摘要： 与时态和空间有关的推理问题是人工智能研究中重要的组成部分，近年来时空逻辑的研究受到相关领域研究者的极大重视。以多维逻辑为框架表示时空知识，提出了一组将度量空间逻辑和时态逻辑相结合的逻辑模型PTL-MS、PTL-MS1、PTL-MS2，表示和推理随时间变化的距离关系，看成是时态逻辑和度量逻辑的迪卡尔乘积，给出了语义和语法，研究了它们的表达能力，用于时空约束满足问题、时空知识库以及移动对象数据库(MOD)等。

关键词: 时态逻辑, 度量空间, 距离, 时空推理

Abstract: Temporal and spatial reasoning are two important parts of artificial intelligence, and have gained much attention from researchers in recent years. This paper uses multi-dimensional logics as frameworks for knowledge representation and, in particular, for representing spatio-temporal information. It constructs two-dimensional logics intended for describing metric relationships that change over time. The family logic, named PTL-MS, PTL-MS1, PTL-MS2 are the Cartesian product of the well-known temporal logic PTL and the propositional metric logic MS[M]. It provides the intended languages with syntactic and semantics, and investigates the expressive power of them. It can be used in spatio-temporal constraint satisfaction problem, spatio-temporal knowledge base and mobile object database (MOD).

Key words: Temporal logic, Metric space, Distance, Spatio-temporal reasoning