Soft Computing

, Volume 19, Issue 3, pp 531–546 | Cite as

Paraconsistency properties in degree-preserving fuzzy logics

  • Rodolfo Ertola
  • Francesc Esteva
  • Tommaso Flaminio
  • Lluís Godo
  • Carles NogueraEmail author


Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. Aiming to find logics that can handle inconsistency and graded truth at once, in this paper we explore the notion of paraconsistent fuzzy logic. We show that degree-preserving fuzzy logics have paraconsistency features and study them as logics of formal inconsistency. We also consider their expansions with additional negation connectives and first-order formalisms and study their paraconsistency properties. Finally, we compare our approach to other paraconsistent logics in the literature.


Mathematical fuzzy logic Degree-preserving fuzzy logics Paraconsistent logics Logics of formal inconsistency 



The authors are indebted to two anonymous referees for their critical and interesting remarks that have led to a significant improvement of the paper. All the authors have been partially supported by the FP7 PIRSES-GA-2009-247584 Project MaToMUVI. Besides, Ertola was supported by FAPESP LOGCONS Project and CONICET Project PIP 112201101006336, Esteva and Godo were supported by the Spanish Project TIN2012-39348-C02-01, Flaminio was supported by the Italian project FIRB 2010 (RBFR10DGUA\(_-\)002) and Noguera was supported by the Grant P202/10/1826 of the Czech Science Foundation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Rodolfo Ertola
    • 1
  • Francesc Esteva
    • 2
  • Tommaso Flaminio
    • 3
  • Lluís Godo
    • 2
  • Carles Noguera
    • 4
    • 5
    Email author
  1. 1.State University of CampinasCampinasBrazil
  2. 2.Artificial Intelligence Research Institute-CSICBellaterraSpain
  3. 3.Dipartimento di Scienze Teoriche e ApplicateUniversità dell’InsubriaVareseItaly
  4. 4.Institute of Information Theory and Automation-ASČRPragueCzech Republic
  5. 5.Institute of Computer Science-ASČRPragueCzech Republic

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