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Journal of Logic and Computation Advance Access published online on September 17, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp052
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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

Arithmetical Complexity of First-order Predicate Fuzzy Logics Over Distinguished Semantics

Franco Montagna and Carles Noguera

Department of Mathematics and Computer Science, University of Siena, Pian dei Mantellini 44, 53100 Siena, Italy.
E-mail: montagna{at}unisi.it; cnoguera{at}iiia.csic.es

Received 16 March 2009.


  Abstract

All promiment examples of first-order predicate fuzzy logics are undecidable. This leads to the problem of the arithmetical complexity of their sets of tautologies and satisfiable sentences. This article is a contribution to the general study of this problem. We propose the classes of first-order core and {Delta}-core fuzzy logics as a good framework to address these arithmetical complexity issues. We obtain general results providing lower bounds for the complexities associated with arbitrary semantics, and we compute upper bounds and exact positions in the arithmetical hierarchy for distinguished semantics: general semantics given by all chains, finite-chain semantics, standard semantics and rational semantics.

Keywords: Arithmetical complexity; core fuzzy logics; finite-chain semantics; first-order predicate fuzzy logics; mathematical fuzzy logic; rational semantics; standard semantics


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