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中文摘要：
目的建立一般非空集合X上的结论闭域和推理空间理论,并对它们的性质进行初步的探讨。方法通过对命题演算系统的共同特征的研究,在公式集的幂集格上得到了一般命题演算系统共同满足的一个推理闭包算子,再借助通过拓扑闭包算子建立拓扑空间的思想提出了推理闭包空间理论。结果探求推理闭包空间的初步性质和模糊命题演算系统的基本性质。结论通过推理闭包空间的建立,丰富了模糊逻辑的研究方法,沟通了拓扑学和逻辑学之间的联系。
英文摘要：
Aim To propose the theory of closed field of conclusion and reasoning space on a usual set, and to study thier primary properties. Methods At first, through the study of the common characteris ties of fuzzy propositional calculus systems, a reasoning operator is obtained on the powerset of fomula set which is satisfied by general fuzzy propositional calculus system;Secondly, with the aid of the thought of cstablishing topological space with topological closure operator, the theory of reasoning closure space is established. Results The elementary properties of reasoning closure space and the basic properties of fuzzy propositional system are studied. Conclusion As the reasoning closure space established, the methods of study of fuzzy logic is enriched, and the connection between topology and fuzzy logics is linked up.
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