Abstract
Whereas set theory is generally treated as a foundation of mathematics (sometimes said “logical foundation”), and this permits to formulate all mathematical results in a few precise set-theoretic terms, there is no such theory for the intelligence - human, artificial, or natural, like the intelligence of evolutionary mechanisms. AI, thus, remains an engineering discipline, without a mathematical framework for unifying various approaches to explicating or modeling intelligence. Development of a foundational theory for AI, primarily one focused on “mental content”, sounds like a high priority collective task for the AI research community. Such theory could be named idea theory by the pattern “set theory”. In this paper, the features of an algebraic idea theory are proposed; one with three primitive operations originating in the algebraic approach to data earlier proposed by the author and named “A3”: aggregation, association, atomification. This theory is supposed to be an extension of a set theory built upon ground mereology, i.e., upon a set theory with inclusion rather than membership as primitive relation. Idea theory is believed to be sufficient for describing and generating all structures built by mind. A virtual machine for generating ideas is described.
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Drugus, I. (2023). Idea Theory: Towards Logical Foundations of Intelligence Science. In: Arai, K. (eds) Proceedings of the Future Technologies Conference (FTC) 2023, Volume 2. FTC 2023. Lecture Notes in Networks and Systems, vol 814. Springer, Cham. https://doi.org/10.1007/978-3-031-47451-4_25
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