We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms （of left A-modules） from graded dense left id...We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms （of left A-modules） from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra.展开更多
A great disturbance was raised by the report of Elkan entitled 'The Paradoxical Success of Fuzzy Logic' at the llth Annual Conference on Artificial Intelligence held in the United States in July, 1993. 15 famo...A great disturbance was raised by the report of Elkan entitled 'The Paradoxical Success of Fuzzy Logic' at the llth Annual Conference on Artificial Intelligence held in the United States in July, 1993. 15 famous experts working in artificial intelligence and fuzzy systems refuted the opinion. Elkan then gave another report entitled 'The Paradoxical Controversy over Fuzzy Logic' as a reply to the refutations mentioned above. Prof. Wu gave a detailed analysis on the controversy (see ref. [3]). This shows that there is no rigid logic foundation for fuzzy propositional calculus. In this note we first point out that it is impossible to keep all classical theorems as tautologies in the field of fuzzy propositional calculus. Then we introduce a formal deductive system in fuzzy propositional calculus by giving up certain classical axioms, and the corresponding soundness theorem is proved.展开更多
文摘We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms （of left A-modules） from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra.
文摘A great disturbance was raised by the report of Elkan entitled 'The Paradoxical Success of Fuzzy Logic' at the llth Annual Conference on Artificial Intelligence held in the United States in July, 1993. 15 famous experts working in artificial intelligence and fuzzy systems refuted the opinion. Elkan then gave another report entitled 'The Paradoxical Controversy over Fuzzy Logic' as a reply to the refutations mentioned above. Prof. Wu gave a detailed analysis on the controversy (see ref. [3]). This shows that there is no rigid logic foundation for fuzzy propositional calculus. In this note we first point out that it is impossible to keep all classical theorems as tautologies in the field of fuzzy propositional calculus. Then we introduce a formal deductive system in fuzzy propositional calculus by giving up certain classical axioms, and the corresponding soundness theorem is proved.
