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A Co-inductive Language and Truth Degrees

  • Shunsuke Yatabe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6878)

Abstract

We investigate what happens if \({\mathbf{PA}\text{{\bf \L}}\mathbf{Tr}_2}\), a co-inductive language, formalizes itself. We analyze the truth concept in fuzzy logics by formalizing truth degree theory in the framework of truth theories in fuzzy logics. Hájek-Paris-Shepherdson’s paradox [HPS00] involves that so called truth degrees do not represent the degrees of truthhood (defined by the truth predicate) correctly in Łukasiewicz infinite-valued predicate logic \(\forall\text{{\bf \L}}\), therefore truth degree theory fails there.

Keywords

Fuzzy Logic Classical Logic Object Language Recursive Function Predicate Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Shunsuke Yatabe
    • 1
  1. 1.Collaborate Research Team for VerificationNational Institute of Advanced Industrial Science and TechnologyJapan

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