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© Cambridge University Press Cambridge Cambridge University Press 978-0-521-89957-4 - Handbook of Practical Logic and Automated Reasoning John Harrison Index More information Index (x, y) (pair), 594 ---, 618 − (negation of literal), 51 -/, 617 − (set difference), 594 //, 617 C− (negation of literal set), 181 ::, 616 ∧ (and), 27 </, 617 ∆0 formula, 547 <=/, 617 ∆1-definable, 564 =/, 617 ⊥ (false), 27 @, 616 ⇔ (iff), 27 #install printer,22 ⇒ (implies), 27 0-saturation, 91 ∩ (intersection), 594 1-consistent, 554 ¬ (not), 27 1-saturation, 91 ∨ (or), 27 3-CNF, 79 Π1-formula, 550 3-SAT, 79 Σ1-formula, 550 (true), 27 Abel, 6 ∪ (union), 594 abelian, 287 ◦ (function composition), 596 abstract syntax, 12 ∂ (degree), 355 abstract syntax tree, 12 ∅ (empty set), 594 abstract type, 469 ≡ (congruent modulo), 594 AC (associative–commutative), 285 ∈ (set membership), 594 AC (Axiom of Choice), 144 κ-categorical, 245 accumulator, 611 → (maps to), 595 Ackermann reduction, 254 | (divides), 593 ad hoc polymorphism, 612 |= (logical consequence), 40, 130 Add,14 |=M (holds in M), 130 add 0, 565 ℘ (power set), 598 add assum, 480 ⊂ (proper subset), 594 add assum’, 497 → (sequent), 471 add default, 436 \ (set difference), 594 add suc, 565 ⊆ (subset), 594 adequate set (of connectives), 46 × (Cartesian product), 594 adjustcoeff, 342 → (function space), 595 AE fragment, 309 → (reduction relation), 258 aedecide, 310 →∗ (reflexive transitive closure of →), 258 affine transformation, 417 →+ (transitive closure of →), 258 affirmative negative rule,81 (provability), 246, 470, 474 afn dlo, 335 {1, 2, 3} (set enumeration), 594 al-Khwarizmi, 6 **, 618 algebra, 6 */, 617 algebra of logic, 7 +/, 617 algebraic number, 527 --, 618 algebraically closed, 352, 397 668 © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-89957-4 - Handbook of Practical Logic and Automated Reasoning John Harrison Index More information Index 669 align,92 axiom distribimp, 477 alldepmappings, 322 axiom doubleneg, 477 allfunctions, 322 axiom eqrefl, 477 allmappings, 322 axiom exists, 477 allnonemptysubsets, 620 axiom existseq, 477 allpairs, 620 axiom funcong, 477 allpartitions, 444 axiom iffimp1, 477 allpredicates, 322 axiom iffimp2, 477 allsatvaluations,56 axiom impall, 477 allsets, 620 axiom impiff, 477 allsubsets, 620 axiom not, 477 alltuples, 322 axiom or, 477 alpha, 493 axiom predcong, 477 alpha-convert, 133 axiom true, 477 alphanumeric,17 axiomatizable, 329 alternation, 8 axiomatized, 329 analogue computer, 63 analytic tableaux, 176 backchain, 207 And,26 backjump,88 and left, 483 backjumping, 88 and pair, 484 backtrack,87 and right, 483 Backus–Naur form, 19 andcnf,78 backward deletion, 190 andcnf3,79 backward replacement, 190 anglicize premiss, 318 bag, 597 anglicize syllogism, 318 BAPA, 454 ante disj, 513 basic complex qelim, 365 antecedent, 31 basic real qelim, 375 antecedent,31 BDD, 100 antisymmetric relation, 595 Bdd, 102 apply, 621 bdd, 102 arity, 119 bdd and, 103 arrangement, 441 bdd iff, 104 arrangement, 442 bdd imp, 104 arreq, 442 bdd or, 104 ASCII, 11 bddnode, 101 askolemize, 149 bddtaut, 104 assertsign, 362 behead, 359 assignment, 131 bell, 444 assoc, 620 