Logic Alphabet - Significance

Significance

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 for NAND (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 ( ). The considerable aesthetic appeal of the logic alphabet has led to exhibitions of Zellweger's work at the Museum of Jurassic Technology in Los 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. Because 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 of natural 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 complex proof system. Various subsets of the sixteen binary connectives (e.g. {∨,&,→,~}, {∨,~}, {&, ~}, {→,~}) are themselves functionally complete in that they suffice to define the remaining connectives. In fact, both NAND and NOR are sole sufficient operators, meaning that the remaining connectives can all be defined solely in terms of either of them.