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QUANTUM TEAM LOGIC AND BELL’S INEQUALITIES

Published online by Cambridge University Press:  11 June 2015

TAPANI HYTTINEN ,
GIANLUCA PAOLINI  and
JOUKO VÄÄNÄNEN
TAPANI HYTTINEN*
Affiliation:
Department of Mathematics and Statistics, University of Helsinki
GIANLUCA PAOLINI*
Affiliation:
Department of Mathematics and Statistics, University of Helsinki
JOUKO VÄÄNÄNEN*
Affiliation:
Department of Mathematics and Statistics, University of Helsinki and University of Amsterdam
*
*DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF HELSINKI FINLAND E-mail: tapani.hyttinen@helsinki.fi
†DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF HELSINKI FINLAND E-mail: gianluca.paolini@helsinki.fi
‡DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF HELSINKI FINLAND and INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION UNIVERSITY OF AMSTERDAM THE NETHERLANDS E-mail: jouko.vaananen@helsinki.fi
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Abstract

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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 4 , December 2015 , pp. 722 - 742
Copyright
Copyright © Association for Symbolic Logic 2015 

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References

BIBLIOGRAOHY

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