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New Directions in Paraconsistent Logic pp 185–210Cite as

Two Consistent Many-Valued Logics for Paraconsistent Phenomena

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 152)

Abstract

In this reviewing paper, we recall the main results of our papers [24, 31] where we introduced two paraconsistent semantics for Pavelka style fuzzy logic. Each logic formula \(\alpha \) is associated with a \(2 \times 2\) matrix called evidence matrix. The two semantics are consistent if they are seen from ‘outside’; the structure of the set of the evidence matrices \({{\textit{M}}}\) is an MV-algebra and there is nothing paraconsistent there. However, seen from ‘inside,’ that is, in the construction of a single evidence matrix paraconsistency comes in, truth and falsehood are not each others complements and there is also contradiction and lack of information (unknown) involved. Moreover, we discuss the possible applications of the two logics in real-world phenomena.

Keywords

  • Mathematical fuzzy logic
  • Paraconsistent logic
  • MV-algebra

Mathematics Subject Classification (2000)

  • 03-02
  • 03620
  • 06D35

The first author acknowledges the support by the Czech Technical University in Prague under project SGS12/ 187/ OHK3/ 3T/ 13. The second author has been partially supported by grant TIN2012-32482 from the Government of Spain and excellence network S2013/ICE–2845 of the Region of Madrid.

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Authors and Affiliations

  1. University of Technology, Vienna, Wiedner Hauptstrasse 8–10, A-1040, Wien, Austria

    Esko Turunen

  2. Faculty of Mathematics, Complutense University, Plaza de Ciencias 3, 28040, Madrid, Spain

    J. Tinguaro Rodríguez

Authors
  1. Esko Turunen
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  2. J. Tinguaro Rodríguez
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Correspondence to Esko Turunen .

Editor information

Editors and Affiliations

  1. Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Jean-Yves Beziau

  2. Indian Statistical Institute Kolkat, Kolkata, India

    Mihir Chakraborty

  3. C.I.T Campus, Institute for Mathematical Sciences, Chennai, Tamil Nadu, India

    Soma Dutta

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Turunen, E., Rodríguez, J.T. (2015). Two Consistent Many-Valued Logics for Paraconsistent Phenomena. In: Beziau, JY., Chakraborty, M., Dutta, S. (eds) New Directions in Paraconsistent Logic. Springer Proceedings in Mathematics & Statistics, vol 152. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2719-9_8

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