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arXiv 2112.02457cs.AI
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Artificial Cognitively-inspired Generation of the Notion of Topological Group in the Context of Artificial Mathematical Intelligence

Institución Universitaria Pascual Bravo(帕斯夸尔·布拉沃大学学院);Visión Real Cognitiva S. A. S.(真实认知视觉公司);Vienna University of Technology(维也纳技术大学)

Danny A. J. Gomez-Ramirez, Yoe A. Herrera-Jaramillo, Florian Geismann

英文摘要:

The new computational paradigm of conceptual computation has been introduced in the research program of Artificial Mathematical Intelligence. We provide the explicit artificial generation (or conceptual computation) for the fundamental mathematical notion of topological groups. Specifically, we start with two basic notions belonging to topology and abstract algebra, and we describe recursively formal specifications in the Common Algebraic Specification Language (CASL). The notion of conceptual blending between such conceptual spaces can be materialized computationally in the Heterogeneous Tool Set (HETS). The fundamental notion of topological groups is explicitly generated through three different artificial specifications based on conceptual blending and conceptual identification, starting with the concepts of continuous functions and mathematical groups (described with minimal set-theoretical conditions). This constitutes in additional heuristic evidence for the third pillar of Artificial Mathematical Intelligence.

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