Some properties of discrete interval truth valued logic

This paper focus on functions defined on a special subset of the power set of {0, 1, ..., r-1} (the elements in the subset will be called discrete interval truth values because they act precisely as intervals) and operations on. The truth values. The operations discussed in this paper will be called regular because they can be seen as an extension of the regularity which was introduced by Kleene in his ternary logic. M. Mukaidono investigated some properties of ternary functions which can be represented by the regular operations. He called such ternary functions "regular ternary logic functions". Regular ternary logic functions are useful for representing and analyzing ambiguities such as transient states and/or initial stated in binary logic circuits that Boolean functions cannot cope with. They are also applicable to studied of fail-safe systems for binary logic circuits. In this paper, we will discuss an extension of regular ternary logic functions to functions on the discrete interval truth values. Section 2 will give some of the basic definitions of discrete interval truth valued logic, and show dome of its mathematical properties. In Section 3 we will give logic formulas which represent minimum and maximum information loss functions.