Representation theorems for probability functions satisfying spectrum exchangeability in inductive logic
type: Item
instance of: scholarly article
title: Representation theorems for probability functions satisfying spectrum exchangeability in inductive logic
zbMATH Open document ID: 1204.03026
author: Jürgen Landes
author: Jeff Paris
author: Alena Vencovská
published in: International Journal of Approximate Reasoning
publication date: 2010-09-02T00:00:00Z
review text: De Finetti's representation theorem [see \textit{H. Gaifman}, ``Applications of de Finetti's theorem to inductive logic'', in: \textit{R. Carnap} and \textit{R. C. Jeffrey} (eds.), Studies in inductive logic and probability. Vol. I. Berkeley--Los Angeles--London: University of California Press, 235--251 (1971; Zbl 0246.02024)] plays a central role in the study of conventional, unary, inductive logic, because it gives a transparent access to examples of probability functions satisfying some basic conditions, and it makes it possible to restyle problems from inductive logic into elementary differential and integral calculus, where intuitions and techniques are already well developed. In this paper, a de Finetti-style representation theorem is proved, covering the class of all probability functions satisfying spectrum exchangeability in polyadic inductive logic and giving an application by characterizing those probability functions satisfying spectrum exchangeability, which can be extended to a language with equality whilst still satisfying this property.
Mathematics Subject Classification ID: 03B48
Mathematics Subject Classification ID: 68T37
zbMATH DE Number: 5777528
zbMATH Keywords: uncertain reasoning
zbMATH Keywords: inductive logic
zbMATH Keywords: probability logic
zbMATH Keywords: spectrum exchangeability
zbMATH Keywords: de Finetti's theorem
zbMATH Keywords: equality
reviewed by: Branislav Boričić
MaRDI profile type: Publication
full work available at URL: j.ijar.2009.07.001
OpenAlex ID: W2013945053
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DOI: 10.1016/J.IJAR.2009.07.001
description: scientific article; zbMATH DE number 5777528