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Boolean-valued function

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33: 603:, interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final 690: 576:, predicate, or proposition. In all of these uses, it is understood that the various terms refer to a mathematical object and not the corresponding 702: 274: 484: 229: 572:, and their applied disciplines, a Boolean-valued function may also be referred to as a characteristic function, 102: 460: 259: 724: 596: 699:, 1st edition, Kluwer Academic Publishers, Norwell, MA. 2nd edition, Dover Publications, Mineola, NY, 2003. 54: 214: 294: 672: 382: 45: 17: 761: 711:, 1st edition, McGraw–Hill, 1970. 2nd edition, McGraw–Hill, 1978. 3rd edition, McGraw–Hill, 2010. 627: 477: 244: 169: 50: 642: 510: 77: 440: 425: 387: 199: 110: 8: 359: 349: 344: 731:, 2nd edition, 2 vols., Kiyosi ItΓ΄ (ed.), MIT Press, Cambridge, MA, 1993. Cited as EDM. 714: 657: 652: 573: 565: 470: 354: 329: 738: 662: 622: 518: 502: 430: 334: 324: 309: 304: 734: 677: 420: 397: 154: 707: 695: 600: 415: 392: 339: 632: 557: 526: 435: 755: 637: 538: 534: 139: 748:, MIT Press, Cambridge, MA, 1969. Revised, 1972. Expanded edition, 1988. 32: 743: 667: 647: 604: 561: 550: 542: 506: 569: 319: 314: 584: 364: 577: 445: 184: 114: 450: 588: 231: 617: 546: 160: 696:Boolean Reasoning: The Logic of Boolean Equations 156: 753: 276: 529:, i.e. a generic two-element set, (for example 533:= {0, 1}), whose elements are interpreted as 478: 132: 746:, An Introduction to Computational Geometry 485: 471: 141: 261: 252: 14: 754: 729:Encyclopedic Dictionary of Mathematics 280: 265: 246: 235: 220: 201: 190: 171: 145: 126: 708:Switching and Finite Automata Theory 216: 207: 26: 24: 25: 773: 719:Discrete Computational Structures 186: 177: 31: 721:, Academic Press, New York, NY. 103:History of the function concept 580:sign or syntactic expression. 13: 1: 725:Mathematical Society of Japan 684: 7: 610: 44:to comply with Knowledge's 10: 778: 517:, where X is an arbitrary 461:List of specific functions 673:Finitary boolean function 513:of the type f : X β†’ 57:may contain suggestions. 42:may need to be rewritten 628:Boolean algebra (logic) 499:Boolean-valued function 643:Propositional calculus 595:is a predicate on the 691:Brown, Frank Markham 501:(sometimes called a 739:Papert, Seymour, A. 715:Korfhage, Robert R. 537:, for example, 0 = 658:Indicator function 653:Logic minimization 574:indicator function 566:mathematical logic 295:Classes/properties 735:Minsky, Marvin L. 623:Boolean data type 545:, i.e., a single 495: 494: 407:Generalizations 72: 71: 46:quality standards 16:(Redirected from 769: 678:Boolean function 487: 480: 473: 285: 284: 278: 270: 269: 263: 255: 254: 250: 240: 239: 233: 225: 224: 218: 210: 209: 205: 195: 194: 188: 180: 179: 175: 165: 164: 158: 150: 149: 143: 135: 134: 130: 97: 74: 73: 67: 64: 58: 35: 27: 21: 777: 776: 772: 771: 770: 768: 767: 766: 762:Boolean algebra 752: 751: 687: 682: 613: 601:formal language 593:truth predicate 585:formal semantic 558:formal sciences 491: 455: 416:Binary relation 402: 369: 289: 283: 275: 268: 260: 249: 245: 238: 230: 223: 215: 204: 200: 193: 185: 174: 170: 163: 155: 148: 140: 129: 125: 84: 68: 62: 59: 49: 36: 23: 22: 15: 12: 11: 5: 775: 765: 764: 750: 749: 732: 722: 712: 700: 686: 683: 681: 680: 675: 670: 665: 660: 655: 650: 645: 640: 635: 633:Boolean domain 630: 625: 