Abstract:Since the importance of automated reasoning and the resolution principle of the fuzzy logic with one negation is mainly studied now, the resolution principle of the fuzzy proposition logic(FLCOM) with three kinds of negation, contradictory negation, opposite negation and medium negation, is discussed. Based on an infinite-valued semantic interpretation of FLCOM, λ-satisfiable and λ-unsatisfiable concepts are proposed, and λ-resolution method is introduced into FLCOM. Besides, λ-resolution deduction of FLCOM is defined and λ-resolution principle of FLCOM is discussed. Moreover, the completeness of λ-resolution method is proved. Based on λ-resolution method and the proved conclusions, some examples providing evidences for the λ-resolution method and the conclusions are listed below the corresponding definitions and theorems. Therefore, whether a fuzzy propositional formula is λ-satisfiable or λ-unsatisfiable can be determined in the range of FLCOM.
赵洁心,潘正华. 具有三种否定的模糊命题逻辑形式系统FLCOM的λ-归结*[J]. 模式识别与人工智能, 2015, 28(3): 202-208.
ZHAO Jie-Xin, PAN Zheng-Hua. λ-Resolution of Fuzzy Propositional Logic System with Three Kinds of Negation FLCOM. , 2015, 28(3): 202-208.
[1] Robinson J A. A Machine-Oriented Logic Based on the Resolution Principle. Journal of the ACM, 1965, 12(1): 23-41 [2] Slagle J R. Automatic Theorem Proving with Renamable and Semantic Resolution. Journal of the ACM, 1967, 14(4): 687-697 [3] Lee R C T, Chang C L. Some Properties of Fuzzy Logic. Information and Control, 1971, 19(5): 417-431 [4] Morgan C G. Resolution for Many-Valued Logics. Logique et Analyse, 1976, 19(74/75/76): 311-339 [5] Liu X H. Generalized Fuzzy Logic and Lock Semantic Resolution Principle. Chinese Journal of Computers, 1980, 3(2): 97-111 (in Chinese) (刘叙华.广义模糊逻辑和锁语义归结原理.计算机学报, 1980, 3(2): 97-111) [6] Liu X H, Xiao H. Operator Fuzzy Logic and Fuzzy Resolution // Proc of the 15th IEEE International Symposium on Multiple-Valued Logic. Kingston, Canada, 1985: 68-75 [7] Yager R R. Inference in a Multivalued Logic System. International Journal of Man-Machine Studies, 1985, 23(1): 27-44 [8] Liu X H, Xiao H. Operator Fuzzy Logic and λ-Resolution. Chinese Journal of Computers, 1989, 12(2): 81-91 (in Chinese) (刘叙华,肖 红.算子Fuzzy逻辑和λ-归结方法.计算机学报, 1989, 12(2): 81-91) [9] Liu X H, An Z. An Improvement of Operator Fuzzy Logic and Its Resolution Deduction. Chinese Journal of Computers, 1990, 13(12): 890-899 (in Chinese) (刘叙华,安 直.算子Fuzzy逻辑及其归结推理的改进.计算机学报, 1990, 13(12): 890-899) [10] Zhu W J, Xiao X A. Predicate Calculus System of Medium Logic (I). Journal of Nanjing University: Natural Sciences, 1988, 24(4): 583-598 (in Chinese) (朱梧槚,肖奚安.中介逻辑的谓词演算系统(I).南京大学学报:自然科学版, 1988, 24(4): 583-598) [11] Zhu W J, Xiao X A. Predicate Calculus System of Medium Logic (II). Journal of Nanjing University: Natural Sciences, 1989, 25(2): 165-183 (in Chinese) (朱梧槚,肖奚安.中介逻辑的谓词演算系统(II).南京大学学报:自然科学版, 1989, 25(2): 165-183) [12] Qiu W D, Zou J. Resolution Principle of the Medium Predicate Calculus System. Journal of Shanghai Polytechnic University, 1990, 11(2): 5-11 (in Chinese) (邱伟德,邹 晶.中介谓词演算系统MF的归结原理.上海工业大学学报, 1990, 11(2): 5-11) [13] Xu Y, Ruan D, Kerre E E, et al. α-Resolution Principle Based on Lattice-Valued Propositional Logic LP(X). Information Science, 2000, 130(1/2/3/4): 195-223 [14] Xu Y, Ruan D, Kerre E E, et al. α-Resolution Principle Based on First-Order Lattice-Valued Logic LF(X). Information Science, 2001, 132(1/2/3/4): 221-239 [15] Pan Z H. λ-Resolution of the Medium Predicate Logic System. Journal of Software, 2003, 14(3): 345-349 (in Chinese) (潘正华.中介谓词逻辑系统的λ-归结.软件学报, 2003, 14(3): 345-349) [16] Zhang S L, Pan Z H. λ-Resolution for Medium Predicate Logic Based on Improved Form of Infinite-Valued Semantic Interpretation. Journal of Shandong University: Natural Science, 2012, 47(2): 109-114,118 (in Chinese) (张胜礼,潘正华.基于改进的无穷值语义解释的中介谓词逻辑的λ-归结.山东大学学报:理学版, 2012, 47(2): 109-114,118) [17] Pan Z H. Three Kinds of Negation of Fuzzy Knowledge and Their Base of Logic // Proc of the 9th International Conference on Intelligent Computing Theories and Technology. Nanning, China, 2013: 83-93 [18] Pan Z H. Three Kinds of Negation of Fuzzy Knowledge and Their Base of Set. Chinese Journal of Computers, 2012, 35(7): 1421-1428 (in Chinese) (潘正华.模糊知识的三种否定及其集合基础.计算机学报, 2012, 35(7): 1421-1428)