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The liar paradox and fuzzy logic

  • Petr Hájek (a1), Jeff Paris (a2) and John Shepherdson (a3)

Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying “x is true” and satisfying the “dequotation schema” for all sentences φ? This problem is investigated in the frame of Łukasiewicz infinitely valued logic.

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[1] L.E.J. Brouwer , Über Abbildungen von Mannigfaltigkeiten, Mathematische Annalen, vol. 71 (1910), pp. 97115.

[6] P. Hájek , Fuzzy logic and arithmetical hierarchy II, Studia Logica, vol. 58 (1997), pp. 129141, to appear.

[7] P. Hájek , Metamathematics of fuzzy logic, Kluwer, 1998.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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