1115:, symmetric, and geometric qualities. These qualities combine to allow an individual to more easily, rapidly and visually manipulate the relationships between entire truth tables. A logic operation performed on a two-dimensional logic alphabet connective, with its geometric qualities, produces a symmetry transformation. When a symmetry transformation occurs, each input symbol, without any further thought, immediately changes into the correct output symbol. For example, by reflecting the symbol for
1184:, meaning that the remaining connectives can all be defined solely in terms of either of them. Nonetheless, the logic alphabet’s two-dimensional geometric letter shapes along with its group symmetry properties can help ease the learning curve for children and adult students alike, as they become familiar with the interrelations and operations on all 16 binary connectives. Giving children and students this advantage is a decided gain.
22:
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1039:
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In effect, the X-stem Logic
Alphabet is derived from three disciplines that have been stacked and combined: (1) mathematics, (2) logic, and (3) semiotics. This happens because, in keeping with the mathelogical semiotics, the connectives have been custom designed in the form of geometric letter shapes
1155:
The value of the logic alphabet lies in its use as a visually simpler pedagogical tool than the traditional system for logic notation. The logic alphabet eases the introduction to the fundamentals of logic, especially for children, at much earlier stages of cognitive development. Because the logic
138:. The major emphasis of his iconic "logic alphabet" is to provide a more cognitively ergonomic notation for logic. Zellweger's visually iconic system more readily reveals, to the novice and expert alike, the underlying
724:
logic alphabet offers a visually systematic way of representing each of the sixteen binary truth functions. The idea behind the logic alphabet is to first represent the sixteen binary truth functions in the form of a
757:
is an O (passing through all squares without stopping). The square matrix corresponding to each binary truth function, as well as its corresponding letter shape, are displayed in the table below.
1164:, for example, generally require introduction and elimination rules for each connective, meaning that the use of all sixteen binary connectives would result in a highly complex
1131:
that serve as iconic replicas of their corresponding square-framed truth tables. Logic cannot do it alone. Logic is sandwiched between mathematics and semiotics. Indeed,
396:
1156:
notation system, in current use today, is so deeply embedded in our computer culture, the "logic alphabets" adoption and value by the field of
1119:(viz. 'h') across the vertical axis we produce the symbol for ←, whereas by reflecting it across the horizontal axis we produce the symbol for
105:
39:
86:
43:
58:
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1145:
1168:
system. Various subsets of the sixteen binary connectives (e.g., {∨,&,→,~}, {∨,~}, {&, ~}, {→,~}) are themselves
65:
1135:
has constructed intriguing structures involving the symbols of the logic alphabet on the basis of these symmetries (
1290:
32:
72:
1295:
1181:
1208:
1169:
147:
54:
173:
truth function, for example, takes a single truth value and maps it to another truth value. Similarly, a
1120:
817:
734:
1198:
1124:
1065:
943:
1165:
1234:
1138:
367:
1161:
1123:, and by reflecting it across both the horizontal and vertical axes we produce the symbol for
750:
730:
182:
1203:
261:
174:
79:
1136:
741:
s in the matrix. When drawing a logic symbol, one passes through each square with assigned
729:
rather than the more familiar tabular format seen in the table above, and then to assign a
1193:
170:
123:
1235:"Crystal Clear: An Interview with Shea Zellweger | Christine Wertheim and Shea Zellweger"
1271:
1127:. Similar symmetry transformations can be obtained by operating upon the other symbols.
264:. In the form of a table, the four unary truth functions may be represented as follows.
1275:
1173:
1141:
1132:
1116:
823:
796:
721:
406:
158:
135:
127:
1284:
1140:). The considerable aesthetic appeal of the logic alphabet has led to exhibitions of
901:
754:
726:
886:
845:
802:
1071:
1050:
1010:
970:
928:
907:
178:
949:
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364:), thus yielding sixteen possible binary truth functions – in general, there are
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1149:
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1031:
991:
922:
781:
185:
truth function maps ordered triples of truth values to truth values, and so on.
166:
21:
830:
1213:
412:. The sixteen possible binary truth functions are listed in the table below.
1112:
893:
852:
809:
122:, also called the X-stem Logic Alphabet (XLA), constitutes an iconic set of
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1017:
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935:
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871:
162:
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in that they suffice to define the remaining connectives. In fact, both
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itself, at this juncture, is questionable. Additionally, systems of
1157:
402:
131:
1261:
964:
15:
196:, and thus four possible unary truth functions: one mapping
1274:, including a discussion between Tilman Piesk and probably
260:, this last one corresponding to the familiar operation of
126:
that systematically represents the sixteen possible binary
332:
In the binary case, there are four possible inputs, viz. (
753:
is a X (stops in all four squares), while the symbol for
188:
In the unary case, there are two possible inputs, viz.
