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A Semantic Analysis of Stone and Dual Stone Negations with Regularity

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Logic and Its Applications (ICLA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10119))

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Abstract

This article investigates whether a few well-known ‘negation’ operators may be termed as negations, using Dunn’s approach. The semantics of the Stone negation is investigated in perp frames, that of dual Stone negation in exhaustive frames, and that of Stone and dual Stone negations with the regularity property, in \(K_{-}\) frames. The study leads to new semantics for the logics corresponding to the classes of Stone algebras, dual Stone algebras and regular double Stone algebras.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Arun Kumar

  2. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, 208016, India

    Mohua Banerjee

Authors
  1. Arun Kumar
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  2. Mohua Banerjee
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Corresponding author

Correspondence to Arun Kumar .

Editor information

Editors and Affiliations

  1. Indian Statistical Institute , Chennai, Tamil Nadu, India

    Sujata Ghosh

  2. Indian Institute of Technology Delhi , New Delhi, India

    Sanjiva Prasad

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Kumar, A., Banerjee, M. (2017). A Semantic Analysis of Stone and Dual Stone Negations with Regularity. In: Ghosh, S., Prasad, S. (eds) Logic and Its Applications. ICLA 2017. Lecture Notes in Computer Science(), vol 10119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54069-5_11

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  • DOI: https://doi.org/10.1007/978-3-662-54069-5_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-54068-8

  • Online ISBN: 978-3-662-54069-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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