Granules and Applications of Granular Computing in Logical Reasoning

The structure and real examples of information granules are discussed in this paper The granules of decision rules are defined based on a rough set approach Granular language is defined Syntax and semantics are also described Operation rules of the granular statements are given Some properties of the language are also discussed Inclusion and closeness between granules are established Granulation base corresponding to decision rules is also constructed A reasoning model based on the concepts is proposed, and may be used in logical reasoning The characteristic of the reasoning model is both logic and set theory By "logic" it is meant that the reasoning obeys the logical derivability; By "set theory" it is meant that the operations corresponding to the meaning sets of logical formulas obey the methods in set theory Finally, the validity and feasibility of the reasoning are illustrated with real examples