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:
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—Henry David Thoreau (1817–1862)
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—Ernest Lehman (b.1920)