Disjunction (Conjunction) normal form theorem in the modal logic system S5 is inductively proved, which can be used for representing complex modal formulas by means of conjunction and disjunction of simplest modal formulas with depth at most 1 in the system S5. As application, it is proved that a knowledge base could answer KB-queries if and only if it could answer queries of non-modal propositions and their negations, which is a basic problem on knowledge base.

modal logic system S5; normal form theorem; knowledge base; KB-formula