{"product_id":"artificial-mathematical-intelligence-cognitive-metamathematical-physical-and-philosophical-foundations-von-danny-a-j-gomez-ramirez","title":"Artificial Mathematical Intelligence","description":"\n                                \n                \u003cp\u003e\u003c\/p\u003e\n                                \n                \u003cp\u003e\n                                        This volume discusses the theoretical foundations of a new inter- and intra-disciplinary meta-research discipline, which can be succinctly called \n                    \n                    \u003ci\u003ecognitive metamathematics\u003c\/i\u003e\n                                        , 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. \n                \n                \u003c\/p\u003e\n                                \n                \u003cp\u003e \u003c\/p\u003e\n                                \n                \u003cp\u003e\n                                        The 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 \n                    \n                    \u003ci\u003ecognitive metamathematics,\u003c\/i\u003e\n                                         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. \n                \n                \u003c\/p\u003e\n                                \n                \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\n                                \n                \u003cp\u003e\u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783030502751\"\u003e\u003ch3\u003eCognitive, (Meta)mathematical, Physical and Philosophical Foundations\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783030502720\"\u003e\u003ch3\u003eCognitive, (Meta)mathematical, Physical and Philosophical Foundations\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783030502751","offer_id":39509053309021,"sku":"9783030502751","price":53.49,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783030502720","offer_id":32917569044573,"sku":"9783030502720","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/af988c0d-8422-45cc-8a68-5390edb78fe5.jpg?v=1772170034","url":"https:\/\/shop.autorenwelt.de\/products\/artificial-mathematical-intelligence-cognitive-metamathematical-physical-and-philosophical-foundations-von-danny-a-j-gomez-ramirez","provider":"Autorenwelt Shop","version":"1.0","type":"link"}