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Thriving Rough Sets pp 237–268Cite as

Knowledge and Consequence in AC Semantics for General Rough Sets

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 708))

Abstract

Antichain based semantics for general rough sets was introduced recently by the present author. In her paper two different semantics, one for general rough sets and another for general approximation spaces over quasi-equivalence relations, were developed. These semantics are improved and studied further from a lateral algebraic logic and an algebraic logic perspective in this research. The framework of granular operator spaces is also generalized. The main results concern the structure of the algebras, deductive systems and the algebraic logic approach. The epistemological aspects of the semantics is also studied in this chapter in some depth and revolve around nature of knowledge representation, Peircean triadic semiotics and temporal aspects of parthood. Examples have been constructed to illustrate various aspects of the theory and applications to human reasoning contexts that fall beyond information systems.

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Acknowledgements

The present author would like to thank the referees for useful comments that helped in improving the readability of this research chapter.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Calcutta, 9/1B, Jatin Bagchi Road, Kolkata (calcutta), 700029, India

    A. Mani

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  1. A. Mani
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Correspondence to A. Mani .

Editor information

Editors and Affiliations

  1. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  2. Institute of Mathematics, University of Warsaw Institute of Mathematics, Warsaw, Poland

    Andrzej Skowron

  3. University of Regina, Department of Computer Science University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

  4. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. Polish-Japanese Academy IT , Warsaw, Poland

    Lech Polkowski

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Mani, A. (2017). Knowledge and Consequence in AC Semantics for General Rough Sets. In: Wang, G., Skowron, A., Yao, Y., Ślęzak, D., Polkowski, L. (eds) Thriving Rough Sets. Studies in Computational Intelligence, vol 708. Springer, Cham. https://doi.org/10.1007/978-3-319-54966-8_12

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  • DOI: https://doi.org/10.1007/978-3-319-54966-8_12

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  • Print ISBN: 978-3-319-54965-1

  • Online ISBN: 978-3-319-54966-8

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