The Logic Alphabet
Dr. Zellweger's 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 square matrix rather than the more familiar tabular format seen in the table above, and then to assign a letter shape to each of these matrices. Letter shapes are derived from the distribution of Ts in the matrix. When drawing a logic symbol, one passes through each square with assigned F values while stopping in a square with assigned T values. In the extreme examples, the symbol for tautology is a X (stops in all four squares), while the symbol for contradiction 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.
| Conventional symbol | Matrix | Logic alphabet shape |
|---|---|---|
| T | ||
| NAND | ||
| → | ||
| ~p | ||
| ← | ||
| ~q | ||
| ↔ | ||
| Logical NOR | ||
| ∨ | ||
| XOR | ||
| q | ||
| N← | ||
| p | ||
| N→ | ||
| ∧ | ||
| F |
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Famous quotes containing the words logic and/or alphabet:
“...some sort of false logic has crept into our schools, for the people whom I have seen doing housework or cooking know nothing of botany or chemistry, and the people who know botany and chemistry do not cook or sweep. The conclusion seems to be, if one knows chemistry she must not cook or do housework.”
—Ellen Henrietta Swallow Richards (1842–1911)
“I believe the alphabet is no longer considered an essential piece of equipment for traveling through life. In my day it was the keystone to knowledge. You learned the alphabet as you learned to count to ten, as you learned “Now I lay me” and the Lord’s Prayer and your father’s and mother’s name and address and telephone number, all in case you were lost.”
—Eudora Welty (b. 1909)