Rough Sets were introduced by Polish computer scientist Z. Pawlak in the year 1982. The objective was knowledge representation and data processing from the angle of computation and decision making. The main idea is to approximate the extension of a concept by two subsets of the universe of discourse, namely, lower and upper approximations. Various types of algebras on the power set of the universe with lower/upper approximation operators were soon proposed, and algebraic studies have since formed an important branch of research for rough set theory. Parallel to this, came into existence the study of logics generated by rough sets, developing over the years in multiple directions.

Logics from rough sets may be divided broadly into two groups: algebraic and modal. In the first,logics are rendered with algebraic semantics where the algebras are abstractions from rough set models. Amongst these algebras, a notable one that has seen a lot of investigation, is the topological quasi-Boolean algebra and algebras related to it. The direction of research includes a study of representation theorems for the abstract algebraic structures in terms of rough set structures, and their subsequent use in formulating a rough set semantics for the corresponding logics. In the second group, various modal logic systems are developed depending upon the properties of the lower/upper approximation operators. Such studies attained a peak with modal logic systems generated from covering based rough sets. These may be compared with neighbourhood–semantics of modal systems. However, several new kinds of modal logic systems, including non-standard ones, have been proposed from rough set models. Interplay between modal systems and rough set theory has thus become a significant area of research.

Yet a third type of development has taken place in which the consequence relation has been generalized to what has been called the rough consequence relation based on rough modus ponens rules. Besides, an axiomatic approach for rough consequence has been developed. These generalized consequence relations have direct implications in approximate reasoning