Fundamental properties of Kleene-Stone logic functions

Kleene-Stone algebras have been proposed as an algebra with the properties of both Kleene algebra and Stone algebra. Therefore, they have connections with ambiguity and modality. A Kleene-Stone logic function is defined as a function F:[0,1]ⁿ→[0,1] represented by a logic formula. A logic formula is defined to be the form constructed by applying the logic operations AND, OR, NOT to the variable x_l,. . .,x_n and the constants 0 and 1. A necessary and sufficient condition for functions to be Kleene-Stone logic functions is shown, and an equation of the number of n-variable Kleene-Stone logic functions is presented