737:. Letter shapes are derived from the distribution of
370:
146:
properties of the sixteen binary connectives within
759:
414:
266:
46:. Unsourced material may be challenged and removed.
390:
749:values. In the extreme examples, the symbol for
745:values while stopping in a square with assigned
1111:The interest of the logic alphabet lies in its
8:
1262:Page dedicated to Zellweger's logic alphabet
380:
375:
369:
181:of truth values to truth values, while a
106:Learn how and when to remove this message
1233:Zellweger, Christine Wertheim and Shea.
1225:
134:. The logic alphabet was developed by
7:
44:adding citations to reliable sources
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31:needs additional citations for
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1146:Museum of Jurassic Technology
1312:
244:, and finally one mapping
1182:sole sufficient operators
405:truth functions for each
391:{\displaystyle 2^{2^{n}}}
1209:Boolean algebra (logic)
733:shape to each of these
416:Binary truth functions
1152:, among other places.
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268:Unary truth functions
1170:functionally complete
772:Logic alphabet shape
393:
766:Conventional symbol
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177:truth function maps
40:improve this article
1239:cabinetmagazine.org
1199:Propositional logic
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269:
169:to truth values. A
161:are functions from
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55:"Logic alphabet"
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1276:Shea Zellweger
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57: –
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51:Find sources:
45:
41:
35:
34:
29:This article
27:
23:
18:
17:
1268:small museum
1242:. Retrieved
1238:
1228:
1154:
1144:work at the
1129:
1110:
1107:Significance
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167:truth values
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50:
38:Please help
33:verification
30:
1150:Los Angeles
1142:Zellweger's
722:Zellweger's
1285:Categories
1244:2024-04-11
1220:References
1214:Logic gate
96:April 2024
66:newspapers
1133:Zellweger
1113:aesthetic
751:tautology
163:sequences
144:geometric
1188:See also
761:Symbols
735:matrices
356:), and (
140:symmetry
769:Matrix
717:Content
183:ternary
124:symbols
80:scholar
731:letter
480:NOT →
472:NOT ←
175:binary
82:
75:
68:
61:
53:
1166:proof
1158:logic
1046:NOT →
1006:NOT ←
434:NAND
171:unary
132:logic
87:JSTOR
73:books
1180:are
1176:and
1174:NAND
1117:NAND
879:NOT
838:NOT
797:NAND
483:AND
464:XOR
458:NOR
449:NOT
440:NOT
348:), (
340:), (
252:and
236:and
220:and
204:and
192:and
118:The
59:news
1178:NOR
1148:in
1066:AND
965:XOR
923:NOR
461:OR
403:ary
256:to
248:to
240:to
232:to
224:to
216:to
208:to
200:to
165:of
130:of
42:by
1287::
1270::
1237:.
944:OR
710:F
654:F
598:F
542:F
486:F
455:↔
446:←
437:→
431:T
360:,
352:,
344:,
336:,
326:T
309:F
286:T
283:F
150:.
1247:.
1125:∨
1121:→
1086:F
1026:p
986:q
902:↔
881:q
860:←
840:p
818:→
777:T
747:T
743:F
739:T
707:F
704:F
701:F
698:F
695:F
692:F
689:F
686:T
683:T
680:T
677:T
674:T
671:T
668:T
665:T
662:F
659:F
651:F
648:F
645:F
642:T
639:T
636:T
633:T
630:F
627:F
624:F
621:F
618:T
615:T
612:T
609:T
606:T
603:F
595:F
592:T
589:T
586:F
583:F
580:T
577:T
574:F
571:F
568:T
565:T
562:F
559:F
556:T
553:T
550:F
547:T
539:T
536:F
533:T
530:F
527:T
524:F
521:T
518:F
515:T
512:F
509:T
506:F
503:T
500:F
497:T
494:T
491:T
476:p
468:q
451:q
442:p
427:q
422:p
410:n
401:-
399:n
382:n
378:2
373:2
362:F
358:F
354:T
350:F
346:F
342:T
338:T
334:T
323:T
320:F
317:F
314:F
306:T
303:F
300:T
297:T
291:p
289:~
279:p
274:p
258:T
254:F
250:F
246:T
242:T
238:F
234:T
230:T
226:F
222:F
218:F
214:T
210:F
206:F
202:T
198:T
194:F
190:T
109:)
103:(
98:)
94:(
84:·
77:·
70:·
63:·
36:.
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