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Two-sorted Modal Logic for Formal and Rough Concepts. (arXiv:2309.04115v1 [math.LO])

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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. On one
hand, 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 \textbf{KB} and \textbf{KF} by proving a
correspondence theorem. It is then shown that, using the formulae with modal
operators in \textbf{KB} and \textbf{KF}, we can capture formal concepts based
on RST and FCA and their lattice structures.

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