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The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp orthoalgebras is isomorphic to the category of D-posets. A completeness theorem for some partial logics based on unsharp orthoalgebras, orthoalgebras and orthomodular posets is proved. 相似文献
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Quantum MV algebras 总被引:1,自引:0,他引:1
Roberto Giuntini 《Studia Logica》1996,56(3):393-417
We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras and we show that the class of all effects of any Hilbert space gives rise to an example of such a structure. We investigate some properties of QMV algebras and we prove that QMV algebras represent non-idempotent extensions of orthomodular lattices.I should like to thank Prof. M.L. Dalla Chiara and Dr. P. Minari for many interesting comments and remarks.
Daniele Mundici 相似文献
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We discuss the interrelations between BCK-algebras and posets with difference. Applications are given to bounded commutative BCK-algebras, difference posets, MV-algebras, quantum MV-algebras and orthoalgebras. 相似文献
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This paper uses a non-distributive system of Boolean fractions (a|b), where a and b are 2-valued propositions or events, to express uncertain conditional propositions and conditional events. These Boolean
fractions, ‘a if b’ or ‘a given b’, ordered pairs of events, which did not exist for the founders of quantum logic, can better represent uncertain conditional
information just as integer fractions can better represent partial distances on a number line. Since the indeterminacy of
some pairs of quantum events is due to the mutual inconsistency of their experimental conditions, this algebra of conditionals can express indeterminacy. In fact, this system is able to express the crucial quantum concepts
of orthogonality, simultaneous verifiability, compatibility, and the superposition of quantum events, all without resorting
to Hilbert space. A conditional (a|b) is said to be “inapplicable” (or “undefined”) in those instances or models for which b is false. Otherwise the conditional takes the truth-value of proposition a. Thus the system is technically 3-valued, but the 3rd value has nothing to do with a state of ignorance, nor to some half-truth.
People already routinely put statements into three categories: true, false, or inapplicable. As such, this system applies
to macroscopic as well as microscopic events. Two conditional propositions turn out to be simultaneously verifiable just in
case the truth of one implies the applicability of the other. Furthermore, two conditional propositions (a|b) and (c|d) reside in a common Boolean sub-algebra of the non-distributive system of conditional propositions just in case b=d, their conditions are equivalent. Since all aspects of quantum mechanics can be represented with this near classical logic,
there is no need to adopt Hilbert space logic as ordinary logic, just a need perhaps to adopt propositional fractions to do
logic, just as we long ago adopted integer fractions to do arithmetic. The algebra of Boolean fractions is a natural, near-Boolean
extension of Boolean algebra adequate to express quantum logic. While this paper explains one group of quantum anomalies,
it nevertheless leaves no less mysterious the ‘influence-at-a-distance’, quantum entanglement phenomena. A quantum realist
must still embrace non-local influences to hold that “hidden variables” are the measured properties of particles. But that
seems easier than imaging wave-particle duality and instant collapse, as offered by proponents of the standard interpretation
of quantum mechanics.
Partial support for this work is gratefully acknowledged from the In-House Independent Research Program and from Code 2737
at the Space & Naval Warfare Systems Center (SSC-SD), San Diego, CA 92152-5001. Presently this work is supported by Data Synthesis,
2919 Luna Avenue, San Diego, CA 92117. 相似文献
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