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Some Results on the Finite Complete Set of the Multi Valued Logic and Fuzzy Logic Functions
Li Junxiong
1992, 11(2):
1-7.
Given any set A whoso elements are functions,if there exists a finite set C,C≡A,such that each function in set A can be implemented by a combinatorial network of the functions in set C,it is said that C is a finite complete set of the functions in A.For example,the function set (x∧x,x∨x,x) is just a finite complete set of the two-valued logic functions.In this paper,a set consisting of 4 functions is given and proved to be a finite complete.set of the α-valued logic functions (α≥2).It is aiso proved that no finite complete set exists for the fuzzy logic functions.In addition to the above results,a formal inference system FUNCc is created and it is proved that each combinatorial network of the functions in C is equivalent to a theorem of the FUNCc.
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