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Quantified Propositional Gödel Logics

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Logic for Programming and Automated Reasoning (LPAR 2000)

Part of the book series: Lecture Notes in Artificial Intelligence ((LNAI,volume 1955))

Abstract

It is shown that Gqp ↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp ↑ as the intersection of all finite-valued quantified propositional Gödel logics.

2000 Mathematics Subject Classification: Primary 03B50; Secondary 03B55.

Research supported by the Austrian Science Fund under grant P-12652 MAT

Research supported by EC Marie Curie fellowship HPMF-CT-19 99-00301

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Author information

Authors and Affiliations

  1. Institut für Algebra und Computermathematik E118.2, Technische Universität Wien, A-1040, Vienna, Austria

    Matthias Baaz & Agata Ciabattoni

  2. Institut für Computersprachen E185.2, Technische Universität Wien, A-1040, Vienna, Austria

    Richard Zach

Authors
  1. Matthias Baaz
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  2. Agata Ciabattoni
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  3. Richard Zach
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Editor information

Editors and Affiliations

  1. CNRS, Université de Paris 7, case 7012, 2 place Jussieu, 75251, Paris Cedex 05, France

    Michel Parigot

  2. Computer Science Department, University of Manchester, Oxford Rd, M13 9PL, Manchester, UK

    Andrei Voronkov

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© 2000 Springer-Verlag Berlin Heidelberg

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Baaz, M., Ciabattoni, A., Zach, R. (2000). Quantified Propositional Gödel Logics. In: Parigot, M., Voronkov, A. (eds) Logic for Programming and Automated Reasoning. LPAR 2000. Lecture Notes in Artificial Intelligence(), vol 1955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44404-1_16

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  • DOI: https://doi.org/10.1007/3-540-44404-1_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41285-4

  • Online ISBN: 978-3-540-44404-6

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