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6.5 X 10.5 Long Title.P65 Cambridge University Press 978-0-521-76268-7 - Relational Mathematics Gunther Schmidt Index More information Index 1-graph, 21 block-transitive, 243, 312, 352 absorbant set, 103, 104, 427 factorization, 243 adjacency, 23 Boole, George, 1, 36, 538, 540 edge-, 228, 333 bound greatest lower, 189 affine incidence plane, 452 least upper, 189 antichain, 196 lower, 185 antisymmetric, 63 upper, 185 Aristotle, 532 Byron, Ada, 543 assignment, 428, 436 associated Cantor’s diagonal enumeration, 111 ordering, 67, 68 cardinality preorder, 148 relation, 21 Cardoso, Rodrigo, 122, 152 strictorder, 67, 68 carr´e(French),96 association rule, 229 category, 158 asymmetric, 63, 70, 351 Cayley, Arthur, 543 attractor, 420 chain, 196 attribute dependency system, 461 chainable, 228, 231, 403 Aumann contact relation, 280, 281 Chipman’s condition, 306 Aumann, Georg, 280 Choquet integral, 379 Choquet, Gustave, 378 baseset, 2, 5 chord, 312, 344, 345, 347, 348 ground, 8 chordal graph, 344 basin, 420 chordless, 348 Bayesian measure, 373 circuit, 93, 344 BDD, 16 clique, 97, 265, 337, 338 belief clique, maximal, 205, 337, 338 mapping, 372 closure, 276 overcredulous, 373 contact, 170, 281 vacuous, 373 difunctional, 227, 228, 407 below, eventually, 503 rectangular, 97 Bentham, George, 535, 539, 540 transitive, 76 Berghammer, Rudolf, 1, 152, 199, 409 weakorder, 320, 321, 357, 358 bijection by concepts, 257 codomain, 91 bijection by maxcliques, 264 cogredient permutation, 101, 304 bijective, 57 column binary decision diagram, 16 -is-contained preorder, 71 biorder, 232, 309 equivalence, 71, 221, 238, 324, 355 bipartitioned graph, 20 mask, 166 Birkhoff–Milgram Theorem, 324 space, 253 bisimulation, 81, 494, 498 column set intersection, 255 block, 96, 200 column union space, 251 block-diagonal form, 47, 74, 213, 216, 238 commonality, 387 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-76268-7 - Relational Mathematics Gunther Schmidt Index More information 562 Index comparability graph, 337 diclique matching, 257 complement, 145, 388, 392 difunctional, 74, 224, 232, 404 complement expansion, 102 closure, 227, 228, 407 complete, 62 factorization, 225 order, 68 relation, 74, 220, 221, 226, 228, 230–232, 352 strictorder, 68 Dilworth Theorem, 199, 314 strongly, 62 direct complete quadrangle, 20, 452 power, 146 completion product, 107, 117 by cuts, 294, 297 sum, 127, 131 by ideals, 294 directed graph, 22 component, strongly connected, 78 DirPow, 141, 512 composition, 40 DirPro, 108, 512 concept bijection, 257 DirSum, 128, 512 concept lattice, 268–270 discharge, fully, 503 cone, 185 disjoint union, 127 lower, 187 domain, 91 upper, 187 dotted arrow convention, 52, 159, 234, 305, cone functional, 168 306, 397 congruence, 80, 229, 500, 520 doubly stochastic, 403 connex, 62, 234, 351 down sets, 295 connex preorder, 527 draw, 424 conorm, t-, 388 dual, 43, 68, 350 conorm, relational, 392 Duns, John (Scotus), 532 consecutive 1 s property, 346 dynamics, 501 contact, 281 echelon form, 233 infectivity, 280 edge-adjacency, 228, 333 contact closure, 170, 278 Egli–Milner contact relation, 280, 281 order, 494 continuous, 193, 373, 487 preorder, 493 contraction, 100, 101, 397, 507 element converse, 39 greatest, 187 coproduct, 131 in powerset, 11 counter-enforce, 461 least, 187 covering of graphs, 445 enforce, 461 covering pair of sets, 98 equivalence, 8, 65, 66, 70, 76, 131, 133, 175 covering set, 98, 206 left, 77 cryptography via projective planes, 456 of columns, 71, 221, 238, 324 cut, 23, 295 of rows, 71, 221, 238, 324 cut completion, 294, 297 partial, 528 cycle, 93 right, 77 cyclic, 396, 400 eventually below, 503 dashed arrow convention, 52, 159, 234, 305, existential image, 145, 484, 504 306, 397 expanding, 277 De Morgan extension complement, 388, 392 Ferrers, 245 triples, 387 linear, 317 De Morgan, Augustus, 536, 537, 540 Szpilrajn, 80, 245, 316, 317, 351, 526, 527 decision diagram, 16 externally stable set, 104 decomposable, partly, 402 Extrude, 136, 512 Dedekind rule, 42, 60, 158, 159, 518, 520 extrusion, 8, 135, 137, 513, 522 dense, 212, 324 factorization dependency system, 461 into dicliques, 260 diagonal enumeration, 111 into maxcliques, 265, 267 diclique, 200 of a block-transitive relation, 243 factorization, 260 of a difunctional relation, 225 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-76268-7 - Relational Mathematics Gunther Schmidt Index More information Index 563 of a Ferrers relation, 237 ground set, 6 Farkas’s Lemma, 459, 460 ordering of, 6 feedback vertex set, 414 ground type, 107 Ferrers Hahn, Hans, 541 closure, 245 Haj´os, G., 345 extension, 245 Hall condition, 208, 403, 432 relation, 69, 215–217, 230, 232–234, 237, Hamilton, Sir William, 