Quantum contextuality implies a logic that does not obey the principle of bivalence

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Abstract

In the paper, a value assignment for projection operators relating to a quantum system is equated with assignment of truth values to the propositions associated with these operators. In consequence, the Kochen–Specker theorem (its localized variant, to be exact) can be treated as the statement that a logic of those projection operators does not obey the principle of bivalence. This implies that such a logic has a gappy (partial) semantics or many-valued semantics.

Original languageEnglish
Pages (from-to)151-159
Number of pages9
JournalQuantum Studies: Mathematics and Foundations
Volume6
Issue number2
DOIs
StatePublished - 1 Jun 2019

Keywords

  • Contextuality
  • Kochen–Specker theorem
  • Many-valued semantics
  • Partial semantics
  • Quantum mechanics
  • Truth values

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics

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