New optimal tests of quantum nonlocality

We explore correlation polytopes to derive a set of all Boole-Bell type conditions of possible classical experience which are both maximal and complete. These are compared with the respective quantum expressions for the Greenberger-Horne-Zeilinger (GHZ) case and for two particles with spin state measurements along three directions.Comment: 10 page

Roots and (re)sources of value (in)definiteness versus contextuality. A contribution to the Pitowsky Volume in memory of Itamar Pitowsky (1950--2010)

In Itamar Pitowsky's reading of the Gleason and the Kochen-Specker theorems, in particular, his Logical Indeterminacy Principle, the emphasis is on the value indefiniteness of observables which are not within the preparation context. This is in stark contrast to the prevalent term {\em contextuality} used by many researchers in informal, heuristic yet omni-realistic and potentially misleading ways. This paper discusses both concepts and argues in favor of value indefiniteness in all but a continuum of contexts intertwining in the vector representing a single pure (prepared) state. Even more restrictively, and inspired by operationalism but not justified by Pitowsky's Logical Indeterminacy Principle or similar, one could identify with a "quantum state" a single quantum context -- aka the respective maximal observable, or, in terms of its spectral decomposition, the associated orthonormal basis - from the continuum of intertwining context, as per the associated maximal observable actually or implicitly measured.Comment: 11 pages, revised and polished, discussion on joint probabilities of observables in different contexts adde

Natural deduction and arbitrary objects

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43180/1/10992_2004_Article_BF00542649.pd