中文摘要：

因素空间是论域U和因素族F的偶对（U,F）,其中F是一个Boole代数。针对因素空间定义中逻辑运算符“∧”和“∨”的意义同Boole代数的经典描述相悖的问题展开讨论,将运算符“∧”和“∨”的意义回归Boole代数的经典用法,从认知本体论的视角讨论因素空间的性质。关于因素的认知能力,发现因素空间的定义显化了解析力、隐化了概括力,因素的解析力主导了因素空间的性质。在这一发现的基础上,利用因素的概括力和解析力的反变关系,采用隐化解析力、显化概括力的数学技术,发现了对偶因素空间。结果表明,无论由因素的概括力还是解析力主导因素空间性质的讨论,因素族F都是一个Boole代数。

英文摘要：

The factor space （U,F） is the dual pair of object domain （U） and factors family （F）, where F is a Boolean algebra. Since the meanings of logical operators （＂ A ＂ and ＂ V ＂） are inconsistent with the classical description of Boolean algebra ,we regress the meanings of logical operators to the classical usage of Boolean algebra, and discuss the property of the factor from the perspective of the cognitive ontology. According to the perception of factor, we discover that the definition of factor space manifests the analysis ability and conceals the abstract ability. The analysis ability dominates the property of the factor space. On the basis of this discovery, the dual space is discovered by using the reverse relationship between the abstract ability and the analytical ability, as well as the mathematical technique of concealing abstract ability and manifesting analysis ability. The results show that the factors family F is always a Boolean algebra, regardless of the property of the factor space is discussed by the abstract ability or the analysis ability.