| 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. |
| 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 |
| DOI：10.3724/SP.J.1001.2013.04231 |
| 分类号: |
| 基金项目:国家自然科学基金(11171200, 61005046, 61103133) |
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| Normal Form of Łukasiewicz Logic Formulae and Related Counting Problems |
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WANG Qing-Ping1,2, WANG Guo-Jun1
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1.Institute of Mathematics, Shaanxi Normal University, Xi'an 710062, China;2.School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, 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. |
| Key words: Shannon expansion n-valued McNaughton function quasi disjunctive (conjunctive) normal form logic equivalence class counting problem |
