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Nienhuys-Cheng S., Wolf R. — Foundations of Inductive Logic Programming
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Название: Foundations of Inductive Logic ProgrammingАвторы: Nienhuys-Cheng S., Wolf R. Аннотация: Inductive Logic Programming is a young and rapidly growing field combining machine learning and logic programming. This self-contained tutorial is the first theoretical introduction to ILP; it provides the reader with a rigorous and sufficiently broad basis for future research in the area. In the first part, a thorough treatment of first-order logic, resolution-based theorem proving, and logic programming is given. The second part introduces the main concepts of ILP and systematically develops the most important results on model inference, inverse resolution, unfolding, refinement operators, least generalizations, and ways to deal with background knowledge. Furthermore, the authors give an overview of PAC learning results in ILP and of some of the most relevant implemented systems.
Язык: Рубрика: Computer science /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1Год издания: 1997Количество страниц: 410Добавлена в каталог: 13.12.2013Операции: Положить на полку |
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Place see "Position" Plotkin, G. ix 175 176 219 226 228 243 248 252 280 283 Polman, M. 326 339 Polynomial sample PAC learnable 325 326 328 Polynomial time fitting 328 Polynomial time identification from equivalence queries 331 Polynomial time PAC learnable 328 329 Polynomial time PAC predictable 330 Polynomial VC dimension 326 Polynomially evaluable representation 327 Popper, K. 174 175n POSITION 228 Positive example 165 172 180 323 Positive literal 36 post-processing 170 Power set 168 Pre-interpretation 24 pre-processing 170 Pre-SLDNF-tree 138 Pre-SLDNF-tree via 141 Predicate invention xiii 172 177 203 346 347 354 Predicate invention, utility of 349 Predicate symbol 18 Predicate topology 356 Prenex 36 Prenex conjunctive normal form 35 36 Prenex conjunctive normal form, transformation to 37 probability distribution 323 Probably approximately correct 321 324 Probably approximately correct learning see "PAC learning" Problem setting of ILP 207 PROGOL 300 357 358 Program clause 130 134 Program transformation 207n 347 Proietti, M. 207n Projection 326 PROLOG xi 105 113 130 154 176 Prolog, computation rule 155 Prolog, cut operator 157 Prolog, declarative side 155 159 PROLOG, depth-first search 155 Prolog, lists 154 Prolog, procedural side 155 159 Prolog, syntax 154 Proof procedure xi 56 57 Propositional language 5 8 Propositional logic xi 3 17 332 Propositional logic, embedded in first-order logic 19 26 68 Puget, J-F. 197 350 Punctuation symbol 4 18 Quasi-order 220 300 Query 330 Quinlan, J.R. 176 300 354 Random classification noise 332 Range restricted clause 335 347 RDT 356 Real numbers 177 358 Recursive atom 338 recursive clause 277 338 Reduced clause 247 310 Reduction algorithm 248 Reduction of clause 247 Refinement graph 301 Refinement graph for optimal cover-refinement operator 316 Refinement operator xii 176 191 220 300 Refinement operator in predicate invention 349 Reflexive relation 220 Refutation 67 71 73 Refutation completeness x xi 58 76 84 Refutation completeness of linear resolution 98 Refutation completeness of SLD-resolution 109 Refutation completeness of unconstrained resolution 84 Reichenbach, H. 174 Reiter, R. 90 94 98 127 Relation 179 220 Relative implication 280 287 Relative subsumption 280 281 287 294 Renaming substitution 62 Representation 327 Representation by definite programs 333 Representation by theories 340 Resolution xi 57 58 65 93 197 317 Resolution, alternative definitions of 91 Resolution, restriction to clauses 66 Resolvent 70 Restriction of a substitution 59 Reynolds, J. ix 175 219 226 228 240 260 Ribl 359 Rieger, A. 347 Rissanen, J. 353 Rivest, R. 55 326 338n Robinson, J.A. 66 76 91 93 Rouveirol, C. 171 197 346 347 350 351 354 359 Ruck, B. 358 Rule schema 356 Russell, B. 18 174 Russell, S. 164 337—339 Sablon, G. 197 Safe computation rule 142 156 Saitta, L. x Sammut, C. 175 197 354 Sample complexity 322 324 Satisfiable 12 31 Satisfy 9 29 Sato, T. 197 210 213 Schmidt-Schauss, M. 88 Scope 21 Search bias 171 346 Search heuristics 346 358 Search space 169 Sebag, M. 359 Selection (of two clauses) 252 Self-saturated clause 273 Semantic resolution 93 Semantics 4 5 22 Semi-decidable 56n Shapiro, E. ix xii 154 155 159 168 175 176 179 184—186 192 205 220 261 299 300 306 310 354 Shatters 325 Shepherdson, J. 118n Shinohara, T. 175 225n 337 Shirato, S. 358 Side clause 94 SIM 300 Simple expression 59 Single-predicate learning 170 334 354 355 357 SIZE 240 