A new paradigm termed granular computing is attracting researchers. We are coping with rule generation and data mining based on granular computing. Generally, a formula � in the form of λi Condition-part � Decision-part is called an implication. We see an implication � is a rule, if � satisfies some appropriate constraints. In this paper, new granules defined by an implication � are proposed. Basically, a set of granules are assigned to any implication �, and we solved that the set of granules assigned to an implication (λ;iPi) � Q � can be obtainable from the set of granules assigned to λiPi Decision and the set of granules assigned to Q Decision. This is termed as the merging procedure. We usually employed table search for rule generation, however it is also possible to generate rules by using the manipulation of granules defined by implications. The soundness and the completeness of rule generation with the merging procedure are also presented. Based on such background, rule generation from heterogeneous information sources and rule generation from information sources with uncertainty are also considered toward granular cognitive computing. © 2018 IEEE.