Quantified propositional Goedel logics

Details Quantified propositional Goedel logics Quantified propositional Goedel logics

2000-06-17

arxiv.org/abs/math/0006122v2

Michel Parigot, Andrei Voronkov (Eds.): Logic for Programming and Automated Reasoning. 7th International Conference, LPAR 2000

Mathematics

Logic

v.2: 17 pages, revised published version (v.1: 15 pages)

Scientific paper

It is shown that G-up, the quantified propositional Goedel-Dummett logic based on the truth-values set V-up = {1 - 1/n : n >= 1} u {1}, is decidable. This result is obtained by reduction to Buechi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of G-up as the intersection of all finite-valued quantified propositional Goedel logics.

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