Journal of Software:2013.24(3):433-453

(陕西师范大学 数学研究所,陕西 西安 710062;江西财经大学 统计学院,江西 南昌 330013)
Normal Form of Łukasiewicz Logic Formulae and Related Counting Problems
WANG Qing-Ping,WANG Guo-Jun
(Institute of Mathematics, Shaanxi Normal University, Xi'an 710062, China;School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China)
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Received:January 05, 2011    Revised:March 19, 2012
> 中文摘要: 将符号化计算树逻辑中的Shannon展开式做了推广,在n值Łukasiewicz逻辑系统Łn中,研究了由逻辑公式导出的n值McNaughton函数的展开式,给出了mn值McNaughton函数的准析取范式和准合取范式.在此基础上,给出了mn值McNaughton函数的计数问题,并在n值Łukasiewicz逻辑系统Łn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.
Abstract:The Shannon expansion in symbolic computation tree logic is generalized. In a n-valued Łukasiewicz logic system, Łn, 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 Łukasiewicz logic system Łn, the construction of formulae and counting problems of their logic equivalence class are provided.
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基金项目:国家自然科学基金(11171200, 61005046, 61103133) 国家自然科学基金(11171200, 61005046, 61103133)
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WANG Qing-Ping,WANG Guo-Jun.Normal Form of Łukasiewicz Logic Formulae and Related Counting Problems.Journal of Software,2013,24(3):433-453