A Semantics for Modal Language Using a Rough Set Model Based on Subset Approximation Structure

Abstract

Motivated by rough set theory, we introduce a novel semantics for the basic modal language based on the possibility lower approximation operator of subset approximation structures. The study investigates axiomatization, expressiveness, and invariance results related to this semantics. From a rough set perspective, it provides a formal language for reasoning about the possibility lower approximation operator. Additionally, the axiomatization results obtained here provide characterizing properties of the operator. © 2025 Copyright held by the owner/author(s).