Quantum Team Logic and Bell's Inequalities
Logic
2016-03-10 v4
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.
Keywords
Cite
@article{arxiv.1409.5537,
title = {Quantum Team Logic and Bell's Inequalities},
author = {Tapani Hyttinen and Gianluca Paolini and Jouko Väänänen},
journal= {arXiv preprint arXiv:1409.5537},
year = {2016}
}