656:(NB. Contains extended versions of the best manuscripts from the 12th International Workshop on Boolean Problems held at the Technische Universität Bergakademie Freiberg, Germany on 2016-09-22/23.)
609:(NB. Contains extended versions of the best manuscripts from the 11th International Workshop on Boolean Problems held at the Technische Universität Bergakademie Freiberg, Germany on 2014-09-17/19.)
821:(NB. Contains extended versions of the best manuscripts from the 15th International Workshop on Boolean Problems (IWSBP 2022) held at the University of Bremen, Bremen, Germany on 2022-09-22/23.)
144:, for example, falsity is represented by the number 0 and truth is represented by the number 1 or −1, and all variables that can take these values can also take any other numerical values.
287:
81:
308:. In these interpretations, a value is interpreted as the "degree" of truth – to what extent a proposition is true, or the probability that the proposition is true.
186:
209:
159:, in which case rather than only taking values 0 or 1, any value between and including 0 and 1 can be assumed. Algebraically, negation (NOT) is replaced with
568:
654:
607:
565:
702:(NB. Contains extended versions of the best manuscripts from the 13th International Workshop on Boolean Problems (IWSBP 2018) held at the
491:
646:
562:
744:(NB. Contains extended versions of the best manuscripts from the 14th International Workshop on Boolean Problems (IWSBP 2020) held
819:
811:
734:
700:
684:
631:
593:
567:(NB. Contains extended versions of the best manuscripts from the 10th International Workshop on Boolean Problems held at the
549:
465:
770:
742:
503:
715:
Recent
Findings in Boolean Techniques - Selected Papers from the 14th International Workshop on Boolean Problems
795:
718:
668:
762:
623:
585:
541:
55:
218:
90:
390:
792:
Advanced
Boolean Techniques - Selected Papers from the 15th International Workshop on Boolean Problems
665:
Advanced
Boolean Techniques - Selected Papers from the 13th International Workshop on Boolean Problems
834:
137:
61:
317:
495:
485:
113:
98:
457:
579:
445:
703:
117:
644:
162:
8:
305:
86:
191:
752:
690:
613:
575:
531:
382:
297:
212:
474:
807:
766:
730:
694:
680:
627:
589:
545:
509:
499:
461:
446:
426:
412:
404:
133:
39:
799:
722:
672:
484:; Kishinevsky, Michael; Kondratyev, Alex; Lavagno, Luciano; Yakovlev, Alex (2002).
481:
378:
109:
31:
756:
650:
617:
535:
102:
787:
710:
660:
360:
342:
94:
803:
726:
676:
828:
513:
153:
121:
20:
301:
293:
27:
480:
453:
790:; Huhn, Sebastian, eds. (2023-05-30). Written at Bremen, Germany.
745:
42:
consisting of exactly two elements whose interpretations include
124:
or symbols for the elements of the
Boolean domain, for example
663:; Soeken, Mathias, eds. (2020) . Written at Bremen, Germany.
490:. Springer Series in Advanced Microelectronics. Vol. 8.
322:
141:
51:
487:
Logic
Synthesis for Asynchronous Controllers and Interfaces
221:
194:
165:
64:
534:, ed. (2014-04-01) . Written at Freiberg, Germany.
132:. However, many programming languages do not have a
58:, a Boolean domain is usually written as {0, 1}, or
755:, ed. (2022-09-29). Written at Freiberg, Germany.
616:, ed. (2018-01-01). Written at Freiberg, Germany.
578:, ed. (2016-05-01). Written at Freiberg, Germany.
188:
conjunction (AND) is replaced with multiplication (
371:
281:
203:
180:
75:
152:The Boolean domain {0, 1} can be replaced by the
89:that naturally builds on a Boolean domain is the
826:
581:Problems and New Solutions in the Boolean Domain
659:
116:that takes values in some Boolean domain. Some
709:
786:
397:
377:
569:Technische Universität Bergakademie Freiberg
437:
353:
335:
619:Further Improvements in the Boolean Domain
492:Springer-Verlag Berlin Heidelberg New York
419:
751:
612:
574:
530:
403:
341:
66:
443:
359:
761:(1 ed.). Newcastle upon Tyne, UK:
622:(1 ed.). Newcastle upon Tyne, UK:
584:(1 ed.). Newcastle upon Tyne, UK:
540:(1 ed.). Newcastle upon Tyne, UK:
211:), and disjunction (OR) is defined via
827:
448:Circuit Complexity and Neural Networks
425:
537:Recent Progress in the Boolean Domain
292:Interpreting these values as logical
713:; Große, Daniel, eds. (2021-04-30).
