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Two Consistent Many-Valued Logics for Paraconsistent Phenomena

Conference paper
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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 

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Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.University of Technology, ViennaWienAustria
  2. 2.Faculty of MathematicsComplutense UniversityMadridSpain

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