Abstract: An apparatus for displaying and performing a complete set of the sixteen binary connectives in a two-valued notational system, the apparatus comprising at least one device in which at least one combination of a plurality of symbols has been placed in at least one configuration. Each symbol has a shape selected to indicate a selected number of from zero to four components arranged with respect to the quadrants of a set of Cartesian coordinates. The shapes of the symbols have iconicity, eusymmetry, and frame consistency with respect to the quadrants of Cartesian coordinates and the alignments of the shapes of the symbols are symmetry positional with respect to the axes of the Cartesian coordinates. The combination and configuration of the symbols are chosen so that the symbols can be positioned by a selected combination of flips, rotations, and counterchange operations to display and perform all sixteen binary connectives.

Abstract: An apparatus for displaying and performing a complete set of the sixteen binary connectives in a two-valued notational system, the apparatus comprising at least one device in which at least one combination of a plurality of symbols has been placed in at least one configuration. Each symbol has a shape selected to indicate a selected number of from zero to four components arranged with respect to the quadrants of a set of Cartesian coordinates. The shapes of the symbols have iconicity, eusymmetry, and frame consistency with respect to the quadrants of Cartesian coordinates and the alignments of the shapes of the symbols are symmetry positional with respect to the axes of the Cartesian coordinates. The combination and configuration of the symbols are chosen so that the symbols can be positioned by a selected combination of flips, rotations, and counterchange operations to display and perform all sixteen binary connectives.

Abstract: A system for displaying or performing operations in a two-valued system comprising a plurality of devices each having at least one symbol, each symbol having iconicity, eusymmetry, and frame consistency so that said symbol is consistent with respect to a selected frame of reference, said symbol further being symmetry positional so that operations in said two-valued system can be displayed or performed by changing the orientation of said symbol symmetrically with respect to said frame. This frame of reference consists of four points in a Cartesian co-ordinate system, preferably defining a basic square. The symbols are preferably letter-shaped symbols which can be assigned a phonetic value.