706:, Bremen, Germany on 2018-09-19/21.)
365:Sets, Logic and Maths for Computing
282:{\displaystyle 1-(1-x)(1-y)=x+y-xy}
13:
524:
409:Introduction to Mathematical Logic
147:
14:
846:
794:(1 ed.). Cham, Switzerland:
717:(1 ed.). Cham, Switzerland:
667:(1 ed.). Cham, Switzerland:
431:A Practical Theory of Programming
91:Boolean algebra with two elements
796:Springer Nature Switzerland AG
758:Advances in the Boolean Domain
719:Springer Nature Switzerland AG
669:Springer Nature Switzerland AG
255:
243:
240:
228:
1:
763:Cambridge Scholars Publishing
624:Cambridge Scholars Publishing
586:Cambridge Scholars Publishing
542:Cambridge Scholars Publishing
328:
76:{\displaystyle \mathbb {B} .}
16:Concept in mathematical logic
571:, Germany on 2012-09-19/21.)
300:, which forms the basis for
56:theoretical computer science
7:
311:
10:
851:
391:Cambridge University Press
112:, a Boolean variable is a
18:
804:10.1007/978-3-031-28916-3
727:10.1007/978-3-030-68071-8
677:10.1007/978-3-030-20323-8
136:in the strict sense. In
19:Not to be confused with
387:Computability and Logic
367:. Springer. p. 13.
349:. Springer. p. 15.
318:Boolean-valued function
444:Parberry, Ian (1994).
433:. Springer. p. 3.
283:
205:
182:
77:
606:(xxxv+1+445+1 pages)
284:
206:
183:
118:programming languages
105:is a Boolean domain.
78:
741:(vii+1+197+5 pages)
704:University of Bremen
219:
192:
181:{\displaystyle 1-x,}
163:
62:
818:(viii+172+6 pages)
383:Jeffrey, Richard C.
347:Logic and Structure
306:probabilistic logic
87:algebraic structure
783:(xxii+231+1 pages)
748:on 2020-09-24/25.)
699:(vii+265+7 pages)
653:(xli+1+494 pages)
649:2019-08-04 at the
427:Hehner, Eric C. R.
413:Chapman & Hall
405:Mendelson, Elliott
298:multi-valued logic
279:
204:{\displaystyle xy}
201:
178:
73:
54:, mathematics and
813:978-3-031-28915-6
736:978-3-030-68070-1
686:978-3-030-20322-1
633:978-1-5275-0371-7
595:978-1-4438-8947-6
551:978-1-4438-5638-6
482:Cortadella, Jordi
467:978-0-262-16148-0
415:/CRC. p. 11.
379:Boolos, George S.
134:Boolean data type
842:
817:
782:
780:
779:
772:978-1527-58872-1
753:Steinbach, Bernd
740:
698:
643:
641:
640:
614:Steinbach, Bernd
605:
603:
602:
576:Steinbach, Bernd
564:(xxx+428 pages)
561:
559:
558:
532:Steinbach, Bernd
518:
517:
478:
472:
471:
451:
441:
435:
434:
423:
417:
416:
401:
395:
394:
375:
369:
368:
357:
351:
350:
339:
288:
286:
285:
280:
210:
208:
207:
202:
187:
185:
184:
179:
158:
131:
127:
110:computer science
103:bounded lattices
82:
80:
79:
74:
69:
32:abstract algebra
850:
849:
845:
844:
843:
841:
840:
839:
835:Boolean algebra
825:
824:
814:
788:Drechsler, Rolf
777:
775:
773:
737:
711:Drechsler, Rolf
687:
661:Drechsler, Rolf
651:Wayback Machine
638:
636:
634:
600:
598:
596:
556:
554:
552:
527:
525:Further reading
522:
521:
506:
479:
475:
468:
442:
438:
424:
420:
402:
398:
376:
372:
361:Makinson, David
358:
354:
343:van Dalen, Dirk
340:
336:
331:
314:
220:
217:
216:
213:De Morgan's law
193:
190:
189:
164:
161:
160:
156:
150:
148:Generalizations
129:
125:
65:
63:
60:
59:
24:
17:
12:
11:
5:
848:
838:
837:
823:
822:
812:
784:
771:
749:
735:
707:
685:
657:
632:
610:
594:
572:
550:
526:
523:
520:
519:
504:
473:
466:
436:
418:
411:(4 ed.).
