Possibilities determine the combinatorial structure of probability polytopes: Foundations of Probability Theory in Psychology and Beyond

Samson Abramsky; Rui Soares Barbosa; Kohei Kishida; Raymond Lal; Shane Mansfield

doi:10.1016/j.jmp.2016.03.006

Possibilities determine the combinatorial structure of probability polytopes: Foundations of Probability Theory in Psychology and Beyond

Samson Abramsky, Rui Soares Barbosa, Kohei Kishida, Raymond Lal, Shane Mansfield

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

Abstract We study the set of no-signalling empirical models on a measurement scenario, and show that the combinatorial structure of the no-signalling polytope is completely determined by the possibilistic information given by the support of the models. This is a special case of a general result which applies to all polytopes presented in a standard form, given by linear equations together with non-negativity constraints on the variables.

Original language	English
Pages (from-to)	58-65
Number of pages	8
Journal	Journal of Mathematical Psychology
Volume	74
Early online date	17 May 2016
DOIs	https://doi.org/10.1016/j.jmp.2016.03.006
Publication status	Published - Oct 2016
Externally published	Yes

Keywords / Materials (for Non-textual outputs)

Contextuality
No-signalling
Quantum information
Polytopes
Face lattice

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10.1016/j.jmp.2016.03.006

1603.07735Accepted author manuscript, 193 KB

http://www.sciencedirect.com/science/article/pii/S0022249616300013

Cite this

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title = "Possibilities determine the combinatorial structure of probability polytopes: Foundations of Probability Theory in Psychology and Beyond",

abstract = "Abstract We study the set of no-signalling empirical models on a measurement scenario, and show that the combinatorial structure of the no-signalling polytope is completely determined by the possibilistic information given by the support of the models. This is a special case of a general result which applies to all polytopes presented in a standard form, given by linear equations together with non-negativity constraints on the variables.",

keywords = "Contextuality, No-signalling, Quantum information, Polytopes, Face lattice",

author = "Samson Abramsky and Barbosa, {Rui Soares} and Kohei Kishida and Raymond Lal and Shane Mansfield",

year = "2016",

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journal = "Journal of Mathematical Psychology",

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AU - Abramsky, Samson

AU - Barbosa, Rui Soares

AU - Kishida, Kohei

AU - Lal, Raymond

AU - Mansfield, Shane

PY - 2016/10

Y1 - 2016/10

N2 - Abstract We study the set of no-signalling empirical models on a measurement scenario, and show that the combinatorial structure of the no-signalling polytope is completely determined by the possibilistic information given by the support of the models. This is a special case of a general result which applies to all polytopes presented in a standard form, given by linear equations together with non-negativity constraints on the variables.

AB - Abstract We study the set of no-signalling empirical models on a measurement scenario, and show that the combinatorial structure of the no-signalling polytope is completely determined by the possibilistic information given by the support of the models. This is a special case of a general result which applies to all polytopes presented in a standard form, given by linear equations together with non-negativity constraints on the variables.

KW - Contextuality

KW - No-signalling

KW - Quantum information

KW - Polytopes

KW - Face lattice

U2 - 10.1016/j.jmp.2016.03.006

DO - 10.1016/j.jmp.2016.03.006

M3 - Article

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VL - 74

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JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

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Possibilities determine the combinatorial structure of probability polytopes: Foundations of Probability Theory in Psychology and Beyond

Abstract / Description of output

Keywords / Materials (for Non-textual outputs)

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Cite this