Measurable Spaces and Their Effect Logic

So-called effect algebras and modules are basic mathematical structures that were first identified in mathematical physics, for the study of quantum logic and quantum probability. They incorporate a double negation law p ⊥⊥ = p. Since then it has been realised that these effect structures form a use...

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Vydáno v:2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science s. 83 - 92
Hlavní autor: Jacobs, Bart
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.06.2013
Témata:
Algebra
Atmospheric measurements
duality
effect algebra
Equations
Extraterrestrial measurements
Giry monad
measurable space
Particle measurements
Probabilistic logic
Probabilistic system
Quantum computing
ISBN:1479904139, 9781479904136
ISSN:1043-6871
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Abstract So-called effect algebras and modules are basic mathematical structures that were first identified in mathematical physics, for the study of quantum logic and quantum probability. They incorporate a double negation law p ⊥⊥ = p. Since then it has been realised that these effect structures form a useful abstraction that covers not only quantum logic, but also Boolean logic and probabilistic logic. Moreover, the duality between effect and convex structures lies at the heart of the duality between predicates and states. These insights are leading to a uniform framework for the semantics of computation and logic. This framework has been elaborated elsewhere for settheoretic, discrete probabilistic, and quantum computation. Here the missing case of continuous probability is shown to fit in the same uniform framework. On a technical level, this involves an investigation of the logical aspects of the Giry monad on measurable spaces and of Lebesgue integration.
AbstractList So-called effect algebras and modules are basic mathematical structures that were first identified in mathematical physics, for the study of quantum logic and quantum probability. They incorporate a double negation law p ⊥⊥ = p. Since then it has been realised that these effect structures form a useful abstraction that covers not only quantum logic, but also Boolean logic and probabilistic logic. Moreover, the duality between effect and convex structures lies at the heart of the duality between predicates and states. These insights are leading to a uniform framework for the semantics of computation and logic. This framework has been elaborated elsewhere for settheoretic, discrete probabilistic, and quantum computation. Here the missing case of continuous probability is shown to fit in the same uniform framework. On a technical level, this involves an investigation of the logical aspects of the Giry monad on measurable spaces and of Lebesgue integration.
Author Jacobs, Bart
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Snippet So-called effect algebras and modules are basic mathematical structures that were first identified in mathematical physics, for the study of quantum logic and...
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StartPage 83
SubjectTerms Algebra
Atmospheric measurements
duality
effect algebra
Equations
Extraterrestrial measurements
Giry monad
measurable space
Particle measurements
Probabilistic logic
Probabilistic system
Quantum computing
Title Measurable Spaces and Their Effect Logic
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