On the Design of Mathematical Concepts
On the Design of Mathematical Concepts
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DOI：
10.1007/3-540-36187-1_65
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发表时间：
2002-12
期刊：
影响因子：
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通讯作者：
Manfred Kerber;Martin Pollet
中科院分区：
文献类型：
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作者：
Manfred Kerber;Martin Pollet
像一阶逻辑或集合论这样的基础系统可以用来构建现有数学和形式推理的大部分，这是深刻的数学见解之一。不幸的是，它被用于自动定理证明领域，作为一个论点，忽视了对各种各样的表示的需要。虽然设计问题在数学概念的形成中起着重要作用，但定理证明界在很大程度上忽略了它们。在本文中，我们认为这不仅会导致人机交互端的问题，而且会导致系统核心的严重问题，即它们的表示和推理能力。
That foundational systems like first-order logic or set theory can be used to construct large parts of existing mathematics and formal reasoning is one of the deep mathematical insights. Unfortunately it has been used in the field of automated theorem proving as an argument to disregard the need for a diverse variety of representations. While design issues play a major r ole in the formation of mathematical concepts, the theorem proving community has largely neglected them. In this paper we argue that this leads not only to problems at the human computer interaction end, but that it causes severe problems at the core of the systems, namely at their representation and reasoning capabilities.