260 310 Size of a concept 327 size, difficulty with 261 Skolem constants 41 Skolem Functions 41 Skolem standard form 42 Skolem substitution 83 Skolem, T. 39 Skolemization 41 Skolemized form 41 SL-resolution 94 Slagle, J.R. 76 93 94 SLD finite failure set 129 131 SLD-deduction 107 128 293 SLD-derivation 107 141 SLD-derivation of infinite length 123 SLD-refutation 107 SLD-refutation via 120 SLD-resolution xi 94 102 105n 198 SLD-tree 123 128 141 SLD-tree via 123 SLD-tree, effect of unfolding on 208 SLDNF-derivation 140 SLDNF-refutation 140 SLDNF-refutation via 141 SLDNF-resolution xi 58n 130 SLDNF-tree 133 140 155 SLDNF-tree via 141 Sloan, R. 332 338 339 Smith, B. 175 SOL-resolution 94 Sommer, E. 347 Soundness 58 Soundness of computed answers 116 122 125 Soundness of deduction 77 Soundness of derivation 73 Soundness of negation as finite failure 151 Soundness of resolution 66 72 Soundness of SLDNF-resolution 152 Specialization xi 169 225 299 Specialization problem xii 207 Specialization under subsumption 305 307 Spectre 357 Spectre II 357 Srinivasan, A. 354n 358 Staerk, R. 106 Stahl, I. 348—350 354 Standard form 35 39 40 42 Standard form of set of formulas 43 Standard form, non-equivalence of 43 Standard form, preserves unsatisfiability 45 Standardized apart 69 114 Statistical query 332n Statistics 359 Sterling, R. 154 155 159 Sternberg, M. 357 358 Stochastic definite program 359 Subsidiary tree 133 138 Substitution 59 Substitution as a mapping 60 Subsume-equivalence class 246 Subsume-equivalent 246 Subsumption xii 76 77 175 191 209 215 246 265 280 282 291 294 304 305 317 352 361 Subsumption for atoms 226 Subsumption is a quasi-order 246 Subsumption is decidable 246 Subsumption is NP-complete 246n Subsumption Theorem x xi 58 76 84 287 318 Subsumption Theorem for linear resolution 99 Subsumption Theorem for SLD-resolution 111 209 Subsumption Theorem for unconstrained resolution 78 83 86 Subsumption, proper 246 Subsumption, weaker than implication 265 Succeeds 140 Success branch 123 Success set 113 Successful SLDNF-tree 138 140 Sufficient condition 11 Symmetric difference 323 Symmetric relation 220 Syntax 4 15 18 T-implication 266 Tamaki, H. 210 213 Target concept 321 Tarski, A. 18 Tausend, B. 171 346 347 Tautology 12 31 45 77 Taylor, K. 197 Term 19 Term assignment 22 25 Term occurrence 228 Term set 268 Term-related clause 339 Test set 357 Teusink, F. 159 Theorem proving, ix 58n Theory 166 Theory revision 169n Time complexity 322 326 328 Time complexity with background knowledge 334 Toni, F. 173 Too strong (with respect to examples) 167 Too weak (with respect to examples) 167 TOP clause 94 107 Top element ( 226 Top-down approach to ILP xii 170 354 356 357 Tracy x 357 Training set 357 Transitive relation 220 TRUE 9 29 Truth table 8 13 Truth value 7 9 27 29 127 153n Turan, G. 338 339 Turing machine 326 Turing, A. 56 TYPE 358 Type 1 program (unfolding) 210 Type 1 program (unfolding), preserves 213 Type 2 program (unfolding) 210 Type 2 program (unfolding), preserves equivalence 213 U-learning 325n UDS specialization xii 209 215 319 Ullman, J. 55 338n Uncountable set 168 Undecidable 56 see Undecidable, clausal implication 88 Undecidable, Horn clause implication 125 Undecidable, language bias shift problem 349 Undecidable, logical implication 56 Undecidable, satisfiability of set of Horn clauses 125 Unfolding xii 197n 208 210 357 Unifiable 63 Unification algorithm 64 227 Unification Theorem 65 Unifier 63 Universal distribution 338 Universal quantification 39 Universal quantifier 18 23 287 Universal quantifier, interpretation of 27 Unsatisfiable 12 31 43 45 Unsoundness of cut 158 Unsoundness of floundering 142 Unsoundness of Prolog 156 Upper bound 221 225 Upward cover xii 223 Upward cover of atom 234 239 240 Upward cover under implication 277 Upward cover under subsumption 257 Upward cover with background knowledge 281 Upward cover, complete set of 224 Upward cover, finite chain of 239 Upward refinement operator xii 300 Upward refinement operator for finite set 310 Upward refinement operator for Horn clauses 304 Upward refinement operator, 316 Upward refinement operator, 309 Upward refinement operator, 302 Upward refinement operator, complete 300 Upward refinement operator, ideal 300 Upward refinement operator, ideal, does not exist 304 Upward refinement operator, locally finite 300 Upward refinement operator, proper 300 Urbancic, T. 358 Utgoff, P. 171 V-operator 200 201 205 Valiant, L. 321 331 Valid 12 31 Validation bias 171 346 van der Laag, P. 220 243 261 266 300 311 van der Torre, L. 243 300 van Emden, M. 106 Van Laer, W. 316 Vapnik — Chervonenkis dimension see "VC dimension" Vapnik, V. 325 Varcek, A. 358
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