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Dialectical Rough Sets, Parthood and Figures of Opposition-I

  • A. ManiEmail author
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Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Rough objects Dialectical rough semantics Granular operator spaces Rough mereology Polytopes of dialectics Antichains Dialectical rough counting Axiomatic approach to granules Constructive algebraic semantics Figures of opposition Unified semantics 
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Notes

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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Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of Calcutta, International Rough Set SocietyKolkata (Calcutta)India

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