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International Conference on Logic for Programming Artificial Intelligence and Reasoning

LPAR 2002: Logic for Programming, Artificial Intelligence, and Reasoning pp 327–336Cite as

Gödel Logics and Cantor-Bendixon Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2514))

Abstract

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.

this work was supported by the Austrian Research Fund (FWF) project P15477-MAT

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References

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Author information

Authors and Affiliations

  1. Institute for Algebra and Computational Mathematics, University of Technology, Vienna, Austria

    Norbert Preining

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  1. Norbert Preining
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Editors and Affiliations

  1. Abteilung für Theoretische Informatik, Institut für Algebra und Diskrete Mathematik, Wiedner Hauptstr. 8-10, 1040, Wien, Austria

    Matthias Baaz

  2. Department of Computer Science, University of Manchester, Kilburn Building, Oxford Road, Manchester, M13, 9PL, UK

    Andrei Voronkov

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© 2002 Springer-Verlag Berlin Heidelberg

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Preining, N. (2002). Gödel Logics and Cantor-Bendixon Analysis. In: Baaz, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2002. Lecture Notes in Computer Science(), vol 2514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36078-6_22

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  • DOI: https://doi.org/10.1007/3-540-36078-6_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00010-5

  • Online ISBN: 978-3-540-36078-0

  • eBook Packages: Springer Book Archive

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