Summary

It was pointed out that combinational processes, are typically expressed as multiple form expressions with meta-coordination that involves elements of arbitrary sufficiency and that the presence of this meta-coordination is an impediment to a satisfactorily understanding of the nature of process expression. It was suggested that it would be advantageous to eliminate this meta-coordination. To this end, the notion of single form completeness of expression was introduced. As a test of the notion the question was asked whether combinational processes could be expressed entirely in terms of logical relationships as a single form complete expression.

It was shown that this can be accomplished with a four value logic; 4NCL. Taking 4NCL as a reference standard, it was shown that as logical completeness was gradually compromised with logics of progressively fewer values that the expression of timing relationships had to be included to restore the completeness of the expression of the process behavior. As logical completeness of expression was compromised by stages it was clear how and why the temporal relationships arose to restore the overall completeness of expression and it was clear how to limit and isolate the temporal expressions within the logical expression to minimize their significance in the complete expression of the behavior of the combinational process. This progression led to 2NCL. A practical 2 value logic which retains sufficient logical expressivity to enable practical logically determined digital system design.

The usefulness of concepts of completeness in considering process expression has been demonstrated by relating a range of process expression forms from logically determined to time determined in terms of completeness concepts and by one of those forms, 2NCL, being a practical 2 value logic which retains sufficient logical expressivity to enable practical logically determined digital system design.