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由于认识论和本体论两方面的原因,存在其成员数可增加的集合,这就是开放集合(OpenSet);又由于认知能力的局限性,认知主体(人或机器)无法枚举开放集合的所有成员。因此,在最基本的集合层面上,认知主体对其研究对象处于部分无知状态。为了描述主体知识的不完全性,提供不完全知识的表达与处理方法,文章从分析认知能力出发,修改了传统的集合定义方式,由此建立了基于性质和可断定性的真值条件理论,从而克服了集合的开放性造成的表达语句含义与真值方面的困难。文章还根据开放类的特征,提出了开放世界假设;在该预设和真值条件理论的基础上,提出和证明了一个独特的非规范3-值否定联结词真值函项;同时,提出和证明了蕴涵联结词真值函项,它们刻画了开放类的逻辑学和集合论特征。最后,在上述真值函项的基础上,文章给出了基于开放世界假设的3-值语句演算系统SLO及其形式语义理论,证明了它的有效性,一致性和完全性。
Due to the epistemology and the ontology, there exists an assembly whose members can be increased. This is called OpenSet. Due to the limitation of cognitive ability, the cognitive subject (human or machine) can not enumerate the open set All members. Therefore, at the most basic level of assembly, cognitive subjects are partially ignorant of their subjects. In order to describe the incompleteness of subject knowledge and provide the expression and processing of incomplete knowledge, the article revised the traditional method of definition of set from the analysis of cognitive ability, and established the theory of truth condition based on property and determinability , Thus overcoming the difficulties of expression meaning and truth value caused by the openness of the collection. Based on the preconditions and the truth conditions theory, the paper proposes and proves a unique non-canonical 3-valued negative connective truth-value function. At the same time, it proposes And prove the truth function of implicative connectives, which characterize the logic of open class and the theory of set theory. Finally, on the basis of the above truth-value function, the paper presents the SLO and its formal semantic theory based on the open-world hypothesis, which proves its validity, consistency and completeness.