Abstract Kumar and Banerjee (Some algebras and logics from quasiorder-generated covering-based approximation spaces. J Appl Non-classical Log 2024;34:248-68) characterized a subclass of quasiorder-generated covering-based approximation spaces for which the algebra of definable sets forms a Stone algebra. In this paper, we characterize those subclasses for which the definable sets form dual Stone, regular double Stone, linear Heyting, and well-connected Heyting algebras. As a consequence, discrete dualities of the aforementioned algebras are also obtained. Furthermore, we provide representation theorems of the aforementioned algebras in terms of rough sets determined by a quasiorder.
Kumar et al. (Wed,) studied this question.