Bell number, 444 association list, 621 belongs, 439 associative, 593 bi-implication, 30, 39 associative–commutative, 285 biconditional, 30 associativity, 12 bijection, 596 assume, 515 bijective, 596 assumps, 511 binary, 119 assumptate, 510 binary decision diagram, 100 AST, 12 binary decision tree, 99 at once, 512 bind, 120, 605 Atom,26 Birkhoff rules, 246 atom, 25 Birkhoff’s theorem, 246 atom, 92, 318 bit, 65 atom union,32 bit-blasting, 455 atomic propositions, 25 bitlength,71 atoms,35 Blank, 558 auto tac, 512 bmeson, 296 axiom, 3, 474 BNF, 19 Axiom of Choice, 144, 598 bool interp, 125 axiom addimp, 477 Boole, 7 axiom allimp, 477 Boolean variable, 25 axiom and, 477 bottom-up method, 172 © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-89957-4 - Handbook of Practical Logic and Automated Reasoning John Harrison Index More information 670 Index bound, 120 commutative, 7, 593 bound variable, 118 compactness (first-order logic), 227 bounded prove, 572 compactness (first-order with equality), 242 boundednum prove, 573 compactness (propositional logic), 107 boundquant step, 571 compatible, 384, 585 bpuremeson, 296 complement edge, 100 bracket, 18 complementary literals, 51, 58 bracket, 626 complete, 247 branching quantifier, 150 complete, 279 brand, 296 complete (proof system), 247 Brand’s transformation, 289 complete (theory), 245, 329 bset, 345 complete induction, 601 Buchberger’s algorithm, 410 complete and simplify, 283 butlast, 618 completeness (first-order logic), 504 by, 511 completion, 278 byte, 65 complex qelim, 366 complits’, 498 C (complex numbers), 594 composition, 596 CAD, 367 computable function, 560 calculemus, 4 computed table (BDD), 103 calculus ratiocinator, 4 concl, 477 can, 618 conclude, 517 canonical, 256, 262 condense, 370 canonical interpretation, 152 conditional, 37 canonize, 621 Config, 559 canonizer, 448 config, 559 cardinality, 597 conflict, 87 carry,66 conflict clause, 89 carry-select adder, 68 confluent, 258 carryselect,68 congruence, 236, 249 Cartesian product, 594 congruence closure, 249 cases, 517 congruent, 594 casesplit, 374 congruent, 250 catch, 616 congruent to,71 categorical, 245 conj intro tac, 508 categoricity, 245 conjoin,67 ccsatisfiable, 253 conjths, 483 ccvalid, 253 certificate, 519 conjunct, 30 characteristic function, 597 conjunction, 8, 30 characteristic of a ring/field, 382 conjunctive normal form, 54 characteristica universalis, 4 conjuncts,30 chooselang, 437 connected relation, 595 chop list, 618 connection tableaux, 215 Church’s theorem, 564 connective, 8 Church’s thesis, 555 consequences,93 Church–Rosser, 260 consequent, 31 Church–Turing thesis, 555 consequent,31 cinterpolate, 434 conservative, 150 classical logic, 528 consider, 517 classify, 550 consistent (theory), 329 clausal, 80 Const,14 clause, 80 constructive proof, 527 Cn, 244 constructor, 612 CNF, 54 continuation, 176 cnf,61 contradiction, 39 cnnf, 332 contradiction (principle), 527 codomain, 596 contrapos, 483 coefficients, 358 contraposition, 3, 45 cofactors, 387 contrapositive, 45, 214 cofinite, 598 contrapositives, 219 © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-89957-4 - Handbook of Practical Logic and Automated Reasoning John Harrison