Granular Language and Its Applications in Problem Solving

Problem solving in AI points out that a global problem is decomposed into several locals, until into elementary sub-problems solved directly. Subsequently, the solutions of various sub-problems are amalgamated into an answer of the global problem. The solving problem in practice is represented by a logical formula, and then the formula is decomposed into several sub-formulas, until into propositions or predicates. The solutions of these sub-formulas are amalgamated into an answer of the global formula. If the formula is described as a granulation, then it will be collapsed into several sub-granules. So, the collapsing algorithm and rules of amalgamating will be defined. In order to realizing the idea in above, a granular language and its calculus will be discussed.