Artificial Mathematical Intelligence : Cognitive, (Meta)mathematical, Physical and Philosophical Foundations. 1st ed. 2020

種類:

電子ブック

責任表示:

by Danny A. J. Gómez Ramírez

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Gómez Ramírez, Danny A. J.
• SpringerLink (Online service)

ISBN:

9783030502737 [3030502732]    

注記:

1. Global Introduction to the Artificial Mathematical Intelligence General Program -- 2. Some Basic Technical (Meta-)Mathematical Preliminaries for Cognitive Mathematics -- Part I. New Cognitive Foundations for Mathematics -- 3. General Considerations for the New Cognitive Foundations' Program -- 4. Towards the (Cognitive) Reality of Mathematics and the Mathematics of (Cognitive) Reality) -- 5. The Physical Numbers -- 6. Dathematics: A Meta-Isomorphic Version of "Standard" Mathematics Based on Proper Classes -- Part II. Global Taxonomy of the Fundamental Cognitive Mathematical Mechanisms Used in Mathematical Research -- 7. Conceptual Blending in Mathematical Creation/Invention -- 8. Formal Analogical Reasoning in Concrete Mathematical Research -- 9. Conceptual Substratum -- 10. (Initial) Global Taxonomy of the Most Fundamental Cognitive Mechanisms Used in Mathematical Creation/Invention -- Part III. Toward a Universal Meta-Modeling of Mathematical Creation/Invention -- 11. Meta-Modeling of Classic and Modern
This volume discusses the theoretical foundations of a new inter- and intra-disciplinary meta-research discipline, which can be succinctly called cognitive metamathematics, with the ultimate goal of achieving a global instance of concrete Artificial Mathematical Intelligence (AMI). In other words, AMI looks for the construction of an (ideal) global artificial agent being able to (co-)solve interactively formal problems with a conceptual mathematical description in a human-style way. It first gives formal guidelines from the philosophical, logical, meta-mathematical, cognitive, and computational points of view supporting the formal existence of such a global AMI framework, examining how much of current mathematics can be completely generated by an interactive computer program and how close we are to constructing a machine that would be able to simulate the way a modern working mathematician handles solvable mathematical conjectures from a conceptual point of view. The thesis that it is possible to meta-model t

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