Weakly Intuitionistic Quantum Logic

Ronnie Hermens*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In this article von Neumann's proposal that in quantum mechanics projections can be seen as propositions is followed. However, the quantum logic derived by Birkhoff and von Neumann is rejected due to the failure of the law of distributivity. The options for constructing a distributive logic while adhering to von Neumann's proposal are investigated. This is done by rejecting the converse of the proposal, namely, that propositions can always be seen as projections. The result is a weakly Heyting algebra for describing the language of quantum mechanics.

Original languageEnglish
Pages (from-to)901-913
Number of pages13
JournalStudia Logica
Volume101
Issue number5
DOIs
Publication statusPublished - Oct-2013

Keywords

  • Quantum logic
  • Intuitionistic logic
  • Weakly Heyting algebras

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