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Paraconsistent Logics: A Survey Focussing on the Rough Set Approach

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Rough Sets (IJCRS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14481))

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Abstract

A survey of approaches yielding paraconsistent logics is made and is summarised through a diagram. The rough set theoretic approach is included in the survey, and it is the focus in the second part of the work. Several new paraconsistent systems are presented, that are obtained by weakening existing rough modus ponens rules.

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Notes

  1. 1.

    The consequence relation \(\vdash \) is used as a meta-linguistic symbol. In the context of a particular logic this can be a relation obtained semantically or syntactically; moreover sometimes the same notion of consequence is represented by an operator from \(\mathcal {P}(FOR)\) to \(\mathcal {P}(FOR)\). The use of notation would be clear from the contexts.

  2. 2.

    This notion is more formally introduced in Sect. 3.1.

  3. 3.

    A subset \(\varGamma \subseteq FOR\) is said to be trivial if \(\varGamma \vdash \alpha \) for every formula \(\alpha \), otherwise it is called non-trivial.

  4. 4.

    The logic CLuN, developed by Diderik Batens, is a predicative paraconsistent logic. The propositional part of CLuN is obtained by adding the axiom-schema \((\alpha \rightarrow \lnot \alpha ) \rightarrow \lnot \alpha \) to \(CPL^{+}\). The adaptive logic CLuN\(^{m}\) is obtained from CLuN based on a strategy, called minimal abnormality..

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India

    Bidhan Saha & Mohua Banerjee

  2. Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

    Soma Dutta

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  1. Bidhan Saha
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  2. Mohua Banerjee
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  3. Soma Dutta
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Correspondence to Bidhan Saha .

Editor information

Editors and Affiliations

  1. IRCCS Istituto Ortopedico Galeazzi, Milano, Italy

    Andrea Campagner

  2. Ghent University, Ghent, Belgium

    Oliver Urs Lenz

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Shuyin Xia

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. AGH University of Science and Technology, Kraków, Poland

    Jarosław Wąs

  6. University of Regina, Regina, SK, Canada

    JingTao Yao

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Saha, B., Banerjee, M., Dutta, S. (2023). Paraconsistent Logics: A Survey Focussing on the Rough Set Approach. In: Campagner, A., Urs Lenz, O., Xia, S., Ślęzak, D., Wąs, J., Yao, J. (eds) Rough Sets. IJCRS 2023. Lecture Notes in Computer Science(), vol 14481. Springer, Cham. https://doi.org/10.1007/978-3-031-50959-9_8

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