- Quantum team logic and Bell's inequalities
- Review of Symbolic Logic
- Volume | Issue number
- 8 | 4
- Pages (from-to)
- Document type
- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
A logical approach to Bell’s Inequalities of quantum mechanics has been introduced by Abramsky and Hardy (Abramsky & Hardy, 2012). We point out that the logical Bell’s Inequalities of Abramsky & Hardy (2012) are provable in the probability logic of Fagin, Halpern and Megiddo (Fagin et al., 1990). 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 (Väänänen, 2007) first to probabilistic team semantics, and then to what we call quantum team semantics.
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© Association for Symbolic Logic 2015
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