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On Conjectures in t-Norm Based Fuzzy Logics

  • Francesc EstevaEmail author
  • Itziar García-Honrado
  • Lluís Godo
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 322)

Abstract

This paper is a humble homage to Enric Trillas. Following his foundational contributions on models of ordinary reasoning in an algebraic setting, we study here elements of these models, like conjectures and hypothesis, in the logical framework of continuous t-norm based fuzzy logics. We consider notions of consistency, conjecture and hypothesis arising from two natural families of consequence operators definable in these logics, namely the ones corresponding to the so-called truth-preserving and degree-preserving consequence relations. We pay special attention to the particular cases of three prominent fuzzy logics: Gödel, Product and Łukasiewicz logics

Keywords

CHC models Consequence operators t-norm based fuzzy logics Consistency Conjectures 

Notes

Acknowledgments

This work has been partially supported by the Spanish projects TIN2012-39348-C02-01 (Esteva and Godo) and TIN2011-29827-C02-01 (García-Honrado).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Francesc Esteva
    • 1
    Email author
  • Itziar García-Honrado
    • 2
  • Lluís Godo
    • 1
  1. 1.Artificial Intelligence Research Institute (IIIA-CSIC)BellaterraSpain
  2. 2.Department of Statistics, Operational Research and Mathematical EducationUniversity of OviedoOviedoSpain

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