Index More information Index 671 convergent, 256 dest and,30 convex, 204, 447 dest def, 443 cooper, 348 dest eq, 235 Cooper’s algorithm, 341 dest iff,30 coordinate, 415 dest iffdef, 105 coordinations, 414 dest imp,31 countable, 598 dest nimp, 105 countermodel, 323 dest numeral, 337 cqelim, 365 dest or,30 Craig interpolation theorem, 427 dholds, 548 crit1, 277 dhquant, 549 critical pair, 275 diag, 537, 539 critical pairs, 277 diagonal lemma, 540 currying, 608 diagonalization, 537 cut, 472 diamond property, 258 cut-free, 472 Dickson’s lemma, 411 cylindrical algebraic decomposition, 367 difference logic, 349 differential algebra, 425 Davis–Putnam procedure (first-order), 162 digital computer, 63 Davis–Putnam procedure (propositional), 79 dilemma rule, 90 davisputnam, 163 Diophantine set, 580 De Morgan’s laws, 46 direction, 558 decidable (theory), 329 disequation, 593 decide finite, 322 disj elim tac, 513 decide fmp, 323 disjoint union, 613 decide monadic, 324 disjunct, 30 decision literal, 87 disjunction, 8, 30 decision problem, 308 disjunctive normal form, 54 declarative programming, 212 disjuncts,30 declarative proof , 516 distinctpairs, 620 decreasing, 619 distrib, 57, 58 Dedekind infinite, 598 divides, 593 dedmatrix, 372 divlcm, 344 Deduced,86 Dixon resultant, 425 deduction theorem, 505 DLO, 333 deepen, 177 dlobasic, 334 default parser, 20, 29, 629 DNF, 54 defcnf, 77, 78 dnf, 56, 59 defcnf3,79 do list, 618 defcnfs,78 dom, 621 definable, 531 domain, 123, 596 defined, 621 double negation, 527 definite clause, 203 downward L¨owenheim–Skolem, 227, 242 definition, 605 DP, 79 definitional CNF, 73 dp,84 defstep,76 dp loop, 163 degree, 355 dp mfn, 163 degree, 358 dp refine, 163 degree (of a polynomial), 358 dp refine loop, 164 delayed theory combination, 450 dplb,89 delconst, 374 dplbsat,89 Delta, 550 dpli,87 demodulation, 255, 297 dplisat,88 dense linear order, 333 dplitaut,88 denumerable, 598 DPLL, 85 depth, 177 dpll,85 derivability conditions (L¨ob), 577 dpllsat,85 derived rule, 479 dplltaut,85 descending chain, 601 dpltaut,89 deskol’, 498 dpsat,84 deskolcont, 503 dptaut,84 © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-89957-4 - Handbook of Practical Logic and Automated Reasoning John Harrison Index More information 672 Index drinker’s principle, 129 exists left, 491 dtermval, 548 exists left th, 491 dual, 48 expand2, 222 dual,48 expand connective, 485 duality, 27, 49 expand le, 569 dyadic, 119 expand lt, 569 expand nle, 569 EA fragment, 311 expand nlt, 569 eager, 450 expand node, 102 earlier, 619 explode, 618 ebddtaut, 106 expression,14 edge (of graph), 62 extensionality, 594 einterpolate, 435 extract thm, 508 el, 618 elementarily equivalent, 245 fa,66 elementary equivalence, 245 factor, 183 elementary theory, 329 factoring, 183 elim bex, 570 False,26 elim skolemvar, 502 Fibonacci sequence, 609 eliminate connective, 485 field, 394 eliminate connective’, 498 filter, 619 emerge, 251 find, 619 emeson, 296 find count,85 emodify, 295 find nestnonvar, 294 empty set, 594 find nvsubterm, 295 end itlist, 618 findasubset, 445 Entscheidungsproblem, 555 findsign, 362 enumerated type, 612 findsubset, 445 eq sym, 489
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