计算机科学与探索Issue(9)：1147-1152,6.DOI:10.3778/j.issn.1673-9418.1411023
三值Łukasiewicz逻辑系统中公式的向量表示及其研究��
Research on Vector Representation of Formula in Three-ValuedŁukasiewicz Propo-sitional Logic System
摘要
Abstract
Based on vector representation of formula of classical propositional logic system, this paper gives a vector representation of formula by using assignment and assignment order of formula in three-valuedŁukasiewicz propo-sitional logic system. Firstly, this paper defines the truth degree of formula and gives the formula to calculate the similarity degree, pseudo-metric among formulas. Secondly, this paper obtains some simple properties of truth degree and similarity degree pseudo-metric among formulas. Thirdly, this paper proves that unary logical connection Ø , binary operation logical connections ® , Ú , Ù are continuous in pseudo-metric space (F(S)'ρ) . The related conclusions of this paper lay a solid foundation for further research of multi-valuedŁukasiewicz propositional logic system.关键词
三值Łukasiewicz逻辑系统/真度/相似度/伪距离Key words
three-valuedŁukasiewicz propositional logic system/truth degree/similarity degree/pseudo-metric分类
数理科学引用本文复制引用
贺锦瑞,惠小静,双靖宁..三值Łukasiewicz逻辑系统中公式的向量表示及其研究��[J].计算机科学与探索,2015,(9):1147-1152,6.基金项目
The National Natural Science Foundation of China under Grant No.11471007(国家自然科学基金) （国家自然科学基金）
the Natural Science Foundation of Shaanxi Province of China under Grant No.2014JM1020(陕西省自然科学基金) （陕西省自然科学基金）
the Special Fund of Higher Level University of Shaanxi Province under Grant No.2012SXTS07(陕西省高水平大学建设专项资金) （陕西省高水平大学建设专项资金）
the Doctoral Foundation of Yan’an University under Grant No. YDBK2013-12(延安大学博士基金) （延安大学博士基金）
the Special Fund of Yan’an under Grant No.2013-KG16(延安市专项基金) （延安市专项基金）
the Graduate Innovation Fund of Yan’an University (延安大学研究生创新基金) （延安大学研究生创新基金）