396:
370:
352:
333:
332:
330:
327:
326:
325:
320:
313:
310:
278:
275:
272:
269:
266:
263:
260:
257:
254:
251:
248:
245:
242:
239:
236:
233:
230:
227:
224:
200:
197:
177:
174:
171:
168:
149:
146:
122:reserved words
95:initial object
72:
68:
36:Boolean domain
15:
9:
6:
4:
3:
2:
847:
836:
833:
832:
830:
820:
815:
809:
805:
801:
797:
793:
789:
785:
774:
768:
764:
760:
759:
754:
750:
747:
743:
738:
732:
728:
724:
720:
716:
712:
708:
705:
701:
696:
692:
688:
682:
678:
674:
670:
666:
662:
658:
655:
652:
648:
645:
635:
629:
625:
621:
620:
615:
611:
608:
597:
591:
587:
583:
582:
577:
573:
570:
566:
563:
553:
547:
543:
539:
538:
533:
529:
528:
515:
511:
507:
505:3-540-43152-7
501:
497:
493:
489:
488:
483:
477:
469:
463:
459:
455:
450:
449:
440:
432:
428:
422:
414:
410:
406:
400:
393:. p. 99.
392:
388:
384:
380:
374:
366:
362:
356:
348:
344:
338:
334:
324:
321:
319:
316:
315:
309:
307:
303:
299:
295:
290:
276:
273:
270:
267:
264:
261:
258:
252:
249:
246:
237:
234:
231:
225:
222:
214:
198:
195:
175:
172:
169:
166:
157:[0,1]
155:
154:unit interval
145:
143:
139:
135:
123:
119:
115:
111:
106:
104:
100:
96:
92:
88:
83:
70:
57:
53:
49:
45:
41:
37:
33:
29:
22:
21:Binary Domain
791:
776:. Retrieved
757:
714:
664:
637:. Retrieved
618:
599:. Retrieved
580:
555:. Retrieved
536:
486:
476:
447:
439:
430:
421:
408:
399:
386:
373:
364:
355:
346:
337:
294:truth values
291:
151:
107:
84:
47:
43:
35:
25:
456:. pp.
302:fuzzy logic
28:mathematics
778:2024-07-15
639:2019-08-04
601:2019-08-04
557:2019-08-04
494:. p.
329:References
746:virtually
695:240782759
514:1437-0387
454:MIT Press
429:(2010) .
296:yields a
271:−
250:−
235:−
226:−
170:−
829:Category
647:Archived
407:(1997).
385:(1980).
363:(2008).
345:(2004).
312:See also
120:feature
114:variable
99:category
97:in the
810:
769:
733:
693:
683:
630:
592:
548:
512:
502:
464:
215:to be
93:. The
691:S2CID
323:GF(2)
142:BASIC
126:false
52:logic
50:. In
44:false
38:is a
808:ISBN
767:ISBN
731:ISBN
681:ISBN
628:ISBN
590:ISBN
546:ISBN
510:ISSN
500:ISBN
462:ISBN
304:and
130:true
128:and
85:The
48:true
46:and
34:, a
30:and
800:doi
723:doi
673:doi
140:or
108:In
101:of
40:set
26:In
831::
806:.
798:.
765:.
729:.
721:.
689:.
679:.
671:.
626:.
588:.
544:.
508:.
498:.
496:73
460:.
458:65
452:.
389:.
381:;
289:.
816:.
802::
781:.
739:.
725::
697:.
675::
642:.
604:.
560:.
516:.
470:.
277:y
274:x
268:y
265:+
262:x
259:=
256:)
253:y
247:1
244:(
241:)
238:x
232:1
229:(
223:1
199:y
196:x
176:,
173:x
167:1
138:C
71:.
67:B
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.