Logic-Based Decision Support: Mixed Integer Model FormulationThis 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. |
Contents
1 | |
3 | |
LOGICBASED APPROACHES TO DECISION SUPPORT | 77 |
Illustrative Examples | 183 |
Solutions to Examples | 191 |
203 | |
Common terms and phrases
A A B algorithms approaches Aries Artificial Intelligence backward chaining binary Cartesian product clausal chaining composite construction Computer Science concept conjunctive normal form constraint set conv(S conv(S1 database decision support deduction disjunctive formulation disjunctive methods disjunctive representation distributive laws domain embedding epi(F epigraph example expert systems exponential false fixed charges function given Grandparent(Zeus graph Harmonia Horn clauses illustrate inconsistency integer programming Lecture Lemma linear affine linear programming logic-based Mathematical Programming MIP constraint MIP formulation MIPP MIPS natural deduction NODES NP-complete obtain occur Operations Research polyhedral polynomial polynomial hierarchy predicate logic Presburger arithmetic proof propositional logic PSPACE quantifier queries Rel(S relation represent resolution restricted rule satisfiability problems sharp representation simplifications solution specific standard formulation structure tautology techniques Theorem theory true truth valuation unification union unit clauses vector