This monograph is based on a series of lectures given by the author at the first Advanced Research Institute on Discrete Applied Mathematics, held at Rutgers University. It emphasizes connections between the representational aspects of mixed integer programming and applied logic, as well as discussing logic-based approaches to decision support which help to create more `intelligent' systems. Dividing naturally into two parts, the first four chapters are an overview of mixed-integer programming representability techniques. This is followed by five chapters on applied logic, expert systems, logic and databases, and complexity theory. It concludes with a summary of open research issues and an attempt to extrapolate trends in this rapidly developing area.
Author(s): Robert G. Jeroslow$ (Eds.)
Series: Annals of Discrete Mathematics 40
Publisher: North-Holland
Year: 1989
Language: English
Pages: ii-xv, 1-222
Content:
Advisory Editors
Page ii
Edited page
Page iii
Copyright page
Page iv
Robert G. Jeroslow 1942 – 1988
Pages v-vii
Egon Balas
Dedication
Pages viii-ix
List of Figures
Page xiv
List of Tables
Page xv
Introduction
Pages 1-2
R. Jeroslow
Lecture 1 Disjunctive Representations: A Fundamental Result and Some Illustrations
Pages 5-21
Lecture 2 Further Illustrations of Disjunctive Representations
Pages 23-41
Lecture 3 Constructions Which Parallel Set Operations and a New Concept of Structure for Mip
Pages 43-55
Lecture 4 Topics in Representability
Pages 57-76
Lecture 5 Propositional Logic and Mixed Integer Programming
Pages 79-102
Lecture 6 A Primer on Predicate Logic
Pages 103-118
Lecture 7 Computational Complexity Above NP: A Retrospective Overview
Pages 119-135
Lecture 8 Theorem-Proving Techniques Which Utilize Discrete Programming
Pages 137-151
Lecture 9 Spatial Embeddings for Linear and Logic Structures
Pages 153-164
Lecture 10 Tasks Ahead
Pages 165-181
Illustrative Examples
Pages 183-190
Solutions to Examples
Pages 191-201
Bibliography
Pages 203-222