620: 614: 612: 609: 535:logical values 527:Boolean domain 493: 492: 490: 489: 482: 475: 467: 464: 463: 457: 456: 454: 453: 448: 443: 438: 433: 428: 423: 418: 412: 409: 408: 404: 403: 401: 400: 395: 390: 385: 379: 376: 375: 371: 370: 368: 367: 362: 357: 352: 347: 342: 337: 332: 327: 322: 317: 312: 307: 301: 298: 297: 291: 290: 288: 287: 281: 272: 266: 257: 247: 242: 236: 227: 221: 212: 202: 197: 191: 182: 172: 167: 161: 152: 146: 137: 127: 121: 118: 117: 106: 105: 99: 98: 81: 80: 70: 69: 39: 37: 30: 9: 6: 4: 3: 2: 774: 763: 760: 759: 757: 747: 745: 740: 736: 733: 730: 726: 723: 720: 716: 713: 710: 709: 704: 701: 698: 697: 692: 689: 688: 679: 676: 674: 671: 669: 666: 664: 661: 659: 656: 654: 651: 649: 646: 644: 641: 639: 638:Boolean logic 636: 634: 631: 629: 626: 624: 621: 619: 616: 615: 608: 606: 602: 598: 594: 590: 586: 581: 579: 575: 571: 567: 563: 559: 554: 552: 548: 544: 540: 536: 532: 528: 524: 520: 516: 512: 508: 504: 500: 488: 483: 481: 476: 474: 469: 468: 466: 465: 462: 459: 458: 452: 449: 447: 444: 442: 439: 437: 434: 432: 429: 427: 424: 422: 419: 417: 414: 413: 411: 410: 406: 405: 399: 396: 394: 391: 389: 386: 384: 381: 380: 378: 377: 374:Constructions 373: 372: 366: 363: 361: 358: 356: 353: 351: 348: 346: 343: 341: 338: 336: 333: 331: 328: 326: 323: 321: 318: 316: 313: 311: 308: 306: 303: 302: 300: 299: 296: 293: 292: 286: 273: 271: 258: 256: 243: 241: 228: 226: 213: 211: 198: 196: 183: 181: 168: 166: 153: 151: 138: 136: 123: 122: 120: 119: 116: 112: 108: 107: 104: 101: 100: 95: 91: 87: 83: 82: 79: 76: 75: 66: 56: 52: 47: 43: 40:This article 38: 34: 29: 28: 19: 742: 728: 718: 706: 694: 592: 587:theories of 582: 555: 530: 522: 514: 498: 496: 441:Higher-order 124: 93: 89: 85: 60: 51:You can help 41: 744:Perceptrons 703:Kohavi, Zvi 668:Proposition 648:Truth table 605:truth value 562:mathematics 551:information 507:proposition 426:Multivalued 388:Composition 383:Restriction 685:References 570:statistics 521:and where 360:Surjective 350:Measurable 345:Continuous 320:Polynomial 63:March 2011 663:Predicate 597:sentences 503:predicate 365:Bijective 355:Injective 330:Algebraic 109:Types by 55:talk page 18:Logic one 756:Category 741:(1988), 717:(1974), 705:(1978), 693:(2003), 611:See also 578:semiotic 541:and 1 = 511:function 446:Morphism 431:Implicit 335:Analytic 325:Rational 310:Identity 305:Constant 115:codomain 92: ( 78:Function 556:In the 509:) is a 451:Functor 421:Partial 398:Inverse 737:, and 340:Smooth 315:Linear 111:domain 53:. The 599:of a 589:truth 539:false 525:is a 505:or a 436:Space 591:, a 543:true 113:and 618:Bit 583:In 549:of 547:bit 519:set 758:: 727:, 607:. 568:, 564:, 560:, 553:. 497:A 279:β†’ 264:β†’ 251:β†’ 234:β†’ 219:β†’ 206:β†’ 189:β†’ 176:β†’ 159:β†’ 157:𝔹 144:β†’ 142:𝔹 133:𝔹 131:β†’ 88:↦ 531:B 523:B 515:B 486:e 479:t 472:v 393:Ξ» 282:X 277:β„‚ 267:X 262:β„‚ 253:β„‚ 248:X 237:X 232:ℝ 222:X 217:ℝ 208:ℝ 203:X 192:X 187:β„€ 178:β„€ 173:X 162:X 147:X 128:X 96:) 94:x 90:f 86:x 65:) 61:( 48:. 20:)

Index

Logic one

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You can help
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Function
History of the function concept
domain
codomain
X β†’ 𝔹
𝔹 β†’ X
𝔹 β†’ X
X β†’ β„€
β„€ β†’ X
X β†’ ℝ
ℝ β†’ X
ℝ β†’ X
X β†’ β„‚
β„‚ β†’ X
β„‚ β†’ X
Classes/properties
Constant
Identity
Linear
Polynomial
Rational
Algebraic
Analytic
Smooth
Continuous

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