Identification of incompletely specified multiple-valued Kleenean functions

This paper focuses on incompletely specified multiple-valued Kleenean functions (1991). It is easy to verify that they do not have functional completeness in the class of all functions on the unit interval. Therefore, not all incompletely specified functions on the unit interval are incompletely specified multiple-valued Kleenean functions. In this paper, we will clarify a necessary and sufficient condition for an incompletely specified function to be an incompletely specified multiple-valued Kleenean function. Further, we show an algorithm which derives one of the logic formulas representing the incompletely specified multiple-valued Kleenean function. In considering the application of multiple-valued Kleenean functions, we will show an example which suggests the possibility that input-output data can be described abstractly in terms of multiple-valued Kleenean functions.