Quantum logic as a dynamic logic

Alexandru Baltag, Sonja Smets*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

30 Citations (Scopus)
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Abstract

We address the old question whether a logical understanding of Quantum Mechanics requires abandoning some of the principles of classical logic. Against Putnam and others (Among whom we may count or not E. W. Beth, depending on how we interpret some of his statements), our answer is a clear "no". Philosophically, our argument is based on combining a formal semantic approach, in the spirit of E. W. Beth's proposal of applying Tarski's semantical methods to the analysis of physical theories, with an empirical-experimental approach to Logic, as advocated by both Beth and Putnam, but understood by us in the view of the operational-realistic tradition of Jauch and Piron, i.e. as an investigation of "the logic of yes-no experiments" (or "questions"). Technically, we use the recently-developed setting of Quantum Dynamic Logic (Baltag and Smets 2005, 2008) to make explicit the operational meaning of quantum-mechanical concepts in our formal semantics. Based on our recent results (Baltag and Smets 2005), we show that the correct interpretation of quantum-logical connectives is dynamical, rather than purely propositional. We conclude that there is no contradiction between classical logic and (our dynamic reinterpretation of) quantum logic. Moreover, we argue that the Dynamic-Logical perspective leads to a better and deeper understanding of the "non-classicality" of quantum behavior than any perspective based on static Propositional Logic.

Original languageEnglish
Pages (from-to)285-306
Number of pages22
JournalSynthese
Volume179
Issue number2
DOIs
Publication statusPublished - Mar-2011

Keywords

  • Dynamic Quantum Logic
  • Semantics of Experimental Theories
  • Empirical Conception of Logic
  • Logic of Quantum Actions
  • SPACES

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