Conditional probability and defeasible inference
type: Item
instance of: scholarly article
title: Conditional probability and defeasible inference
zbMATH Open document ID: 1082.03023
author: N. E. Zubov
published in: Journal of Philosophical Logic
publication date: 2006-02-08T00:00:00Z
full work available at URL: https://figshare.com/articles/journal_contribution/Conditional_Probability_and_Defeasible_Inference/6491273
review text: Building on work of \textit{B. C. van Fraassen} [``Fine-grained opinion, probability, and the logic of full belief'', J. Philos. Log. 24, 349--377 (1995; Zbl 0825.03015)], the authors show how the qualitative concept of a rational consequence relation (i.e. a preferential consequence satisfying the condition of rational monotony) may be characterized in terms of nonstandard probability functions (specifically, two-place functions \(p(x,a)\) into the real interval, satisfying the multiplicative condition and whose projections formed by fixing \(a\) are either standard Kolmogorov probability functions or equal to the function with constant value 1). They show that each of their probabilistically generated inference relations is rational, and that for finite languages the converse holds.
Mathematics Subject Classification ID: 03B48
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 68T27
zbMATH DE Number: 5004555
zbMATH Keywords: belief revision
zbMATH Keywords: conditional probability
zbMATH Keywords: countable additivity
zbMATH Keywords: nonmonotonic logic
reviewed by: David Makinson
MaRDI profile type: Publication
OpenAlex ID: W2053836415
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DOI: 10.1007/S10992-004-5553-6
description: scientific article; zbMATH DE number 5004555