This paper continues the theoretical study of weighted structures in mathematical fuzzy logic focusing on the finite model theory of fuzzy logics valued on arbitrary finite MTL-chains. We show that for any first-order (or infinitary with finitely many variables) formula phi, there is a unique truth-value that phi takes almost surely in every finite many-valued model and such that every other truth-value is almost surely not taken. This generalizes a theorem in the fuzzy setting due to Robert Kosik and Christian G. Fermuller.
Badia, G., & Noguera, C. (2021). A 0-1 Law in Mathematical Fuzzy Logic. IEEE TRANSACTIONS ON FUZZY SYSTEMS [10.1109/TFUZZ.2021.3131200].
A 0-1 Law in Mathematical Fuzzy Logic
Noguera C.
2021
Abstract
This paper continues the theoretical study of weighted structures in mathematical fuzzy logic focusing on the finite model theory of fuzzy logics valued on arbitrary finite MTL-chains. We show that for any first-order (or infinitary with finitely many variables) formula phi, there is a unique truth-value that phi takes almost surely in every finite many-valued model and such that every other truth-value is almost surely not taken. This generalizes a theorem in the fuzzy setting due to Robert Kosik and Christian G. Fermuller.
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http://hdl.handle.net/11365/1199916