UID:
almahu_9947367849202882
Format:
1 online resource (239 p.)
ISBN:
1-281-79042-7
,
9786611790424
,
0-08-086780-4
Series Statement:
Annals of discrete mathematics ; 40
Content:
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 syste
Note:
Description based upon print version of record.
,
Front Cover; Logic-Based Decision Support: Mixed Integer Model Formulation; Copyright Page; Contents; Introduction; PART I: MIXED-INTEGER MODEL FORMULATION; Lecture 1. Disjunctive Representations; 1.1 Introduction; 1.2 Some definitions and a basic result; 1.3 Some small examples; 1.4 Related Work; 1.5 Exercises; Lecture 2. Furthtr Illustrations; 2.1 Some further examples; 2.2 A simplification in the disjunctive representation for some multiple rhs instances; 2.3 'Separate' vs . 'joint' formulations; 2.4 Exercises; Lecture 3. Constructions which Parallel Set Operations
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3.1 Definitions and basic constructions3.2 The union construction; 3.3 Some other constructions; 3.4 Some technical properties of the basic constructions; 3.5 Composite constructions and 'structure' in MIP; 3.6 Two central technical results; 3.7 Hereditary sharpness; Lecture 4. Topics in Representability; 4.1 Reformulation via distributive laws; 4.2 Convex union representability; 4.3 Using combinatorial principles in representability; 4.4 Some experimental results; PART II: LOGIC-BASED APPROACHES TO DECISION SUPPORT; Lecture 5. Propositional Logic and Mixed Integer Programming
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5.1 Introduction5.2 A ""natural deduction"" system for propositional logic; 5.3 Propositional logic as done by integer programming; 5.4 Clausal chaining: a subroutine; 5.5 Some properties of frequently-used algorithms of expert systems; 5.6 The Davis-Putnam Algorithm in Two Forms; 5.7 Some recent developments (December 1987); 5.8 Exercises; Lecture 6. A Primer on Predicate Logic; 6.1 Introduction; 6.2 Predicate logic: basic concepts, notation; 6.3 Applications for problem-solving; Lecture 7. Computational Complexity above NP: A Retrospective Overview; 7.1 Introduction
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7.2 The fundamental distinction: conceptions vs . their instances7.3 Two fundamental results; 7.4 What if we increase expressability ""a little bit""?; 7.5 The Polynomial Hierarchy, Probabilistic Models, and Games; Lecture 8. Theorem-Proving Techniques which Utilise Discrete Programming; 8.1 Reduction of Predicate Logic to a Structured Propositional Logic; 8.2 Preliminary discussion; 8.3 The algorithm framework; 8.4 Illustrations and comments; 8.5 A generalization: predicate logic together with linear constraints; Lecture 9. Spatial Embeddings for Linear and Logic Structures
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9.1 Definition of an Embedding9.2 Illustrations of embeddings; 9.3 Results for predicate logic embeddings; 9.4 Logic an pre-processing routines for MIP: an example via the DP/DPL algorithm; Lecture 10. Tasks Ahead; 10.1 Three ""top-down"" Views of Mathematical Programming; 10.2 Some research challenges related to these lectures; 10.3 Some other research programs in the AI/OR Interface; 10.4 Some programs and courses in the AI/OR Interface; 10.5 Guessing Ahead; Illustrative Examples; Solutions to Examples; Bibliography
,
English
Additional Edition:
ISBN 0-444-87119-5
Language:
English
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