Semantics for fuzzy logic supporting truth functionality
Discovering the world with fuzzy logic
Sequent and hypersequent calculi for abelian and łukasiewicz logics
ACM Transactions on Computational Logic (TOCL)
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Mathematical Fuzzy Logic: An Invitation to Interesting Research Areas
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
Fuzzy Sets and Systems
A semantic model for vague quantifiers combining fuzzy theory and supervaluation theory
LORI'11 Proceedings of the Third international conference on Logic, rationality, and interaction
Mathematical Fuzzy Logic: An Invitation to Interesting Research Areas
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
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Two popular approaches to formalize adequate reasoning with vague propositions are usually deemed incompatible: On the one hand, there is supervaluation with respect to precisification spaces, which consist in collections of classical interpretations that represent admissible ways of making vague atomic statements precise. On the other hand, t-norm based fuzzy logics model truth functional reasoning, where reals in the unit interval [0,1] are interpreted as degrees of truth. We show that both types of reasoning can be combined within a single logic SŁ, that extends both: Łukasiewicz logic Ł and (classical) S5, where the modality corresponds to '...is true in all complete precisifications'. Our main result consists in a game theoretic interpretation of SŁ, building on ideas already introduced by Robin Giles in the 1970s to obtain a characterization of Ł in terms of a Lorenzen style dialogue game combined with bets on the results of binary experiments that may show dispersion. In our case the experiments are replaced by random evaluations with respect to a given probability distribution over permissible precisifications.