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Gödel logics and Cantor-Bendixson analysis. (English) Zbl 1023.03015
Baaz, Matthias (ed.) et al., Logic for programming, artificial intelligence, and reasoning. 9th international conference, LPAR 2002, Tbilisi, Georgia, October 14-18, 2002. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 2514, 327-336 (2002).
Summary: This paper presents an analysis of Gödel logics with countable truth value sets with respect to the topological and order-theoretic structure of the underlying truth value set. Gödel logics have taken an important rôle in various areas of computer science, e.g. logic programming and foundations of parallel computing. As shown in a forthcoming paper all these logics are not recursively axiomatizable. We show that certain topological properties of the truth value set can distinguish between various logics. Complete separation of a class of countable valued logics will be proven and direction for further separation results given.
For the entire collection see [Zbl 1007.00026].

03B50 Many-valued logic
03B52 Fuzzy logic; logic of vagueness
03E15 Descriptive set theory
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