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Infinite-valued Gödel logics with 0-1-projections and relativizations. (English) Zbl 0862.03015
Hájek, Petr (ed.), Gödel ’96. Logical foundations of mathematics, computer science and physics – Kurt Gödel’s legacy. Proceedings of a conference, Brno, Czech Republic, August 1996. Berlin: Springer-Verlag. Lect. Notes Log. 6, 23-33 (1996).
Summary: Infinite-valued Gödel logic, i.e., Dummett’s LC, is extended by projection modalities and relativizations to truth value sets. An axiomatization for the corresponding propositional logic (sound and complete relative to any infinite set of truth values) is given. It is shown that certain simple infinite sets of truth values correspond to first-order Gödel logics which are not recursively axiomatizable.
For the entire collection see [Zbl 0844.00017].

MSC:
03B50 Many-valued logic
03B45 Modal logic (including the logic of norms)
03B55 Intermediate logics
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