Hilbertian systems, analytic fuzzy tableaux and cut rule elimination in rational pavelka logic

ABSTRACT

In this paper a sound and complete tableau system for the Rational Pavelka Logic is introduced. The completeness is proved thanks to fuzzy hilbertian system formulated by Hajek. A fuzzy tableau cut rule is introduced but a cut elimination theorem is proved.

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INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES
      F.4.1 Mathematical Logic
          Subjects: Proof theory

General Terms:
Theory

Keywords:
MV-algebra, completeness, cut rule, fuzzy prepositional logic, galois relation, pavelka semantics, soundness, tableaux