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arXiv · 1409.5537

Quantum Team Logic and Bell's Inequalities

Tapani Hyttinen·Gianluca Paolini·Jouko Väänänen
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Abstract

A logical approach to Bell's Inequalities of quantum mechanics has been introduced by Abramsky and Hardy [2]. We point out that the logical Bell's Inequalities of [2] are provable in the probability logic of Fagin, Halpern and Megiddo [4]. Since it is now considered empirically established that quantum mechanics violates Bell's Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell's Inequalities are not provable, and prove a Completeness Theorem for this logic. For this end we generalise the team semantics of dependence logic [7] first to probabilistic team semantics, and then to what we call quantum team semantics.

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Tapani Hyttinen, Gianluca Paolini, Jouko Väänänen. 2016-03-09. Quantum Team Logic and Bell's Inequalities. https://doi.org/10.1017/s1755020315000192

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