Logic on Similarity Based Rough Sets

Pawlak's indiscernibility relation (which is an equivalence relation) represents a limit of our knowledge embedded in an information system. Covering approximation spaces generated by tolerance relations treat objects which are similar to a given object in the same way. Similarity based rough sets rely on the similarity of objects in general and preserve the benefit of pairwise disjoint system of base sets. By using correlation clustering not only a pairwise disjoint system of base sets can be generated but representative members of base sets can be defined. These representative members have an important logical usage. The author shows that there is a logical system relying on similarity base sets in which the truth values of first-order formulas can be counted in an effective simple way.