Quantum logic as a dynamic logic

We address the old question whether a logical understanding of Quantum Mechanics requires abandoning some of the principles of classical logic. Against Putnam and others1 , 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 [4, 6] to make explicit the operational meaning of quantum-mechanical concepts in our formal semantics. Based on our recent results [4], we show that the correct interpretation of quantum-logical connectives is dynamical, rather than purely proposit...

• Type: Journal
• Year: 2011
• Where: SYNTHESE
• Authors: Alexandru Baltag, Sonja Smets
• Keywords: Classical Logic, Formal Semantics, Logic, SYNTHESE 2011