Knowledge (XXG)

Conditioned disjunction

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24: 1121: 1101: 221: 537: 667: 84: 283: 329: 405: 118: 851: 830: 809: 890: 784: 715: 136: 398: 1162: 391: 1105: 462: 23: 1181: 673: 1186: 619: 36: 1155: 234: 227: 129: 296: 370: 1191: 289: 1148: 430: 360: 97: 427: 335: 1132: 1078: 733: 728:
In conjunction with truth constants denoting each truth-value, conditioned disjunction is
836: 815: 794: 729: 216:{\displaystyle {\overline {p}}{\overline {q}}r+p{\overline {q}}r+pq{\overline {r}}+pqr} 857: 751: 682: 1175: 1043: 1023: 434: 1048:"Conditioned disjunction as a primitive connective for the propositional calculus" 745: 722: 453: 450: 90: 1082: 1027: 1120: 1100: 721:). In electronic logic terms, it may also be viewed as a single-bit 736:. There are other truth-functionally complete ternary connectives. 1128: 532:{\displaystyle \Leftrightarrow (q\to p)\land (\neg q\to r).} 1069:
Wesselkamper, T. C. (1975). "A sole sufficient operator".
1047: 456:, the meaning of the conditioned disjunction is given by 1136: 860: 839: 818: 797: 754: 685: 622: 465: 299: 237: 139: 100: 39: 379: 369: 359: 351: 343: 334: 288: 226: 128: 123: 89: 30: 884: 845: 824: 803: 778: 709: 661: 613:The conditioned disjunction is also equivalent to 531: 323: 277: 215: 112: 78: 662:{\displaystyle (q\land p)\lor (\neg q\land r)} 1156: 399: 8: 16: 79:{\displaystyle (q\to p)\land (\neg q\to r)} 1163: 1149: 406: 392: 859: 838: 817: 796: 753: 684: 621: 464: 298: 241: 236: 191: 169: 150: 140: 138: 99: 38: 788: 278:{\displaystyle ({\overline {q}}+p)(q+r)} 1015: 15: 7: 1117: 1115: 679:in many programming languages (with 672:and has the same truth table as the 324:{\displaystyle qp\oplus qr\oplus r} 1135:. You can help Knowledge (XXG) by 1071:Notre Dame Journal of Formal Logic 1029:Introduction to Mathematical Logic 644: 511: 61: 14: 542:In words, is equivalent to: "if 1119: 1099: 598:, the value of is the value of 22: 570:". This may also be stated as " 879: 861: 773: 755: 704: 686: 656: 641: 635: 623: 523: 517: 508: 502: 496: 490: 487: 484: 466: 272: 260: 257: 238: 107: 101: 73: 67: 58: 52: 46: 40: 1: 1032:. Princeton University Press. 606:is true, and is the value of 674:ternary conditional operator 246: 196: 174: 155: 145: 730:truth-functionally complete 1208: 1114: 113:{\displaystyle (01000111)} 586:". So, for any values of 387: 21: 1083:10.1305/ndjfl/1093891614 1106:Conditioned disjunction 1052:Portugaliae Mathematica 424:conditional disjunction 420:conditioned disjunction 17:Conditioned disjunction 1131:-related article is a 886: 847: 826: 805: 780: 711: 663: 533: 325: 279: 217: 114: 80: 887: 848: 827: 806: 781: 712: 664: 534: 326: 280: 218: 115: 81: 1108:at Wikimedia Commons 858: 837: 816: 795: 752: 717:being equivalent to 683: 620: 463: 297: 290:Zhegalkin polynomial 235: 137: 98: 37: 1182:Logical connectives 719:a ? b : c 18: 1187:Ternary operations 882: 843: 822: 801: 776: 707: 659: 529: 449:, which represent 431:logical connective 422:(sometimes called 321: 275: 213: 110: 76: 1144: 1143: 1104:Media related to 1007: 1006: 846:{\displaystyle r} 825:{\displaystyle q} 804:{\displaystyle p} 437:. Given operands 416: 415: 249: 199: 177: 158: 148: 1199: 1165: 1158: 1151: 1123: 1116: 1103: 1087: 1086: 1066: 1060: 1059: 1040: 1034: 1033: 1020: 891: 889: 888: 885:{\displaystyle } 883: 852: 850: 849: 844: 831: 829: 828: 823: 810: 808: 807: 802: 789: 785: 783: 782: 779:{\displaystyle } 777: 720: 716: 714: 713: 710:{\displaystyle } 708: 678: 668: 666: 665: 660: 538: 536: 535: 530: 408: 401: 394: 338: 330: 328: 327: 322: 284: 282: 281: 276: 250: 242: 222: 220: 219: 214: 200: 192: 178: 170: 159: 151: 149: 141: 119: 117: 116: 111: 85: 83: 82: 77: 26: 19: 1207: 1206: 1202: 1201: 1200: 1198: 1197: 1196: 1172: 1171: 1170: 1169: 1112: 1096: 1091: 1090: 1068: 1067: 1063: 1042: 1041: 1037: 1022: 1021: 1017: 1012: 856: 855: 835: 834: 814: 813: 793: 792: 750: 749: 742: 734:classical logic 718: 681: 680: 676: 618: 617: 562:, according as 461: 460: 412: 337:Post's lattices 336: 295: 294: 233: 232: 135: 134: 96: 95: 35: 34: 12: 11: 5: 1205: 1203: 1195: 1194: 1189: 1184: 1174: 1173: 1168: 