| 多值Łukasiewicz逻辑公式的范式表示和计数问题 |
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| 引用本文： | 王庆平,王国俊.多值Łukasiewicz逻辑公式的范式表示和计数问题[J].软件学报,2013,24(3):433-453. |
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| 作者姓名： | 王庆平 王国俊 |
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| 作者单位： | 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;陕西师范大学 数学研究所,陕西 西安 710062 |
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| 基金项目： | 国家自然科学基金(11171200, 61005046, 61103133) |
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| 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.
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| 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 |
| 收稿时间： | 1/5/2011 12:00:00 AM |
| 修稿时间： | 2012/3/19 0:00:00 |
Normal Form of Łukasiewicz Logic Formulae and Related Counting Problems |
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| WANG Qing-Ping and WANG Guo-Jun.Normal Form of Łukasiewicz Logic Formulae and Related Counting Problems[J].Journal of Software,2013,24(3):433-453. |
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| Authors: | WANG Qing-Ping and WANG Guo-Jun |
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| Affiliation: | Institute of Mathematics, Shaanxi Normal University, Xi'an 710062, China;School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China;Institute of Mathematics, Shaanxi Normal University, Xi'an 710062, China |
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| 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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| Keywords: | Shannon expansion n-valued McNaughton function quasi disjunctive (conjunctive) normal form logic equivalence class counting problem |
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