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logic alphabet
The logic alphabet, also called the X-stem Logic Alphabet (XLA), constitutes an iconic set of symbols that systematically represents the sixteen possible binary truth functions of logic. The logic alphabet was developed by Shea Zellweger. 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 symmetry relationships and geometric properties of the sixteen binary connectives within Boolean algebra.
==Truth functions==
Truth functions are functions from sequences of truth values to truth values. A unary truth function, for example, takes a single truth value and maps it onto another truth value. Similarly, a binary truth function maps ordered pairs of truth values onto truth values, while a ternary truth function maps ordered triples of truth values onto truth values, and so on.
In the unary case, there are two possible inputs, viz. T and F, and thus four possible unary truth functions: one mapping T to T and F to F, one mapping T to F and F to F, one mapping T to T and F to T, and finally one mapping T to F and F to T, this last one corresponding to the familiar operation of logical negation. In the form of a table, the four unary truth functions may be represented as follows.
In the binary case, there are four possible inputs, viz. (T,T), (T,F), (F,T), and (F,F), thus yielding sixteen possible binary truth functions. Quite generally, for any number ''n'', there are possible ''n''-ary truth functions. The sixteen possible binary truth functions are listed in the table below.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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