中文摘要：

研究基于可信度的模糊一阶模态逻辑，给出了基于常域的模糊一阶模态逻辑语义以及推理形式系统描述．为有效进行模糊断言间的推理，考虑了模糊约束的概念．模糊约束是一个表达式，其中既有语法成分又包含意义信息．模糊推理形式系统中的基本对象是模糊约束，针对模糊约束引进可满足性概念，研究模糊约束可满足性相关性质，利用模糊约束的概念，模糊断言间的推理可以直接在语义环境下加以考虑，因此，以模糊约束为基本元素的模糊推理形式系统随之建立．主要分析新产生断言有效性与模糊约束集可满足性之间的关系，并在此基础上给出了模糊推理形式系统的推理规则．进一步的工作可探讨模糊推理形式系统的可靠性与完全性，建立推理过程的能行机制．研究结果可在人工智能和计算机科学等领域得以应用．

英文摘要：

As an extension of traditional modal logics, this paper proposes a fuzzy first-order modal logic based on beilievable degree, and gives out a description of the fuzzy first-order modal logic based on constant domain semantics. In order to make the reasoning procedure between the fuzzy assertions efficiently, the notion of the fuzzy constraint is considered. A fuzzy constraint is an expression in which both syntax ingredient and semantics information are contained. By using the notion of the constraint, the reasoning procedure between the fuzzy assertions can be directly considered in the semantics environment, thus a fuzzy reasoning formal system which contains fuzzy constraint as its basic element is developed. As a main work of the paper, the relationship between the validity of the new assertion and the satisfiability of the fuzzy constraints is analyzed, and reasoning rules of the fuzzy reasoning formal system based on first order modal logic are given out. Further work could be done by considering the soundness and completeness of the formal system, and by building an efficient mechanism of reasoning procedure. The results have potential application in the areas of artificial intelligence and computer science.