- Logic alphabet
The

**logic alphabet**was developed by Dr.Shea Zellweger in the1950 s while working as aswitchboard operator . It constitutes an iconic set ofsymbol s systematically representing the sixteen possible binarytruth function s.Dr. Zellweger, now retired, was Chair of the Psychology Department for Mount Union College and served as a Professor of Experimental Psychology for over twenty five years. He has numerous published articles and has been a keynote speaker on human notation and sign system engineering at various semiotic symposiums. The major emphasis of his iconic "logic alphabet" is to provide a more cognitively ergonomic notation for logic. Dr. 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 function s are functions fromsequence s oftruth value s to truth values. Aunary truth function, for example, takes a single truth value and maps it onto another truth value. Similarly, a binary truth function mapsordered pair s of truth values onto truth values, while a tenary 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 oflogical negation . In the form of a table, the four unary truth functions may be represented as follows.**ignificance**The interest of the logic alphabet lies in its

aesthetic , symmetric, and geometric qualities that allow an individual to more easily, rapidly and visually manipulate the relationships between entire truth tables. For example, by reflecting the symbol forNAND (viz. 'h') across the vertical axis we produce the symbol for ←, whereas by reflecting it across the horizontal axis we produce the symbol for →, and by reflecting it across both the horizontal and vertical axes we produce the symbol for ∨. Similar geometrical transformation can be obtained by operating upon the other symbols. Indeed, Zellweger has constructed intriguing structures involving the symbols of the logic alphabet on the basis of these symmetries ( [*http://www.logic-alphabet.net/images/logicbug_2345_2.jpg*] [*http://www.logic-alphabet.net/images/clockcompass_2353_2.jpg*] ). The considerable aesthetic appeal of the logic alphabet has led to exhibitions of Zellweger's work at theMuseum of Jurassic Technology inLos Angeles , among other places.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. Due to the fact that the logic notation system, in current use today, is so deeply embedded in our computer culture, the "logic alphabets" adoption and value by the field of

logic itself, at this juncture, is questionable. Additionally, systems ofnatural deduction , 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 complexproof system. It should be noted that various subsets of the sixteen binary connectives (e.g. {∨,&,→,~}, {∨,~}, {&, ~}, {→,~}) are themselves functionally complete in that they suffice to define the remaining connectives. In fact, bothNAND andNOR aresole sufficient operator s, meaning that the remaining connectives can all be defined solely in terms of either of them.**ee also***

Polish notation

*Propositional logic

*Boolean function

*Boolean algebra (logic)

*Logic gate **External links*** [

*http://www.logic-alphabet.net/ Page dedicated to Zellweger's logic alphabet*]

* [*http://www.flickr.com/photos/43992178@N00/387339135/ Exhibition in Museum of Jurassic Technology*]

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