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 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 cognitive metamathematics, 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. The 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.

Mathematical Methods in Artificial Intelligence introduces the student to the important mathematical foundations and tools in AI and describes their applications to the design of AI algorithms. This useful text presents an introductory AI course based on the most important mathematics and its applications. It focuses on important topics that are proven useful in AI and involve the most broadly applicable mathematics. The book explores AI from three different viewpoints: goals, methods or tools, and achievements and failures. Its goals of reasoning, planning, learning, or language understanding and use are centered around the expert system idea. The tools of AI are presented in terms of what can be incorporated in the data structures. The book looks into the concepts and tools of limited structure, mathematical logic, logic-like representation, numerical information, and nonsymbolic structures. The text emphasizes the main mathematical tools for representing and manipulating knowledge symbolically. These are various forms of logic for qualitative knowledge, and probability and related concepts for quantitative knowledge. The main tools for manipulating knowledge nonsymbolically, as neural nets, are optimization methods and statistics. This material is covered in the text by topics such as trees and search, classical mathematical logic, and uncertainty and reasoning. A solutions diskette is available, please call for more information.

A fresh exploration into the 'human nature versus technology’ argument, revealing an unexpected advantage that humans have over our future robot masters: we’re actually good at mathematics. There’s so much discussion about the threat posed by intelligent machines that it sometimes seems as though we should simply surrender to our robot overlords now. But Junaid Mubeen isn’t ready to throw in the towel just yet. As far as he is concerned, we have the creative edge over computers, because of a remarkable system of thought that humans have developed over the millennia. It’s familiar to us all, but often badly taught in schools and misrepresented in popular discourse—math. Computers are, of course, brilliant at totting up sums, pattern-seeking, and performing mindless tasks of, well, computation. For all things calculation, machines reign supreme. But Junaid identifies seven areas of intelligence where humans can retain a crucial edge. And in exploring these areas, he opens up a fascinating world where we can develop our uniquely human mathematical talents. Just a few of the fascinating subjects covered in MATHEMATICAL INTELLIGENCE include: -Humans are endowed with a natural sense of numbers that is based on approximation rather than precise calculation. Our in-built estimation skills complement the precision of computers. Interpreting the real world depends on both. -What sets humans apart from other animals is language and abstraction. We have an extraordinary ability to create powerful representations of knowledge— more diverse than the binary language of computers. -Mathematics confers the most robust, logical framework for establishing permanent truths. Reasoning shields us from the dubious claims of pure pattern-recognition systems. -All mathematical truths are derived from a starting set of assumptions, or axioms. Unlike computers, humans have the freedom to break free of convention and examine the logical consequences of our choices. Mathematics rewards our imagination with fascinating and, on occasion, applicable concepts that originate from breaking the rules. -Computers can be tasked to solve a range of problems, but which problems are worth the effort? Questioning is as vital to our repertoire of thinking skills as problem-solving itself.

Artificial and Mathematical Theory of Computation is a collection of papers that discusses the technical, historical, and philosophical problems related to artificial intelligence and the mathematical theory of computation. Papers cover the logical approach to artificial intelligence; knowledge representation and common sense reasoning; automated deduction; logic programming; nonmonotonic reasoning and circumscription. One paper suggests that the design of parallel programming languages will invariably become more sophisticated as human skill in programming and software developments improves to attain faster running programs. An example of metaprogramming to systems concerns the design and control of operations of factory devices, such as robots and numerically controlled machine tools. Metaprogramming involves two design aspects: that of the activity of a single device and that of the interaction with other devices. One paper cites the application of artificial intelligence pertaining to the project "proof checker for first-order logic" at the Stanford Artificial Intelligence Laboratory. Another paper explains why the bisection algorithm widely used in computer science does not work. This book can prove valuable to engineers and researchers of electrical, computer, and mechanical engineering, as well as, for computer programmers and designers of industrial processes.

Traces the revolution in statistics that gave rise to artificial intelligence and predictive algorithms refiguring contemporary capitalism. Our finances, politics, media, opportunities, information, shopping and knowledge production are mediated through algorithms and their statistical approaches to knowledge; increasingly, these methods form the organizational backbone of contemporary capitalism. Revolutionary Mathematics traces the revolution in statistics and probability that has quietly underwritten the explosion of machine learning, big data and predictive algorithms that now decide many aspects of our lives. Exploring shifts in the philosophical understanding of probability in the late twentieth century, Joque shows how this was not merely a technical change but a wholesale philosophical transformation in the production of knowledge and the extraction of value. This book provides a new and unique perspective on the dangers of allowing artificial intelligence and big data to manage society. It is essential reading for those who want to understand the underlying ideological and philosophical changes that have fueled the rise of algorithms and convinced so many to blindly trust their outputs, reshaping our current political and economic situation.

Computational mechanics is a scientific discipline that marries physics, computers, and mathematics to emulate natural physical phenomena. It is a technology that allows scientists to study and predict the performance of various productsâ€"important for research and development in the industrialized world. This book describes current trends and future research directions in computational mechanics in areas where gaps exist in current knowledge and where major advances are crucial to continued technological developments in the United States.

This book features research presented at the 1st International Conference on Artificial Intelligence and Applied Mathematics in Engineering, held on 20–22 April 2019 at Antalya, Manavgat (Turkey). In today’s world, various engineering areas are essential components of technological innovations and effective real-world solutions for a better future. In this context, the book focuses on problems in engineering and discusses research using artificial intelligence and applied mathematics. Intended for scientists, experts, M.Sc. and Ph.D. students, postdocs and anyone interested in the subjects covered, the book can also be used as a reference resource for courses related to artificial intelligence and applied mathematics.