NULL Convention Logic (NCL) is a symbolically
complete logic which expresses process completely
in terms of the logic itself and inherently and
conveniently expresses asynchronous digital circuits.
The traditional form of Boolean logic is not symbolically
complete in the sense that it requires the participation
of a fundamentally different form of expression-time
in the form of the clock - which has to be
very carefully coordinated with the logic part
of the expression to completely and effectively
express a process. We introduce NULL Convention
Logic in relation to Boolean logic as a four value
logic, and as a three value logic, and finally
as two value logic - - quite different
from traditional Boolean logic. We then show how
systems can be constructed entirely in terms of
NULL Convention Logic.
NULL Convention Logic (NCL) 
is derived directly from the Invocation Model
of Process Expression. The Invocation Model is
a conceptual model of general process expression
in contrast to a model of computation. It transcends
limiting mathematical notions of computation to
provide a unifying conceptual framework which
relates all forms of process expression from the
simplest physical and chemical processes to the
most complex natural and artificial processes.
For instance, the processes of cell metabolism
and of digital computers are characterized in
terms of the same concepts and relationships.
They simply occupy different places in a single
expression space defined by the Invocation Model.
A central concept of the Invocation Model is the
general notion of completeness. Just how
fundamental the notion of completeness is will
become clear in the course of this discussion.
It will appear in many guises in different aspects
of process expression, but always in service of
providing necessary and sufficient conditions.
We will begin with the notion of symbolic completeness
of expression. Symbolically complete expression
is complete in and of itself solely in terms of
the relationships among symbol values in the expression.
It integrates the expression of data transformation
and what is generally viewed as the expression
of control in a single symbolically determined
expression, without appeal to any extra-symbolic
expression such as a clock or a controller. Processes
in nature are symbolically complete, resolving
spontaneously and autonomously without appeal
to any global time authorities or control sequencers.
The artificial processes devised by humans can
also be symbolically complete.
Traditional Boolean logic is not symbolically
complete. Among its component elements, a traditional
Boolean logic circuit exhibits time dependent
relationships as well as symbolic-value-dependent
relationships. The symbolic-value-dependent relationships
depend on the interconnection of the logic gates
and their truth tables. The time-dependent relationships
depend on the propagation delay times of the component
elements to express the validity of data values
and the invalidity of data values. These two aspects
of expression are independent of each other in
that the time relationships can be expressed quite
arbitrarily in relation to the expression of symbolic
relationships and vice versa. These two quite
independent and partial expressions must be carefully
and explicitly coordinated to provide a complete
correctly resolvable expression of a process.
A carefully engineered Boolean logic circuit with
its clock is a complete expression and can be
made to work, but it is not a symbolically