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Dialectical Rough Sets, Parthood and Figures of Opposition-I

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Book cover Transactions on Rough Sets XXI

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 10810))

Abstract

In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and variants were recently introduced by the present author as an optimal framework for anti-chain based algebraic semantics of general rough sets and the inverse problem. In the framework, various sub-types of crisp and non-crisp objects are identifiable that may be missed in more restrictive formalism. This is also because in the latter cases concepts of complementation and negation are taken for granted - while in reality they have a complicated dialectical basis. This motivates a general approach to dialectical rough sets building on previous work of the present author and figures of opposition. In this paper dialectical rough logics are invented from a semantic perspective, a concept of dialectical predicates is formalized, connection with dialetheias and glutty negation are established, parthood analyzed and studied from the viewpoint of classical and dialectical figures of opposition by the present author. The proposed method become more geometrical and encompass parthood as a primary relation (as opposed to roughly equivalent objects) for algebraic semantics.

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Acknowledgement

The present author would like to thank the referees for detailed remarks that led to improvement (especially of the readability) of the research paper.

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

    A. Mani

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  1. University of Manitoba, Winnipeg, MB, Canada

    James F. Peters

  2. University of Warsaw, Warsaw, Poland

    Andrzej Skowron

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Mani, A. (2019). Dialectical Rough Sets, Parthood and Figures of Opposition-I. In: Peters, J., Skowron, A. (eds) Transactions on Rough Sets XXI. Lecture Notes in Computer Science(), vol 10810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58768-3_4

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