Paper Info
Title
A 0-1 Law in Mathematical Fuzzy Logic
Abstract
This article continues the theoretical study of weighted structures in mathematical fuzzy logic focusing on the finite model theory of fuzzy logics valued on arbitrary finite <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{MTL}$</tex-math></inline-formula> -chains. We show that for any first-order (or infinitary with finitely many variables) formula <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varphi$</tex-math></inline-formula> , there is a truth-value that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varphi$</tex-math></inline-formula> 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. Fermüller.
Year
DOI
Venue
2022
10.1109/TFUZZ.2021.3131200
IEEE Transactions on Fuzzy Systems
Keywords
DocType
Volume
Finite weighted structures,first-order fuzzy logics,mathematical fuzzy logic,monoidal t-norms
Journal
30
Issue
ISSN
Citations 
9
1063-6706
0
PageRank 
References 
Authors
0.34
17
2
Name
Order
Citations
PageRank
Guillermo Badia100.34
Carles Noguera246233.93