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PROBABILISTIC ENTAILMENT ON FIRST ORDER LANGUAGES AND REASONING WITH INCONSISTENCIES

Part of: General logic Mathematical Logic and Foundations

Published online by Cambridge University Press:  07 July 2022

SOROUSH RAFIEE RAD
SOROUSH RAFIEE RAD*
Affiliation:
DUTCH INSTITUTE FOR EMERGENT PHENOMENA (DIEP) UNIVERSITY OF AMSTERDAM, AMSTERDAM, THE NETHERLANDS and THE INSTITUTE FOR LOGIC LANGUAGE AND COMPUTATION (ILLC), AMSTERDAM, THE NETHERLANDS
*
E-mail: S.RafieeRad@uva.nl
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Abstract

We investigate an approach for drawing logical inference from inconsistent premisses. The main idea in this approach is that the inconsistencies in the premisses should be interpreted as uncertainty of the information. We propose a mechanism, based on Kinght’s [14] study of inconsistency, for revising an inconsistent set of premisses to a minimally uncertain, probabilistically consistent one. We will then generalise the probabilistic entailment relation introduced in [15] for propositional languages to the first order case to draw logical inference from a probabilistic set of premisses. We will show how this combination can allow us to limit the effect of uncertainty introduced by inconsistent premisses to only the reasoning on the part of the premise set that is relevant to the inconsistency.

Keywords

probabilistic reasoninginconsistency

MSC classification

Primary: 03-02: Research exposition (monographs, survey articles)
Secondary: 03B42: Logics of knowledge and belief (including belief change) 03B48: Probability and inductive logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 16 , Issue 2 , June 2023 , pp. 351 - 368
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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