Corpus ID: 237492132

A natural deduction system for orthomodular logic

  title={A natural deduction system for orthomodular logic},
  author={Andre Kornell},
Orthomodular logic is a fragment 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… Expand

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