1167: 1160: 1153: 1145: 1142: 1141: 1124: 1110: 1109: 1095: 1094:External links 1092: 1089: 1088: 1061: 1044:Church, Alonzo 1035: 1024:Church, Alonzo 1014: 1013: 1011: 1008: 1005: 1004: 1001: 998: 995: 991: 990: 987: 984: 981: 977: 976: 973: 970: 967: 963: 962: 959: 956: 953: 949: 948: 945: 942: 939: 935: 934: 931: 928: 925: 921: 920: 917: 914: 911: 907: 906: 903: 900: 897: 893: 892: 881: 878: 875: 872: 869: 866: 863: 853: 842: 832: 821: 811: 800: 775: 772: 769: 766: 763: 760: 757: 741: 738: 706: 703: 700: 697: 694: 691: 688: 670: 669: 658: 655: 652: 649: 646: 643: 640: 637: 634: 631: 628: 625: 540: 539: 528: 525: 522: 519: 516: 513: 510: 507: 504: 501: 498: 495: 492: 489: 486: 483: 480: 477: 474: 471: 468: 433:introduced by 414: 413: 411: 410: 403: 396: 388: 385: 384: 381: 377: 376: 373: 367: 366: 363: 357: 356: 353: 349: 348: 345: 341: 340: 332: 331: 320: 317: 314: 311: 308: 305: 302: 292: 286: 285: 274: 271: 268: 265: 262: 259: 256: 253: 248: 245: 240: 230: 224: 223: 212: 209: 206: 203: 198: 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514: 505: 499: 493: 481: 478: 475: 472: 469: 459: 458: 457: 455: 452: 448: 444: 440: 436: 432: 429: 425: 421: 409: 404: 402: 397: 395: 390: 389: 386: 382: 378: 374: 372: 368: 364: 362: 358: 354: 350: 346: 342: 339: 333: 318: 315: 312: 309: 306: 303: 300: 293: 291: 287: 269: 266: 263: 254: 251: 243: 231: 229: 225: 210: 207: 204: 201: 193: 188: 185: 182: 179: 171: 166: 163: 160: 152: 142: 133: 131: 127: 122: 104: 94: 92: 88: 70: 64: 55: 49: 43: 33: 29: 25: 20: 1137:expanding it 1126: 1111: 1077:(1): 86–88. 1074: 1070: 1064: 1055: 1051: 1038: 1028: 1018: 743: 727: 671: 612: 607: 603: 599: 595: 591: 587: 583: 579: 575: 571: 567: 563: 559: 555: 551: 547: 543: 541: 454:propositions 451:truth-valued 446: 442: 438: 423: 419: 417: 352:1-preserving 344:0-preserving 124:Normal forms 1192:Logic stubs 746:truth table 740:Truth table 723:multiplexer 610:otherwise. 228:Conjunctive 130:Disjunctive 91:Truth table 1176:Categories 1010:References 578:, and not 418:In logic, 31:Definition 651:∧ 645:¬ 639:∨ 630:∧ 518:→ 512:¬ 506:∧ 497:→ 488:⇔ 380:Self-dual 316:⊕ 307:⊕ 247:¯ 197:¯ 175:¯ 156:¯ 146:¯ 68:→ 62:¬ 56:∧ 47:→ 1058:: 87–90. 1046:(1948). 1026:(1956). 582:implies 574:implies 361:Monotone 105:01000111 566:or not 554:", or " 550:, else 546:, then 428:ternary 426:) is a 1003:False 975:False 961:False 947:False 594:, and 445:, and 435:Church 371:Affine 1129:logic 1127:This 1000:False 997:False 994:False 989:True 983:False 980:False 972:False 966:False 952:False 944:False 941:False 933:True 927:False 919:True 916:False 905:True 602:when 1133:stub 986:True 969:True 958:True 955:True 938:True 930:True 924:True 913:True 910:True 902:True 899:True 896:True 748:for 744:The 732:for 1079:doi 1075:XVI 558:or 355:yes 347:yes 1178:: 1073:. 1054:. 1050:. 786:: 725:. 677:?: 590:, 441:, 383:no 375:no 365:no 1164:e 1157:t 1150:v 1139:. 1085:. 1081:: 1056:7 880:] 877:r 874:, 871:q 868:, 865:p 862:[ 841:r 820:q 799:p 774:] 771:r 768:, 765:q 762:, 759:p 756:[ 705:] 702:c 699:, 696:a 693:, 690:b 687:[ 657:) 654:r 648:q 642:( 636:) 633:p 627:q 624:( 608:r 604:q 600:p 596:r 592:q 588:p 584:r 580:q 576:p 572:q 568:q 564:q 560:r 556:p 552:r 548:p 544:q 527:. 524:) 521:r 515:q 509:( 503:) 500:p 494:q 491:( 485:] 482:r 479:, 476:q 473:, 470:p 467:[ 447:r 443:q 439:p 407:e 400:t 393:v 319:r 313:r 310:q 304:p 301:q 273:) 270:r 267:+ 264:q 261:( 258:) 255:p 252:+ 244:q 239:( 211:r 208:q 205:p 202:+ 194:r 189:q 186:p 183:+ 180:r 172:q 167:p 164:+ 161:r 153:q 143:p 108:) 102:( 74:) 71:r 65:q 59:( 53:) 50:p 44:q 41:(

Index

Venn diagram of Conditioned disjunction
Truth table
Disjunctive
Conjunctive
Zhegalkin polynomial
Post's lattices
Monotone
Affine
v
t
e
ternary
logical connective
Church
truth-valued
propositions
ternary conditional operator
multiplexer
truth-functionally complete
classical logic
truth table
Church, Alonzo
Introduction to Mathematical Logic
Church, Alonzo
"Conditioned disjunction as a primitive connective for the propositional calculus"
doi
10.1305/ndjfl/1093891614

Conditioned disjunction
Stub icon

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