Abstract
We construct a formula true in all models of the product fuzzy predicate logic over the standard product algebra on the unit real interval but unprovable in the product fuzzy logic (and hence having truth value less than 1 in some model over a non-standard linearly ordered product algebra). Gödel’s construction of a true unprovable formula of arithmetic is heavily used.
Partial support of ITI (the project No. LN00A056 (ITI) of Ministry of Education (MŠMT) of the Czech Republic) is recognized.
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References
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© 2004 Springer-Verlag Berlin Heidelberg
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Hájek, P. (2004). A True Unprovable Formula of Fuzzy Predicate Logic. In: Lenski, W. (eds) Logic versus Approximation. Lecture Notes in Computer Science, vol 3075. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25967-1_1
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DOI: https://doi.org/10.1007/978-3-540-25967-1_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22562-1
Online ISBN: 978-3-540-25967-1
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