The uncertain reasoner's companion: a mathematical perspective
The uncertain reasoner's companion: a mathematical perspective
Regular Article: Tensor Products and the Loomis驴Sikorski Theorem for MV-Algebras
Advances in Applied Mathematics
Complexity of fuzzy probability logics II
Fuzzy Sets and Systems
De Finetti theorem and Borel states in [0,1]-valued algebraic logic
International Journal of Approximate Reasoning
MV-algebras with internal states and probabilistic fuzzy logics
International Journal of Approximate Reasoning
The coherence of Łukasiewicz assessments is NP-complete
International Journal of Approximate Reasoning
Models for Many-Valued Probabilistic Reasoning
Journal of Logic and Computation
A logical characterization of coherence for imprecise probabilities
International Journal of Approximate Reasoning
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A bad bet is a bet for which we can find an alternative system of bets over the same class of events ensuring to the bettor a strictly better payoff, independently on the truth values of the events involved. In this paper we study the computational complexity for the problem of deciding whether a book arranged on fuzzy events avoids bad bets or not. Call admissible a book that avoids bad bets. Following the approach initiated by Mundici and pursued by Flaminio and Bova for reversible betting situations, we settle the complexity of the admissibility-problem to be NP-complete. We also present a variety of algebras, and an algebraizable modal logic, that allow us to characterize admissible books in terms of 1-satisfiability of suitable defined theories. Studying the computational complexity for the 1-satisfiability problem of a formula in this variety, we provide a second, algebraic-based, NP algorithm to check admissible books.