Two-sorted Modal Logic for Formal and Rough Concepts
Abstract
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 contains ordinary necessity and possibility modalities and can represent rough set-based concepts. On the other hand, the logic 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.
Keywords
Cite
@article{arxiv.2309.04115,
title = {Two-sorted Modal Logic for Formal and Rough Concepts},
author = {Prosenjit Howlader and Churn-Jung Liau},
journal= {arXiv preprint arXiv:2309.04115},
year = {2023}
}