归结与调解方法的有效性和完备性——基于扩充模糊逻辑  

Validity and Completeness of Resolution and Paramodulation Based on a Generalized Fuzzy Logic with Similarity

作　　者：刘富春[1] 

机构地区：[1]广东工业大学应用数学学院,广州510090

出　　处：《计算机工程与应用》2006年第2期73-75,175,共4页Computer Engineering and Applications

基　　金：广东省自然科学基金资助项目(编号:020146;031541);广东工业大学青年基金项目(编号:042027)

摘　　要：模糊集与模糊逻辑是处理大量存在的不确定性与模糊性信息的重要数学工具,在近似推理等领域有着广泛的应用。该文将王家兵等人提出的真值取在[0,1]区间上的带有相似性关系的模糊逻辑,扩充到很一般的与滋可比的有余完全分配格值逻辑中,将王家兵等人的许多结论进行了推广。首先对带有相似性关系的模糊逻辑的语义描述进行了扩充,然后讨论了在这种模糊推理中归结式与调解式的有效性,最后通过证明一个子句集在扩充模糊逻辑中的不可满足性与它在带有相等关系的二值逻辑中的不可满足性是等价的,得到了基于归结与调解方法对这种广义模糊演算的完备性。Fuzzy sets and fuzzy logic are important mathematical tools for processing uncertain and vague information, which has been widely applied to approximate reasoning and so on. In this paper,the fuzzy logic with similarity, is generalized to the complete distributive lattice with complement of which elements are comparable with μ.Firstly,the generalized fuzzy logic with similarity is proposed and its semantics are given. Secondly,the validity of the generalized fuzzy logical inference both by resolution and by paramodulation are discussed.Furthermore,it is proved that a clause set is unsatisfiable in the generalized fuzzy logic if and only if it is unsatisfiable in classical logic.Finally,the completeness of the resolution and paramodulation is presented for the generalized fuzzy predicate calculus.

关 键 词：模糊逻辑 近似推理 归结方法 调解方法 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]