Symbolic Integration

This first volume in the series "Algorithms and Computation in Mathematics", is destined to become the standard reference work in the field. Manuel Bronstein is the number-one expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration.

A variety of ideas, approaches, and techniques exist -- in terms of both architecture and learning -- and this abundance seems to lead to many exciting possibilities in terms of theoretical advances and application potentials. Despite the apparent diversity, there is clearly an underlying unifying theme: architectures that bring together symbolic and connectionist models to achieve a synthesis and synergy of the two different paradigms, and the learning and knowledge acquisition methods for developing such architectures. More effort needs to be extended to exploit the possibilities and opportunities in this area. This book is the outgrowth of The IJCAI Workshop on Connectionist-Symbolic Integration: From Unified to Hybrid Approaches, held in conjunction with the fourteenth International Joint Conference on Artificial Intelligence (IJCAI '95). Featuring various presentations and discussions, this two-day workshop brought to light many new ideas, controversies, and syntheses which lead to the present volume. This book is concerned with the development, analysis, and application of hybrid connectionist-symbolic models in artificial intelligence and cognitive science. Drawing contributions from a large international group of experts, it describes and compares a variety of models in this area. The types of models discussed cover a wide range of the evolving spectrum of hybrid models, thus serving as a well-balanced progress report on the state of the art. As such, this volume provides an information clearinghouse for various proposed approaches and models that share the common belief that connectionist and symbolic models can be usefully combined and integrated, and such integration may lead to significant advances in understanding intelligence.

This work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms–placedintothe limelightbyDonKnuth’stalkat the 1970ICM –provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati?cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: “I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ” Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual “input size” parameters of computer science seem inadequate, and although some natural “geometric” parameters have been identi?ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state.

When it comes to robotics and bioinformatics, the Holy Grail everyone is seeking is how to dovetail logic-based inference and statistical machine learning. This volume offers some possible solutions to this eternal problem. Edited with flair and sensitivity by Hammer and Hitzler, the book contains state-of-the-art contributions in neural-symbolic integration, covering `loose' coupling by means of structure kernels or recursive models as well as `strong' coupling of logic and neural networks.

This is Volume VII of seven in a collection on Social Psychology. Originally published in 1928, the study looks at the origin of the symbolic process and "thinking" in individuals. The main task of this book is an explanation of the social processes in the genesis, integration, and functioning of symbols.

Computational Architectures Integrating Neural and Symbolic Processes: A Perspective on the State of the Art focuses on a currently emerging body of research. With the reemergence of neural networks in the 1980s with their emphasis on overcoming some of the limitations of symbolic AI, there is clearly a need to support some form of high-level symbolic processing in connectionist networks. As argued by many researchers, on both the symbolic AI and connectionist sides, many cognitive tasks, e.g. language understanding and common sense reasoning, seem to require high-level symbolic capabilities. How these capabilities are realized in connectionist networks is a difficult question and it constitutes the focus of this book. Computational Architectures Integrating Neural and Symbolic Processes addresses the underlying architectural aspects of the integration of neural and symbolic processes. In order to provide a basis for a deeper understanding of existing divergent approaches and provide insight for further developments in this field, this book presents: (1) an examination of specific architectures (grouped together according to their approaches), their strengths and weaknesses, why they work, and what they predict, and (2) a critique/comparison of these approaches. Computational Architectures Integrating Neural and Symbolic Processes is of interest to researchers, graduate students, and interested laymen, in areas such as cognitive science, artificial intelligence, computer science, cognitive psychology, and neurocomputing, in keeping up-to-date with the newest research trends. It is a comprehensive, in-depth introduction to this new emerging field.

An essential guide to using Maxima, a popular open source symbolic mathematics engine to solve problems, build models, analyze data and explore fundamental concepts Symbolic Mathematics for Chemists offers students of chemistry a guide to Maxima, a popular open source symbolic mathematics engine that can be used to solve problems, build models, analyze data, and explore fundamental chemistry concepts. The author — a noted expert in the field — focuses on the analysis of experimental data obtained in a laboratory setting and the fitting of data and modeling experiments. The text contains a wide variety of illustrative examples and applications in physical chemistry, quantitative analysis and instrumental techniques. Designed as a practical resource, the book is organized around a series of worksheets that are provided in a companion website. Each worksheet has clearly defined goals and learning objectives and a detailed abstract that provides motivation and context for the material. This important resource: Offers an text that shows how to use popular symbolic mathematics engines to solve problems Includes a series of worksheet that are prepared in Maxima Contains step-by-step instructions written in clear terms and includes illustrative examples to enhance critical thinking, creative problem solving and the ability to connect concepts in chemistry Offers hints and case studies that help to master the basics while proficient users are offered more advanced avenues for exploration Written for advanced undergraduate and graduate students in chemistry and instructors looking to enhance their lecture or lab course with symbolic mathematics materials, Symbolic Mathematics for Chemists: A Guide for Maxima Users is an essential resource for solving and exploring quantitative problems in chemistry.