Summary: A propositional logic PRL for rough sets was proposed in [

*M. Banerjee*, ibid. 31, No. 3–4, 213–220 (1997;

Zbl 0895.03007)]. In this paper, we initially introduce the concepts of rough (upper, lower) truth degrees on the set of formulas in PRL. Then, by grading the rough equality relations, we propose the concepts of rough (upper, lower) similarity degree. Finally, three different pseudo-metrics on the set of rough formulas are obtained, and thus an approximate reasoning mechanism is established.