Rough sets, modal logic and approximate reasoning

•This paper introduces an approximate reasoning method based on rough sets and modal logic.•Different Approximate Modus Ponens (AMP) rules are presented and validated.•A comparative analysis is provided for fuzzy and rough based approaches.•Provide a real case analysis to logically model some issues of legal interest. This paper introduces an approximate reasoning method based on rough sets and modal logic. Various Approximate Modus Ponens rules are investigated and defined in Modal Logic systems interpreted in the rough set language. Although this is primarily theoretical work, we expect natural applications of the technique in real-life scenarios. An attempt in this direction is made in a real case analysis to logically model some issues of legal interest.