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The liar paradox and fuzzy logic

Published online by Cambridge University Press:  12 March 2014

Petr Hájek ,
Jeff Paris  and
John Shepherdson
Petr Hájek
Affiliation:
Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodarenskou Vezi 2, 182 07 Prague 8, Czech Republic, E-mail: hajek@uivt1.uivt.cas.cz
Jeff Paris
Affiliation:
Department of Mathematics, University of Manchester, Manchester M139PL, U.K., E-mail: jeff@ma.man.ac.uk
John Shepherdson
Affiliation:
Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, U.K., E-mail: john.shepherdson@bristol.ac.uk
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 1 , March 2000 , pp. 339 - 346
Copyright
Copyright © Association for Symbolic Logic 2000

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References

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