多值Lukasiewicz逻辑公式的范式表示和计数问题  

Normal Form of Lukasiewicz Logic Formulae and Related Counting Problems

作　　者：王庆平[1,2] 王国俊[1] 

机构地区：[1]陕西师范大学数学研究所,陕西西安710062 [2]江西财经大学统计学院,江西南昌330013

出　　处：《软件学报》2013年第3期433-453,共21页Journal of Software

基　　金：国家自然科学基金(11171200;61005046;61103133)

摘　　要：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 Lukasiewicz logic system, Ln, 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 Lukasiewicz logic system Ln, the construction of formulae and counting problems of their logic equivalence class are provided.

关 键 词：Shannon展开式 n值McNaughton函数 准析(合)取范式 逻辑等价类 计数问题 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]