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.

Strict coherence on many valued-events / T. Flaminio, H. Hosni, F. Montagna. - In: THE JOURNAL OF SYMBOLIC LOGIC. - ISSN 0022-4812. - 83:1(2018 Mar), pp. 55-69. [10.1017/jsl.2017.34]

Strict coherence on many valued-events

H. Hosni;
2018-03

Abstract

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.
probability logic; coherence; mv-algebras
Settore M-FIL/02 - Logica e Filosofia della Scienza
Settore MAT/01 - Logica Matematica
12-feb-2018
THE JOURNAL OF SYMBOLIC LOGIC
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/514432
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