In this paper, the n-variable-m-dimensional fundamental phrases and clauses are used to completely build the universal basis for the general CNF and DNF. Furthermore, the general n-variable-m-dimensional CNF and DNF are also defined in order to construct the generally standard expressions of different axiom-based CNFs and DNFs such as 11-axiom-based Boolean CNF and Boolean DNF, 9-axiom-based fuzzy CNF and fuzzy DNF, and 5-axiom-basedt -norm-t-conorm CNF and t-norm-t-conorm DNF. Especially, the general algorithm to construct the generaln -variable-m-dimensional CNF (DNF) from any given DNF (CNF) is proposed. In general, the intrinsic relations among the axioms, the space of the fundamental phrases (clauses), and the general CNF and DNF are briefly studied. Additionally, some interesting applications of knowledge representation by using the axiom-based CNF and DNF are also discussed. Finally, some new conclusions are drawn based on the new algorithm and the applications.