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Herbrand Theorems and Skolemization for Prenex Fuzzy Logics

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Logic and Theory of Algorithms (CiE 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5028))

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Abstract

Approximate Herbrand theorems are established for first-order fuzzy logics based on continuous t-norms, and used to provide proof-theoretic proofs of Skolemization for their Prenex fragments. Decidability and complexity results for particular fragments are obtained as consequences.

Research Supported by FWF Project P17503-N12.

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References

  1. Baaz, M., Ciabattoni, A., Fermüller, C.G.: Herbrand’s theorem for prenex Gödel logic and its consequences for theorem proving. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS (LNAI), vol. 2250, pp. 201–216. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  2. Baaz, M., Ciabattoni, A., Montagna, F.: Analytic calculi for monoidal t-norm based logic. Fundamenta Informaticae 59(4), 315–332 (2004)

    MathSciNet  MATH  Google Scholar 

  3. Baaz, M., Iemhoff, R.: The skolemization of existential quantifiers in intuitionistic logic. Annals of Pure and Applied Logic 142(1-3), 269–295 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baaz, M., Metcalfe, G.: Herbrand’s theorem, skolemization, and proof systems for Łukasiewicz logic (submitted), http://www.math.vanderbilt.edu/people/metcalfe/publications

  5. Baaz, M., Zach, R.: Hypersequents and the proof theory of intuitionistic fuzzy logic. In: Clote, P.G., Schwichtenberg, H. (eds.) CSL 2000. LNCS, vol. 1862, pp. 187–201. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)

    MATH  Google Scholar 

  7. Hájek, P.: Arithmetical complexity of fuzzy logic – a survey. Soft Computing 9, 935–941 (2005)

    Article  MATH  Google Scholar 

  8. Hájek, P.: Making fuzzy description logic more general. Fuzzy Sets and Systems 154(1), 1–15 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hanikova, Z.: A note on the complexity of tautologies of individual t-algebras. Neural Network World 12(5), 453–460 (2002)

    Google Scholar 

  10. Montagna, F.: Three complexity problems in quantified fuzzy logic. Studia Logica 68(1), 143–152 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mostert, P.S., Shields, A.L.: On the structure of semigroups on a compact manifold with boundary. Annals of Mathematics 65, 117–143 (1957)

    Article  MathSciNet  Google Scholar 

  12. Novák, V.: On the Hilbert-Ackermann theorem in fuzzy logic. Acta Mathematica et Informatica Universitatis Ostraviensis 4, 57–74 (1996)

    MathSciNet  MATH  Google Scholar 

  13. Ragaz, M.E.: Arithmetische Klassifikation von Formelmengen der unendlichwertigen Logik. PhD thesis, ETH Zürich (1981)

    Google Scholar 

  14. Straccia, U.: Reasoning within fuzzy description logics. Journal of Artificial Intelligence Research 14, 137–166 (2001)

    MathSciNet  MATH  Google Scholar 

  15. Vojtás, P.: Fuzzy logic programming. Fuzzy Sets and Systems 124, 361–370 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Willard, S.: General Topology. Dover (2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria

    Matthias Baaz

  2. Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA

    George Metcalfe

Authors
  1. Matthias Baaz
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  2. George Metcalfe
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Editor information

Arnold Beckmann Costas Dimitracopoulos Benedikt Löwe

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© 2008 Springer-Verlag Berlin Heidelberg

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Baaz, M., Metcalfe, G. (2008). Herbrand Theorems and Skolemization for Prenex Fuzzy Logics. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_3

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  • DOI: https://doi.org/10.1007/978-3-540-69407-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69405-2

  • Online ISBN: 978-3-540-69407-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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