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Two-Sorted Modal Logic for Formal and Rough Concepts

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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

In this paper, we propose two-sorted modal logics for the representation and reasoning of concepts arising from rough set theory (RST) and formal concept analysis (FCA). These logics are interpreted in two-sorted bidirectional frames, which are essentially formal contexts with converse relations. The logic \({\textbf {KB}}\) contains ordinary necessity and possibility modalities and can represent rough set-based concepts. On the other hand, the logic \({\textbf {KF}}\) has window modality that can represent formal concepts. We study the relationship between KB and KF by proving a correspondence theorem. It is then shown that, using the formulae with modal operators in KB and KF, we can capture formal concepts based on RST and FCA and their lattice structures.

This work is partially supported by National Science and Technology Council (NSTC) of Taiwan under Grant No. 110-2221-E-001-022-MY3.

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Authors and Affiliations

  1. Institute of Information Science, Academia Sinica, Taipei, 115, Taiwan

    Prosenjit Howlader & Churn-Jung Liau

Authors
  1. Prosenjit Howlader
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  2. Churn-Jung Liau
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Correspondence to Prosenjit Howlader .

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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Howlader, P., Liau, CJ. (2023). Two-Sorted Modal Logic for Formal and Rough Concepts. 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_11

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  • DOI: https://doi.org/10.1007/978-3-031-50959-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-50958-2

  • Online ISBN: 978-3-031-50959-9

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