Formalization for Granular Computing Based on Logical Formulas

In order to make formalization for granular computing,some kinds of formulas are constructed on a universe by a logical method. Every formula expresses a property, and can separate a semantic set which consists of all of the objects satisfying the formula.Therefore a granular space on the universe is produced based on the formulas, and the semantic sets separated by the formulas are taken as a formal definition for granules,and are called abstract granules.Furthermore,it is proved that any specific granule from an extended mathematical system can be formalized into an abstract granule,the conclusions is obtained that specific granules from approximate spaces and information systems can also be formalized into abstract granules. Based on a granular space and abstract granules,granular computing is defined,which finally realizes the goal of formalization for granular computing.