Resumen de De Finetti theorem and Borel states in [0, 1]-valued algebraic logic
In this paper de Finetti�s (no-Dutch-Book) criterion for coherent probability assignments is extended to large classes of logics and their algebras. Given a set A of �events� and a closed set of �possible worlds� we show that a map s:A?[0,1] satisfies de Finetti�s criterion if, and only if, it has the form for some probability measure µ on . Our results are applicable to all logics whose connectives are continuous operations on [0,1], notably (i) every [0,1]-valued logic with finitely many truth-values, (ii) every logic whose conjunction is a continuous t-norm, and whose negation is ¬x=1-x, possibly also equipped with its t-conorm and with some continuous implication, (iii) any extension of Lukasiewicz logic with constants or with a product-like connective. We also extend de Finetti�s criterion to the noncommutative underlying logic of GMV-algebras.
