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Analytic Calculi for Projective Logics

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1617))

Abstract

The class of projective propositional logics is defined by a certain format of the definition of truth functions for their connectives with respect to a semantic theory. All finite valued logics, but also infinite valued Gödel logic are shown to be projective. Analytic Gentzen type calculi are uniformly derived for all projective logics. Admissibility of cut rules and other structural rules is investigated. The special case of Gödel logics is exemplified in detail and compared with the previous approach of Avron (based on hypersequents).

Partly supported by COST-Action No. 15 and FWF grant P-12652-MAT.

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References

  1. Kurt Schütte. Proof Theory. Springer, Berlin and New York, 1977.

    MATH  Google Scholar 

  2. Nicholas Rescher. Many-valued Logic. McGraw-Hill, New York, 1969.

    MATH  Google Scholar 

  3. Petr Hajek. Metamathematics of Fuzzy Logic. Kluwer, 1998.

    Google Scholar 

  4. G. Rousseau. Sequents in many valued logic I. Fundamenta Mathematicae, 60:23–33, 1967.

    MathSciNet  Google Scholar 

  5. Kurt Gödel. Zum intuitionistischen Aussagenkalkül. Anzeiger der Akademie der Wissenschaften in Wien, 69:65–66, 1932.

    Google Scholar 

  6. Reiner Hähnle. Automated Deduction in Multiple-valued Logics. Clarendon Press, Oxford, 1993.

    MATH  Google Scholar 

  7. Michael Dummett. A propositional logic with denumerable matrix. Journal of Symbolic Logic, 24:96–107, 1959.

    MathSciNet  Google Scholar 

  8. Moto-o Takahashi. Many-valued logics of extended Gentzen style I. Sci. Rep. Tokyo Kyoiku Daigaku Sect. A, 9(271):95–110, 1968.

    Google Scholar 

  9. Gerhard Gentzen. Untersuchungen über das logische Schließen I–II. Mathematische Zeitschrift, 39:176–210 and 405–431, 1934–35.

    Article  MATH  MathSciNet  Google Scholar 

  10. Hans Jürgen Ohlbach. Computer support for the development and investigation of logics. Technical Report MPI-I-94-228, Max-Planck-Institut für Informatik, Saarbrücken, Germany, 1994.

    Google Scholar 

  11. Arnon Avron. Hypersequents, logical consequence and intermediate logics for concurrency. Annals of Mathematics and Artificial Intelligence, 4(199):225–248, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  12. Matthias Baaz and Christian G. Fermüller. Resolution-based theorem proving for many-valued logics. Journal of Symbolic Computation, 19:353–391, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  13. Arnon Avron. The method of hypersequents in proof theory of propositional nonclassical logics. In Logic: from foundations to applications. European logic colloquium, Keele, UK, July 20–29, 1993, pages 1–32, Oxford, 1996. Clarendon Press.

    Google Scholar 

  14. Matthias Baaz, Gernot Salzer, Christian G. Fermüller, and Richard Zach. MUlt-log 1.0: Towards an expert system for many-valued logics. In 13th Int. Conf. on Automated Deduction (CADE’96), volume 1104 of Lecture Notes in Artificial Intelligence, pages 226–230. Springer, 1996.

    Google Scholar 

  15. Matthias Baaz, Christian G. Fermüller, and Richard Zach. Elimination of cuts in first-order finite-valued logics. J. Inform. Process. Cybernet. EIK, 29(6):333–355, 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Technische Universität Wien, A-1040, Vienna, Austria

    Matthias Baaz & Christian G. Fermüller

Authors
  1. Matthias Baaz
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  2. Christian G. Fermüller
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Editors and Affiliations

  1. Department of Computer Science, Institute for Programming and Logics, University at Albany - SUNY, Albany, NY, 12222, USA

    Neil V. Murray

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© 1999 Springer-Verlag Berlin Heidelberg

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Baaz, M., Fermüller, C.G. (1999). Analytic Calculi for Projective Logics. In: Murray, N.V. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1999. Lecture Notes in Computer Science(), vol 1617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48754-9_8

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  • DOI: https://doi.org/10.1007/3-540-48754-9_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66086-6

  • Online ISBN: 978-3-540-48754-8

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