Proof Theory for First Order Łukasiewicz Logic

  • Matthias Baaz
  • George Metcalfe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4548)

Abstract

An approximate Herbrand theorem is proved and used to establish Skolemization for first-order Łukasiewicz logic. Proof systems are then defined in the framework of hypersequents. In particular, extending a hypersequent calculus for propositional Łukasiewicz logic with usual Gentzen quantifier rules gives a calculus that is complete with respect to interpretations in safe MV-algebras, but lacks cut-elimination. Adding an infinitary rule to the cut-free version of this calculus gives a system that is complete for the full logic. Finally, a cut-free calculus with finitary rules is obtained for the one-variable fragment by relaxing the eigenvariable condition for quantifier rules.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Matthias Baaz
    • 1
  • George Metcalfe
    • 2
  1. 1.Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040 WienAustria
  2. 2.Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville TN 37240USA

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