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. (2022). A 0-1 Law in Mathematical Fuzzy Logic. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 30(9), 3833-3840 [10.1109/TFUZZ.2021.3131200].
A 0-1 Law in Mathematical Fuzzy Logic
Noguera C.
2022-01-01
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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https://hdl.handle.net/11365/1199916