Symbolic Integration I

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.

First edition received rave reviews The second edition offers a new chapter on parallel integration Includes additional exercises

Using a unique step-by-step, integrated approach, this text organizes the basic concepts of symbolic interactionism in such a way that students understand them clearly and are able to apply them to their own lives. It emphasizes the active side of human beings-humans as definers and users of the environment, humans as problem solvers and in control of their own actions-and it shows students how society makes us, and how we in turn shape society.

This book brings together two streams of computer algebra: symbolic summation and integration on the one hand, and fast algorithmics on the other hand. In symbolic integration and summation, not too many algorithms with analyzed run times are known, and until now the mathematically oriented world of integration and summation and the computer science world of algorithm analysis have not had much to say to each other. The progress presented in this work towards overcoming this situation is threefold: - a clear framework for algorithm analysis with the appropriate parameters is provided, - modular algorithmic techniques are introduced in this area, and - almost optimal algorithms are presented for the basic problems.

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.

Artificial Intelligence is concerned with producing devices that help or replace human beings in their daily activities. Neural-symbolic learning systems play a central role in this task by combining, and trying to benefit from, the advantages of both the neural and symbolic paradigms of artificial intelligence. This book provides a comprehensive introduction to the field of neural-symbolic learning systems, and an invaluable overview of the latest research issues in this area. It is divided into three sections, covering the main topics of neural-symbolic integration - theoretical advances in knowledge representation and learning, knowledge extraction from trained neural networks, and inconsistency handling in neural-symbolic systems. Each section provides a balance of theory and practice, giving the results of applications using real-world problems in areas such as DNA sequence analysis, power systems fault diagnosis, and software requirements specifications. Neural-Symbolic Learning Systems will be invaluable reading for researchers and graduate students in Engineering, Computing Science, Artificial Intelligence, Machine Learning and Neurocomputing. It will also be of interest to Intelligent Systems practitioners and anyone interested in applications of hybrid artificial intelligence systems.