The relationship between strong belief and assumption

Adam Brandenburger; Amanda Friedenberg; H. Jerome Keisler

doi:10.1007/s11229-023-04167-6

The relationship between strong belief and assumption

Adam Brandenburger, Amanda Friedenberg, H. Jerome Keisler

Economics

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

1 Scopus citations

Abstract

We define two maps, one map from the set of conditional probability systems (CPS’s) onto the set of lexicographic probability systems (LPS’s), and another map from the set of LPS’s with full support onto the set of CPS’s. We use these maps to establish a relationship between strong belief (defined on CPS’s) and assumption (defined on LPS’s). This establishes a relationship at the abstract level between these two widely used notions of belief in an extended probability-theoretic setting.

Original language	English (US)
Article number	175
Journal	Synthese
Volume	201
Issue number	5
DOIs	https://doi.org/10.1007/s11229-023-04167-6
State	Published - May 2023

Keywords

Assumption
Conditional probability systems
Lexicographic probability systems
Strong belief

ASJC Scopus subject areas

Philosophy
General Social Sciences

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10.1007/s11229-023-04167-6

Cite this

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title = "The relationship between strong belief and assumption",

abstract = "We define two maps, one map from the set of conditional probability systems (CPS{\textquoteright}s) onto the set of lexicographic probability systems (LPS{\textquoteright}s), and another map from the set of LPS{\textquoteright}s with full support onto the set of CPS{\textquoteright}s. We use these maps to establish a relationship between strong belief (defined on CPS{\textquoteright}s) and assumption (defined on LPS{\textquoteright}s). This establishes a relationship at the abstract level between these two widely used notions of belief in an extended probability-theoretic setting.",

keywords = "Assumption, Conditional probability systems, Lexicographic probability systems, Strong belief",

author = "Adam Brandenburger and Amanda Friedenberg and Keisler, {H. Jerome}",

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AU - Friedenberg, Amanda

AU - Keisler, H. Jerome

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N2 - We define two maps, one map from the set of conditional probability systems (CPS’s) onto the set of lexicographic probability systems (LPS’s), and another map from the set of LPS’s with full support onto the set of CPS’s. We use these maps to establish a relationship between strong belief (defined on CPS’s) and assumption (defined on LPS’s). This establishes a relationship at the abstract level between these two widely used notions of belief in an extended probability-theoretic setting.

AB - We define two maps, one map from the set of conditional probability systems (CPS’s) onto the set of lexicographic probability systems (LPS’s), and another map from the set of LPS’s with full support onto the set of CPS’s. We use these maps to establish a relationship between strong belief (defined on CPS’s) and assumption (defined on LPS’s). This establishes a relationship at the abstract level between these two widely used notions of belief in an extended probability-theoretic setting.

KW - Assumption

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KW - Lexicographic probability systems

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The relationship between strong belief and assumption

Abstract

Keywords

ASJC Scopus subject areas

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