Deduction for Quantum Logic


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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  1. We are using slightly different symbols and names than those used in [13].


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Correspondence to K. Tokuo.

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Tokuo, K. Natural Deduction for Quantum Logic. Log. Univers. (2022).

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  • Quantum logic
  • Natural deduction
  • \(\lambda \)-Calculus
  • Curry–Howard isomorphism
  • Normalization

Mathematics Subject Classification

  • Primary 03G12
  • Secondary 03B60
  • 03F03
  • 68N18
  • 81P10