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Partial classical logic, the Lindenbaum property and the hidden variable problem

  • M. Dalla Chiara
  • R. Giuntini
  • R. Greechie
Part of the Trends in Logic book series (TREN, volume 22)

Abstract

Orthologic and orthomodular quantum logic are examples of total logics: their language is syntactically closed under the logical connectives and any molecular sentence always has a meaning both in the algebraic and in the Kripkean semantics. We will now investigate a form of quantum logic (first proposed by Kochen and Specker (1965b)) based on a different idea. From the semantic point of view, the crucial relation will be represented by a compatibility relation, that may hold between the meanings of two sentences. As expected, the intended physical interpretation of the compatibility relation will be the following: two sentences α and β will have compatible meanings iff α and β can be simultaneously tested.

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Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • M. Dalla Chiara
    • 1
  • R. Giuntini
    • 2
  • R. Greechie
    • 3
  1. 1.University of FlorenceItaly
  2. 2.University of CagliariItaly
  3. 3.Louisiana Tech UniversityRustonUSA

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