| Notes on illustrations | p. ix |
| Preface | p. xi |
| Introduction | p. 1 |
| Representations of Relations | |
| Sets, subsets, and elements | p. 5 |
| Set representation | p. 6 |
| Element representation | p. 8 |
| Subset representation | p. 9 |
| Relations | p. 15 |
| Relation representation | p. 15 |
| Relations describing graphs | p. 19 |
| Relations generated by cuts | p. 23 |
| Relations generated randomly | p. 25 |
| Function representation | p. 26 |
| Permutation representation | p. 28 |
| Partition representation | p. 31 |
| Operations and Constructions | |
| Algebraic operations on relations | p. 35 |
| Typing relations | p. 35 |
| Boolean operations | p. 37 |
| Relational operations proper | p. 38 |
| Composite operations | p. 43 |
| Order and function: the standard view | p. 49 |
| Functions | p. 49 |
| Mappings and points | p. 57 |
| Order and strictorder | p. 61 |
| Equivalence and quotient | p. 70 |
| Transitive closure | p. 76 |
| Congruences | p. 80 |
| Homomorphisms | p. 84 |
| Relations and vectors | p. 91 |
| Domain and codomain | p. 91 |
| Rectangular zones | p. 94 |
| Independent pair of sets and covering pair of sets | p. 98 |
| Reducing vectors | p. 99 |
| Progressively infinite subsets | p. 101 |
| Stable and absorbant sets | p. 103 |
| Domain construction | p. 106 |
| Domains of ground type | p. 107 |
| Direct product | p. 107 |
| Direct sum | p. 127 |
| Quotient domain | p. 131 |
| Subset extrusion | p. 135 |
| Direct power | p. 140 |
| Domain permutation | p. 148 |
| Remarks on further constructions | p. 150 |
| Equivalent representations | p. 152 |
| Algebra | |
| Relation algebra | p. 157 |
| Laws of relation algebra | p. 157 |
| Visualizing the algebraic laws | p. 159 |
| Elementary properties of relations | p. 165 |
| Cancellation properties of residuals and cones | p. 167 |
| Cancellation properties of the symmetric quotient | p. 171 |
| Tarski rule and Point Axiom | p. 181 |
| Orders and lattices | p. 183 |
| Maxima and minima | p. 183 |
| Bounds and cones | p. 185 |
| Least and greatest elements | p. 187 |
| Greatest lower and least upper bounds | p. 188 |
| Lattices | p. 190 |
| Rectangles, fringes, inverses | p. 200 |
| Non-enlargeable rectangles | p. 200 |
| Independent pairs and covering pairs of sets | p. 206 |
| Fringes | p. 210 |
| Difunctional relations | p. 220 |
| Ferrers relations | p. 232 |
| Block-transitive relations | p. 242 |
| Inverses | p. 247 |
| Concept analysis | p. 251 |
| Row and column spaces | p. 251 |
| Factorizations | p. 257 |
| Concept lattices | p. 268 |
| Closure and contact | p. 276 |
| Completion of an ordering | p. 293 |
| Applications | |
| Orderings: an advanced view | p. 303 |
| Additional properties of orderings | p. 304 |
| The hierarchy of orderings | p. 308 |
| Block-transitive strictorders | p. 312 |
| Order extensions | p. 315 |
| Relating preference and utility | p. 323 |
| Intervalorders and interval graphs | p. 332 |
| Preference and indifference | p. 349 |
| Duality | p. 349 |
| Modelling indifference | p. 352 |
| Modelling thresholds | p. 356 |
| Preference structures | p. 359 |
| Aggregating preferences | p. 368 |
| Modelling preferences | p. 368 |
| Introductory example | p. 369 |
| Relational measures | p. 371 |
| Relational integration | p. 376 |
| Defining relational measures | p. 379 |
| De Morgan triples | p. 387 |
| Relational graph theory | p. 396 |
| Reducibility and irreducibility | p. 396 |
| Homogeneous difunctional relations | p. 403 |
| Subsets characterized by relational properties | p. 408 |
| Standard Galois mechanisms | p. 415 |
| Galois iteration | p. 415 |
| Termination | p. 417 |
| Games | p. 422 |
| Specialization to kernels | p. 426 |
| Matching and assignment | p. 428 |
| König's Theorems | p. 435 |
| Advanced Topics | |
| Mathematical applications | p. 441 |
| Multi-coverings | p. 441 |
| Covering of graphs and path equivalence | p. 444 |
| Homomorphism and Isomorphism Theorems | p. 445 |
| Further mathematical snippets | p. 452 |
| Implication structures | p. 461 |
| Attribute dependency | p. 461 |
| Examples of implication closures | p. 472 |
| Power operations | p. 483 |
| Existential image and power transpose | p. 483 |
| Simulation and bisimulation | p. 494 |
| State transition dynamics | p. 501 |
| Notation | p. 511 |
| Proofs postponed from Part II | p. 516 |
| Algebraic visualization | p. 524 |
| Historical annotations | p. 531 |
| References | p. 549 |
| Symbols | p. 558 |
| Index | p. 561 |
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