536 239, 241, 304, 309, 310, 328, 352, 363 Hamilton, Sir William Rowan, 541, 543 strongly, 235 hammock, 413 Ferrers relation factorization, 237 Haskell, xii, 6, 25, 33, 34, 127, 511, 513 Ferrers, Norman Macleod, 232 Hasse Fishburn, Peter C., 309, 323 diagram, 67 flexible availability, 469 relation, 67 forbid, 461 Hausdorff, Felix, 457 fork operator, 115 heterogeneous, 16 forward simulation, 496 homogeneous, 16 fringe, 211, 213, 214, 216, 217 homomorphism, 84 fringe-partial homomorphism theorem, 446 column equivalence, 217 hypergraph, 20 row equivalence, 217 ideal completion, 294 Frobenius–K¨onig Theorem, 437 idempotent, 70, 277, 528 fully discharge, 503 symmetric, 217 fully indecomposable, 402 identity, 40 function, 26, 49, 50 immediate set-valued, 15, 16 predecessor, 67 fuzzy measure, 372 successor, 67 Galois correspondence, 463, 485 implication structure, 461 Galois iteration, 415 incidence, 20, 452 games, 422 incomparability, 358, 360, 361 generalized inverse, 127, 210, 247 indecomposable geometry fully, 402 affine, 452 totally, 402 projective, 455 independent pair of sets, 98, 206 Ghouil`a-Houri, Alain, 345 independent set, 206, 231 glb, 188, 189 indifference, 352–355, 358, 359, 361, 363 glbR, 189 strict, 361 G¨odel, Kurt, 541 infectivity of contact, 280 Gram matrix, 267 infimum, 189 Gram, Jørgen Pedersen, 267 initial part, 418 graph Inject, 136, 512 1-, 21 injection, 131, 135 bipartitioned, 20 natural, 137, 522 chordal, 344 injective, 50, 57 comparability-, 337 integral directed, 22 Choquet, 379 intersection-, 333 relational, 376 interval-, 333, 337 Sugeno, 371, 376, 378, 379 simple, 23 intermediate point theorem, 182, 493 triangulated, 344 intermediate vector theorem, 493 graph covering, 445 internally stable, 348 gre, 187 internally stable set, 104 greatest intersection graph, 333 element, 187 interval lower bound, 189 (strict)order, 309 ground, 9 graph, 333, 337 baseset, 8 order, 61, 308, 309, 323, 330, 332, 352 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-76268-7 - Relational Mathematics Gunther Schmidt Index More information 564 Index inverse, 248 mapping, 57 generalized, 127, 210 Marczewski, Edward (see Szpilrajn), 69 Moore–Penrose, 210 mask, 166 Thierrin–Vagner, 247, 249 matching, 56, 74, 428, 429, 436 Iota, 128, 512 by dicliques, 257 irreducible, 396, 397, 407 by maxcliques, 264 irreflexive, 70, 351 matrix, Gramian, 267 isomorphism theorem, 446 max, 184 isotone, 84, 277 maxclique, 205, 265, 267, 337, 338 Jevons, William Stanley, 537 bijection, 264 join operator, 115 factorization, 265, 267 jump part, 386 matching, 264 measure Kappa, 128, 512 Bayesian, 373 kernel, 426 fuzzy, 372 Klein four-group, 27 relational, 371, 372, 376 knowledge acquisition, 229, 230 , 141, 512 knowledge discovery, 221 Member membership relation, 140 K¨onig–Egerv´aryTheorem, 436 Kowa, Seki (Kowa) Takakazu, 542 Milgram Kronecker product, 116, 127 Theorem of Birkhoff–, 324 Kuratowski Theorem, 198 min, 184 mincut, 194, 477 L -simulation, 496, 501 minorant, 185 Ladd-Franklin, Christine, 544 modular law, 158 lattice, 183, 190 monotone, 84 lattice-continuous, 193, 373 monotype, 36 lbd, 186 Moore–Penrose, 247, 249, 406 lea, 187 Moore–Penrose inverse, 210 least Morgan triples, 387 element, 187 Morgan, Augustus De, 536, 537, 540 upper bound, 189 morphism set, 158 left multi-covering, 441–443, 500 equivalence, 77 multiplication, 40 identity, 40 multirelation, 148 residual, 44 multivalent Leibniz, Gottfried Wilhelm, 533, 534, 537, 539, part, 92 542, 543 zone, 92 lexicographic order, 112 lifting property, 444 natural injection, 137, 522 line covering, 98, 436 natural projection, 131, 133 linear negation, 389 extension, 317 strict, 389 order, 68 strong, 389 strictorder, 68 negation, relational, 392 L¨owenheim, Leopold, 547 negatively transitive, 306, 351 loss, 424 non-enlargeable rectangle, 200, 217 Lovelace, Ada, 543 non-value zone, 92 lower bound, 185 norm, t-, 388 cone functional, 168 norm, relational, 392 greatest, 189 NP-complete, 467, 474, 477 lower cone, 187, 295 Ockham, William of, 38, 539 lub, 188, 189 order, 61, 65, 66 lubR, 189 -dense, 324 Luce, R. Duncan, 167, 312, 353 -shape, 242 machine learning, 221, 229 Egli–Milner, 494 Maddux, Roger Duncan, 122, 139 interval, 61, 309, 323, 330, 332, 352 majorant, 185 lexicographic, 112 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-76268-7 - Relational Mathematics Gunther Schmidt Index More information Index 565 linear, 68 predictive modelling, 229 semi-, 61, 321, 328 preference, 352, 359, 360 strict-, 66 weak, 360 total, 68 preference structure, 359 weak-, 61, 306 preorder, 65, 66, 71 order ideal, 295 column-is-contained, 71 ordering, associated, 67, 68 connex, 527 ordre fort, 308 Egli–Milner,
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