{"product_id":"9783030502751","title":"Artificial Mathematical Intelligence: Cognitive, (Meta)mathematical, Physical and Philosophical Foundations","description":"\u003ch1\u003eArtificial Mathematical Intelligence: Cognitive, (Meta)mathematical, Physical and Philosophical Foundations\u003c\/h1\u003e \u003ch2\u003eGómez Ramírez, Danny A. J.\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis volume discusses the theoretical foundations of a new inter- and intra-disciplinary meta-research discipline, which can be succinctly called \u003ci\u003ecognitive metamathematics\u003c\/i\u003e, 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. \u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe thesis that it is possible to meta-model the intellectual job of a working mathematician is heuristically supported by the computational theory of mind, which posits that the mind is in fact a computational system, and by the meta-fact that genuine mathematical proofs are, in principle, algorithmically verifiable, at least theoretically. The introduction to this volume provides then the grounding multifaceted principles of \u003ci\u003ecognitive metamathematics,\u003c\/i\u003e and, at the same time gives an overview of some of the most outstanding results in this direction, keeping in mind that the main focus is human-style proofs, and not simply formal verification. \u003c\/p\u003e\u003cp\u003eThe first part of the book presents the new cognitive foundations of mathematics’ program dealing with the construction of formal refinements of seminal (meta-)mathematical notions and facts. The second develops positions and formalizations of a global taxonomy of classic and new cognitive abilities, and computational tools allowing for calculation of formal conceptual blends are described. In particular, a new cognitive characterization of the Church-Turing Thesis is presented. In the last part, classic and new results concerning the co-generation of a vast amount of old and new mathematical concepts and the key parts of several standard proofs in Hilbert-style deductive systems are shown as well, filling explicitly a well-known gap in the mechanization of mathematics concerning artificial conceptual generation.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2021-10-25\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030502751\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-50273-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 259\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":46548023869580,"sku":"9783030502751","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030502751.jpg?v=1776045610","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783030502751","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}