Logic-Based Decision Support: Mixed Integer Model Formulation

Description

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. 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