A propositional probabilistic logic with discrete linear time for reasoning about evidence
type: Item
instance of: scholarly article
title: A propositional probabilistic logic with discrete linear time for reasoning about evidence
zbMATH Open document ID: 1269.03033
author: Zoran Ognjanović
author: Zoran Marković
author: Miodrag Rašković
author: Dragan Doder
author: Aleksandar Perović
published in: Annals of Mathematics and Artificial Intelligence
publication date: 2013-01-04T00:00:00Z
review text: The introduction and Section 2 of this paper are devoted to setting this paper in a wider context. To this end, the authors trace the combination of logic and probability back to Leibniz, Bernoulli, Laplace and other great historic figures. For the purposes of this paper the most relevant modern-day work is one of \textit{J. Y. Halpern} and \textit{R. Pucella} [J. Artif. Intell. Res. (JAIR) 26, 1--34 (2006; Zbl 1182.68244)] which contained an open question. This paper is aimed at answering this question.\newline In Section 3 the authors introduce a propositional logic which allows reasoning about evidence, prior and posterior probabilities, for which they define syntax and semantics. For a deducibility relation with countably many deduction steps the authors prove that the introduced logic is strongly complete.\newline The fourth section is devoted to a propositional logic for evidence and hypotheses that is enriched by two temporal operators, one operator for ``next'' and one operator for ``until''. This logic is shown to be sound and strongly complete.\newline Section 5 contains the conclusions. Here the authors explain why their completeness results required infinitary inference rules by considering the example of polynomials of odd degree over the real numbers.
reviewed by: Jürgen Landes
Mathematics Subject Classification ID: 03B62
Mathematics Subject Classification ID: 03B44
Mathematics Subject Classification ID: 68T27
zbMATH DE Number: 6122045
zbMATH Keywords: strong completeness
zbMATH Keywords: temporal logic
zbMATH Keywords: probabilistic logic
zbMATH Keywords: evidence
MaRDI profile type: Publication
full work available at URL: s10472-012-9307-9
OpenAlex ID: W2011593799
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DOI: 10.1007/S10472-012-9307-9
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description: scientific article; zbMATH DE number 6122045