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STRICT COHERENCE ON MANY-VALUED EVENTS

Published online by Cambridge University Press:  12 February 2018

TOMMASO FLAMINIO ,
HYKEL HOSNI  and
FRANCO MONTAGNA
TOMMASO FLAMINIO
Affiliation:
DEPARTMENT OF PURE AND APPLIED SCIENCES UNIVERSITY OF INSUBRIA VIA MAZZINI, 5 21100 VARESE, ITALY and DEPARTMENT OF PHILOSOPHY UNIVERSITY OF MILAN VIA FESTA DEL PERDONO 7, 20122MILANO, ITALY E-mail:[email protected]
HYKEL HOSNI
Affiliation:
DEPARTMENT OF PURE AND APPLIED SCIENCES UNIVERSITY OF INSUBRIA VIA MAZZINI, 5 21100 VARESE, ITALY and DEPARTMENT OF PHILOSOPHY UNIVERSITY OF MILAN VIA FESTA DEL PERDONO 7, 20122MILANO, ITALYE-mail:[email protected]
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Abstract

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We investigate the property of strict coherence in the setting of many-valued logics. Our main results read as follows: (i) a map from an MV-algebra to [0,1] is strictly coherent if and only if it satisfies Carnap’s regularity condition, and (ii) a [0,1]-valued book on a finite set of many-valued events is strictly coherent if and only if it extends to a faithful state of an MV-algebra that contains them. Remarkably this latter result allows us to relax the rather demanding conditions for the Shimony-Kemeny characterisation of strict coherence put forward in the mid 1950s in this Journal.

Keywords

Primary 03B48Secondary 60A0506D3506F2052B11Probability logicstrict coherenceMV-algebrasfaithful statesmany-valued logics
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 55 - 69
Copyright
Copyright © The Association for Symbolic Logic 2018 

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