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Journal of Logic and Computation Advance Access published online on September 13, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp058
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Comments on Interpretability and Decidability in Fuzzy Logic

Petr Hájek

Institute of Computer Science, Academy of Science of the Czech Republic, 182 07 Prague, Czech Republic.
E-mail: hajek{at}cs.cas.cz

Received 15 September 2008.


  Abstract

A particular notion of an interpretation of a theory over a fuzzy predicate logic in another such theory is discussed. For interpretability with the domain defined by a provably crisp formula, which is of course a syntactical notion, a semantic characterization is established. In the last section, we discuss the question of whether the extension of a decidable theory by a single new axiom is decidable and present an erratum to the paper (Hájek, 2007, Fundamenta informaticae, 81, 155–163).

Keywords: Mathematical fuzzy logic; interpretability; decidability


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