The Theory of Spectrum Exchangeability

Howarth, E. and Paris, J.B. (2015) The Theory of Spectrum Exchangeability. Review of Symbolic Logic, 8 (01). pp. 108-130.

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Spectrum Exchangeability, Sx, is an irrelevance principle of Pure Inductive Logic, and arguably the most natural (but not the only) extension of Atom Exchangeability to polyadic languages. It has been shown that all probability functions which satisfy Sx are comprised of a mixture of two essential types of probability functions; heterogeneous and homogeneous functions. We determine the theory of Spectrum Exchangeability, which for a fixed language L is the set of sentences of L which must be assigned probability 1 by every probability function satisfying Sx, by examining separately the theories of heterogeneity and homogeneity. We find that the theory of Sx is equal to the theory of finite structures, i.e. those sentences true in all finite structures for L, and it emerges that Sx is inconsistent with the principle of Super-Regularity (Universal Certainty). As a further consequence we are able to characterize those probability functions which satisfy Sx and the Finite Values Property.

Item Type: Article
Uncontrolled Keywords: Spectrum Exchangeability, Finite Values Property, Inductive Logic, Logical Probability, Rationality, Uncertain Reasoning
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations
MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Professor Jeff Paris
Date Deposited: 04 Aug 2015
Last Modified: 20 Oct 2017 14:13

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