Artificial Cognitively-inspired Generation of the Notion of Topological Group in the Context of Artificial Mathematical Intelligence

TL;DR

This paper introduces a novel computational approach to generate the mathematical concept of topological groups using artificial conceptual blending and formal specifications, advancing the field of Artificial Mathematical Intelligence.

Contribution

It presents a new method for explicitly generating the notion of topological groups through recursive formal specifications and conceptual blending in an artificial intelligence framework.

Findings

Successfully generated topological groups from basic concepts

Demonstrated the use of CASL and HETS for conceptual computation

Provided heuristic evidence supporting Artificial Mathematical Intelligence

Abstract

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.