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表达能力和推理复杂性是一个逻辑的两个重要特征,也是一对相互制约的关系。解释之间的互模拟关系是从语义的角度刻画逻辑表达能力的一个有效途径,其代表性的结果是命题模态逻辑表达能力的刻画定理-van Benthem刻画定理。文中给出了描述逻辑FL0(含构造子:原子概念、顶概念、概念交、全称量词约束)的模拟关系,建立了FL0中概念和术语公理集的表达能力刻画定理,即一阶逻辑公式与FL0概念和术语公理集等价的充分必要条件。上述结果为寻求表达能力与推理复杂性之间的最佳平衡提供了有效的支持。
The ability to express and the complexity of reasoning are two important features of a logic and are also a pair of mutually restrictive relations. The inter-simulative relationship between explanations is an effective way to depict the logical expression ability from the perspective of semantics. The representative result is the characterization theorem of propositional modal logic -van Benthem’s characterization theorem. In this paper, the simulation relation describing logic FL0 (including constructors: atomic concept, top concept, conceptual intersection, full quantifier constraint) is given, and the representation ability representation theorem of concepts and terms axioms in FL0 is established, that is, first- Necessary and Sufficient Conditions for the Equivalence of FL0 Concepts and Terminology Axioms. The above results provide effective support for seeking the best balance between expressive ability and inference complexity.