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首页> 外文会议>International Conference on Conceptual Structures(ICCS 2004); 20040719-20040723; Huntsville,AL; US >'Particles' and 'Waves' as Understood by Temporal Concept Analysis
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'Particles' and 'Waves' as Understood by Temporal Concept Analysis

机译：时间概念分析对“粒子”和“波”的理解

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摘要

A qualitative mathematical framework for a granular representation of relational information about general objects, as for examples particles, waves, persons, families, institutions or other systems in discrete or continuous "space-time" is introduced. That leads to a common description of particles and waves in physics, such that the intuitive physical notion of "wave packet" can be captured by the mathematical notion of a general object or a packet in a spatio-temporal Conceptual Semantic System. In these systems particles and waves are defined as special packets. It is proved, that "classical objects" and "classical waves" can be represented as, respectively, particles and waves in spatio-temporal Conceptual Semantic Systems. The underlying mathematical framework is Formal Concept Analysis and its subdiscipline Temporal Concept Analysis. That allows for describing continuously fine or arbitrarily coarse granularity in the same conceptual framework. The central idea for a "symmetric" description of objects, space, and time is the introduction of "instances" representing information units of observations, connecting the granules for objects, space, and time.
机译：引入了一种用于数学表示有关一般对象的关系信息的定性数学框架，例如离散，连续“时空”中的粒子，波浪，人，家庭，机构或其他系统。这导致了物理学中对粒子和波的共同描述，因此“波包”的直观物理概念可以通过时空概念语义系统中的一般对象或包的数学概念来捕获。在这些系统中，粒子和波被定义为特殊数据包。事实证明，“古典对象”和“古典波”可以分别表示为时空概念语义系统中的粒子和波。基本的数学框架是形式概念分析及其子学科时间概念分析。这允许在同一概念框架中描述连续的细粒度或任意粗粒度。对对象，空间和时间进行“对称”描述的中心思想是引入“实例”，这些实例表示观测的信息单元，连接对象，空间和时间的颗粒。

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