| Randomization of classical inference patterns and its application |
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| 作者单位： | WANG GuoJun（Institute of Mathematics,Shaanxi Normal University, Xi'an 710062,China;Research Center for Science,Xi'an Jiaotong University,Xi'an 710049,China） ;
HUI XiaoJing（Institute of Mathematics,Shaanxi Normal University, Xi'an 710062,China;College of Mathematics and Computer Science,Yan'an University,716000,China） ; |
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| 摘 要： | By means of randomization, the concept of D-randomized truth degree of formulas in two-valued propositional logic is introduced, and it is proved that the set of values of D-randomized truth degree of formulas has no isolated point in 0,1]. The concepts of D-logic pseudo-metric and D-logic metric space are also introduced and it is proved that there is no isolated point in the space. The new built D-randomized concepts are extensions of the corresponding concepts in quantified logic. Moreover, it is proved that the basic logic connectives are continuous operators in D-logic metric space. Lastly, three different types of approximate reasoning patterns are proposed.
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Randomization of classical inference patterns and its application |
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| Authors: | Wang GuoJun Hui XiaoJing |
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| Affiliation: | 1. Institute of Mathematics,Shaanxi Normal University, Xi'an 710062,China;Research Center for Science,Xi'an Jiaotong University,Xi'an 710049,China
2. Institute of Mathematics,Shaanxi Normal University, Xi'an 710062,China;College of Mathematics and Computer Science,Yan'an University,716000,China |
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| Abstract: | By means of randomization, the concept of D-randomized truth degree of formulas in two-valued propositional logic is introduced, and it is proved that the set of values of D-randomized truth degree of formulas has no isolated point in 0,1]. The concepts of D-logic pseudo-metric and D-logic metric space are also introduced and it is proved that there is no isolated point in the space. The new built D-randomized concepts are extensions of the corresponding concepts in quantified logic. Moreover, it is proved that the basic logic connectives are continuous operators in D-logic metric space. Lastly, three different types of approximate reasoning patterns are proposed. |
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| Keywords: | D-randomized mapping D-randomized truth degree D-similarity D-logic metric space approximate reasoning |
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