Approximate reasoning based on granular computing in granular logic

The paper proposes a granular logic which defines the syntax and semantics of the logic. The formula in the logic is a granule or any Boolean combination of the granules. We discuss a reasoning based on the granular computing. The reasoning is used in expert systems, and is also an extension of matching reasoning in production rules. The inclusion and closeness degree between granules are defined in the paper. Finding the match among granules satisfying the given closeness degree completes the approximate reasoning. The paper defines the granular operation based on both logic and the set theory. Finally, the matching reasoning and deductive inference is illustrated with real examples.