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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Bibliographic Details
Published in:2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 83 - 92
Main Author: Jacobs, Bart
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2013
Subjects:
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
Online Access:Get full text
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Summary: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.
ISBN:1479904139
9781479904136
ISSN:1043-6871
DOI:10.1109/LICS.2013.13