Correlations, Contextuality and Quantum Logic

J Philos Logic (2013) 42:483–499 DOI 10.1007/s10992-013-9272-8 Correlations, Contextuality and Quantum Logic Allen Stairs · Jeffrey Bub Received: 28 February 2010 / Accepted: 13 February 2011 / Published online: 2 April 2013 © Springer Science+BusinessMedia Dordrecht 2013 Abstract Quantum theory is a probabilistic theory that embodies notoriously striking correlations, stronger than any that classical theories allow but not as strong as those of hypothetical ‘super-quantum’ theories. This raises the question ‘Why the quantum?’—whether there is a handful of principles that account for the character of quantum probability.We ask what quantum-logical notions correspond to this investigation. This project isn’t meant to compete with the many beautiful results that information-theoretic approaches have yielded but rather aims to complement that work. Keywords PR-Box · Polytope · Convex set · Logic · Quantum logic