Strict coherence on many-valued events

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: s. Probability logic, strict coherence, MV-algebras, faithful states, many-valued logics.

Flaminio, T., H. Hosni, and F. Montagna. (2018). “Strict Coherence on Many Valued Events” Journal of Symbolic Logic . 83(1), 55-69. DOI:10.1017/jsl.2017.34