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2 results

  • THREE CHARACTERIZATIONS OF STRICT COHERENCE ON INFINITE-VALUED EVENTS

  • TOMMASO FLAMINIO
  • Journal:
    The Review of Symbolic Logic / Volume 13 / Issue 3 / September 2020
    Published online by Cambridge University Press:
    04 October 2019, pp. 593-610
    Print publication:
    September 2020

  • This article builds on a recent paper coauthored by the present author, H. Hosni and F. Montagna. It is meant to contribute to the logical foundations of probability theory on many-valued events and, specifically, to a deeper understanding of the notion of strict coherence. In particular, we will make use of geometrical, measure-theoretical and logical methods to provide three characterizations of strict coherence on formulas of infinite-valued Łukasiewicz logic.

  • STRICT COHERENCE ON MANY-VALUED EVENTS

  • TOMMASO FLAMINIO, HYKEL HOSNI, FRANCO MONTAGNA
  • Journal:
    The Journal of Symbolic Logic / Volume 83 / Issue 1 / March 2018
    Published online by Cambridge University Press:
    12 February 2018, pp. 55-69
    Print publication:
    March 2018
    • Article
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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.