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首页> 外文会议>International Conference on Conceptual Structures(ICCS 2004); 20040719-20040723; Huntsville,AL; US >Types and Tokens for Logic with Diagrams
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Types and Tokens for Logic with Diagrams

机译：逻辑图的类型和标记

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摘要

It is well accepted that diagrams play a crucial role in human reasoning. But in mathematics, diagrams are most often only used for visualizations, but it is doubted that diagrams are rigor enough to play an essential role in a proof. This paper takes the opposite point of view: It is argued that rigor formal logic can carried out with diagrams. In order to do that, it is first analyzed which problems can occur in diagrammatic systems, and how a diagrammatic system has to be designed in order to get a rigor logic system. Particularly, it will turn out that a separation between diagrams as representations of structures and these structures themselves is needed, and the structures should be defined mathematically. The argumentation for this point of view will be embedded into a case study, namely the existential graphs of Peirce. In the second part of this paper, the theoretical considerations are practically carried out by providing mathematical definitions for the semantics and the calculus of existential Alpha graphs, and by proving mathematically that the calculus is sound and complete.
机译：众所周知，图在人类推理中起着至关重要的作用。但是在数学中，图通常仅用于可视化，但是怀疑图是否足够严格以在证明中扮演重要角色。本文采取了相反的观点：认为严格的形式逻辑可以用图来执行。为此，首先分析在图形系统中可能出现哪些问题，以及如何设计图形系统才能获得严格的逻辑系统。特别地，将证明需要在作为结构的表示的图与这些结构本身之间进行分离，并且应该在数学上定义结构。这种观点的论点将被嵌入到案例研究中，即Peirce的存在图。在本文的第二部分中，通过为存在的Alpha图的语义和演算提供数学定义，并通过数学证明演算是健全且完整的，从而在实践中进行了理论上的考虑。

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