De Finetti's bets on partially evaluated Kripke frames
Publication Type:Conference Paper
Source:Computability in Europe - Turing's Centenary, Cambridge, UK (2012)
De Finetti's conception of events is one of the most distinctive aspects of his theory of probability, yet it appears to be somewhat elusive. The purpose of this note is to set up a formal framework in which a rigorous characterisation of this notion, and its cognate modelling assumptions, gives rise to a detailed formalisation of the betting problem which underlies the celebrated Dutch Book Argument. In particular, we introduce partially evaluated Kripke frames, relational structures which put the implicit modal semantics of events on a rigorous footing and allow us to refine the notion of coherence originally put forward by de Finetti. As our main result shows, this refinement captures an intuitive condition which de Finetti imposed on the betting problem, namely that it is irrational to bet on an event which may be true, but whose truth will never be ascertained by the players.