**Proceedings of Symposia in Applied Mathematics**

Volume: 55;
1998;
275 pp;
Hardcover

MSC: Primary 68;
Secondary 03; 05; 51; 60; 90

**Print ISBN: 978-0-8218-0611-1
Product Code: PSAPM/55**

List Price: $67.00

AMS Member Price: $53.60

MAA Member Price: $60.30

**Electronic ISBN: 978-0-8218-9270-1
Product Code: PSAPM/55.E**

List Price: $63.00

AMS Member Price: $50.40

MAA Member Price: $56.70

# Mathematical Aspects of Artificial Intelligence

Share this page *Edited by *
*Frederick Hoffman*

There exists a history of great expectations and large
investments involving Artificial Intelligence (AI). There are also
notable shortfalls and memorable disappointments. One major
controversy regarding AI is just how mathematical a field it is or
should be.

This text includes contributions that examine the connections
between AI and mathematics, demonstrating the potential for
mathematical applications and exposing some of the more mathematical
areas within AI. The goal is to stimulate interest in people who can
contribute to the field or use its results.

Included is work by M. Newborn on the famous Deep Blue chess
match. He discusses highly mathematical techniques involving graph
theory, combinatorics and probability and statistics. G. Shafer offers
his development of probability through probability trees with some of
the results appearing here for the first time. M. Golumbic treats
temporal reasoning with ties to the famous Frame Problem. His
contribution involves logic, combinatorics and graph theory and leads
to two chapters with logical themes. H. Kirchner explains how
ordering techniques in automated reasoning systems make deduction more
efficient. Constraint logic programming is discussed by C. Lassez, who
shows its intimate ties to linear programming with crucial theorems
going back to Fourier. V. Nalwa's work provides a brief tour of
computer vision, tying it to mathematics—from combinatorics,
probability and geometry to partial differential equations.

All authors are gifted expositors and are current contributors to
the field. The wide scope of the volume includes research problems,
research tools and good motivational material for teaching.

#### Readership

Graduate students and research mathematicians interested in artificial intelligence; possibly those interested in philosophy.

#### Reviews & Endorsements

Although this book was written to introduce mathematicians to AI, the book is also likely to be a valuable resource for cognitive scientists and mathematical psychologists.

-- Journal of Mathematical Psychology

Seven excellent papers are included, covering important AI topics.

-- Mathematical Reviews

# Table of Contents

## Mathematical Aspects of Artificial Intelligence

- Contents vii8 free
- Preface ix10 free
- Introduction and History 114 free
- Reasoning about Time 1932
- Orderings in Automated Theorem Proving 5568
- Programming with Constraints: Some Aspects of the Mathematical Foundations 97110
- The Basis of Computer Vision 139152
- Outsearching Kasparov 175188
- Mathematical Foundations for Probability and Causality 207220
- Index 271284