A General Representation Theorem for Probability Functions Satisfying Spectrum Exchangeability

Paris, Jeffrey; Vencovská, Alena

doi:10.1007/978-3-642-03073-4_39

Cited by 3 publications

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“…. , b i+1 ) not uniform randomly as was the case for u p L but, roughly speaking, with a probability proportional to the number of ways of extending this state description to one of spectrum of length exactly t, again requiring that whenever c i = c j then b i , b j remain forever 13 The Ladder Theorem representation of u p L is given explicitly in Landes (2009, p. 71) and Paris and Vencovská (2009). [149] 36 Synthese (2011) 181:19-47 indistinguishable. For the precise details of this construction we refer the reader to Landes et al (2009) and Paris and Vencovská (2007).…”

Section: [A Very Full Account Of This Construction Is Given In Landesmentioning

confidence: 98%

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A survey of some recent results on Spectrum Exchangeability in Polyadic Inductive Logic

2010

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Section: [A Very Full Account Of This Construction Is Given In Landesmentioning

confidence: 98%

“…The answer is 'yes', though it is not clear that it will yet be of much use! Precisely the following is proved in Paris and Vencovská (2009): Theorem 7 Every probability function w satisfying Sx is of the form…”

Section: Theorem 6 a Probability Function W Satisfies Sx And LI If Anmentioning

confidence: 99%

A survey of some recent results on Spectrum Exchangeability in Polyadic Inductive Logic

2010

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“…This is analogous to the situation with Atom Exchangeability, Ax, and its generalization to Polyadic Pure Inductive Logic, Spectrum Exchangeability, see [12]. This analogy also extends to the General Representation Theorem, stating that each probability function satisfying Px is a scaled difference of probability functions satisfying ULi (see [14]).…”

Section: Discussionmentioning

confidence: 80%

Predicate Exchangeability and Language Invariance in Pure Inductive Logic

Kließ,

Paris

2013

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In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language L and replacing each occurrence of a predicate in an L-sentence ϕ according to this permutation should not change our belief in the truth of ϕ. In this paper we study when a probability function w on a purely unary language L satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.

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Pure Inductive Logic

Paris

Vencovská

2015

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Pure inductive logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years plus the main contributions of the authors and their collaborators over the last decade to present a comprehensive account of the discipline within a single unified context. The exposition is structured around the traditional bases of rationality, such as avoiding Dutch Books, respecting symmetry and ignoring irrelevant information. The authors uncover further rationality concepts, both in the unary and in the newly emerging polyadic languages, such as conformity, spectrum exchangeability, similarity and language invariance. For logicians with a mathematical grounding, this book provides a complete self-contained course on the subject, taking the reader from the basics up to the most recent developments. It is also a useful reference for a wider audience from philosophy and computer science.

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A General Representation Theorem for Probability Functions Satisfying Spectrum Exchangeability

Cited by 3 publications

References 6 publications

A survey of some recent results on Spectrum Exchangeability in Polyadic Inductive Logic

A survey of some recent results on Spectrum Exchangeability in Polyadic Inductive Logic

Predicate Exchangeability and Language Invariance in Pure Inductive Logic

Pure Inductive Logic

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