将符号化计算树逻辑中的Shannon展开式做了推广,在n值?ukasiewicz逻辑系统?n中,研究了由逻辑公式导出的n值McNaughton函数的展开式,给出了m元n值McNaughton函数的准析取范式和准合取范式.在此基础上,给出了m元n值McNaughton函数的计数问题,并在n值?ukasiewicz逻辑系统?n中,给出了m元逻辑公式的构造方法及其逻辑等价类的计数问题.“,”The Shannon expansion in symbolic computation tree logic is generalized. In a n-valued ?ukasiewicz logic system, ?n, the expansion of n-valued McNaughton functions which are induced by logical formulae is studied. The quasi disjunctive normal form and quasi conjunctive normal form of m-ary n-valued McNaughton functions, and the counting problems of m-ary n-valued McNaughton functions are given. In n-valued ?ukasiewicz logic system ?n, the construction of formulae and counting problems of their logic equivalence class are provided.