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Contexts in quantum, classical and partition logic
 In Handbook of Quantum Logic
, 2006
"... Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud ..."
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Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud
Embedding Quantum Universes in Classical Ones
, 1999
"... this paper; the propositional structure encountered in the quantum mechanics of spin  state measurements of a spin onehalf particle along two directions ( mod p) , that is, the modular, orthocomplemented lattice MO 2 drawn in Fig. 1 ( where p 2 = ( p + ) and q 2 = ( q + ) ) ..."
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Cited by 3 (1 self)
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this paper; the propositional structure encountered in the quantum mechanics of spin  state measurements of a spin onehalf particle along two directions ( mod p) , that is, the modular, orthocomplemented lattice MO 2 drawn in Fig. 1 ( where p 2 = ( p + ) and q 2 = ( q + ) )
Generalizations of Kochen and Specker’s theorem and the effectiveness of Gleason’s theorem
 Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35, 177194
, 2004
"... Abstract. Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s th ..."
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Abstract. Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated. 1. Gleason’s Theorem and Logical Compactness Kochen and Specker’s (1967) theorem (KS) puts a severe constraint on possible hiddenvariable interpretations of quantum mechanics. Often it is considered an improvement on a similar argument derived from Gleason (1957) theorem (see, for example, Held. 2000). This is true in the sense that KS provide an explicit construction of a finite set of rays on which no twovalued homomorphism exists. However, the fact that there is such a finite set follows from Gleason’s theorem using a simple logical compactness argument (Pitowsky 1998, a similar point is made in Bell 1996). The existence of finite sets of rays with other interesting features
Quantum logic. A brief outline
, 2005
"... A more complete introduction of the author can be found in the book ..."
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A more complete introduction of the author can be found in the book
An obstruction based approach to the KochenSpecker theorem
, 1999
"... In [1] it was shown that the Kochen Specker theorem can be written in terms of the nonexistence of global elements of a certain varying set over the category W of boolean subalgebras of projection operators on some Hilbert space H. In this paper, we show how obstructions to the construction of such ..."
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In [1] it was shown that the Kochen Specker theorem can be written in terms of the nonexistence of global elements of a certain varying set over the category W of boolean subalgebras of projection operators on some Hilbert space H. In this paper, we show how obstructions to the construction of such global elements arise, and how this provides a new way of looking at proofs of the theorem.
I. BASIC IDEAS
, 2005
"... Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical evidence of the quantum world. We give a brief outline of quant ..."
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Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical evidence of the quantum world. We give a brief outline of quantum logic, and some of its algebraic properties, such as nondistributivity, whereby emphasis is given to concrete experimental setups related to quantum logical entities. A probability theory based on quantum logic is fundamentally and sometimes even spectacularly different from probabilities based on classical Boolean logic. We give a brief outline of its nonclassical aspects; in particular violations of BooleBell type consistency constraints on joint probabilities, as well as the KochenSpecker theorem, demonstrating in a constructive, finite way the scarcity and even nonexistence of twovalued states interpretable as classical truth assignments. A more complete introduction of the author can be found in the book Quantum Logic (Springer, 1998) PACS numbers: 03.67.Hk,03.65.Ud,03.65.Ta,03.67.Mn
Proposed Running Head: Maximal Beable Subalgebras Please address correspondence to:
, 1999
"... be accessible. ..."