Non-standard probability, coherence and conditional probability on many-valued events

The usual coherence criterion by de Finetti is extended both to many-valued events and to conditional probability. Special attention is paid to assessments in which the betting odds for conditioning events are zero. This case is treated bymeans of infinitesimal probabilities. We propose a rationality criterion, called stable coherence, which is stronger than coherence in the sense of no sure loss

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\u2019s 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