  We present a method for logical specification of the behavior of a system
based on the specification of its components and for representing and
specifying the effect of a class of communication "signaling pathways" among
them. Variations in the actions and effects (semantics) of the pathways can be
seen in the resulting system. We show how to "enrich" the behavior of the
original components by exactly what is provided by the signaling pathways. This
has the potential to allow a formal proof of a property of the system as a
whole, or a formal diagnosis why a system of communicating modules may not
satisfy a desired specification, and if and how it can be "fixed." There are
five distinct stages in our view: 1. A description of the connections between
potential components at the level of which potential modules are connected. 2.
Specific choices for those modules 3. An "elaboration" of the connections among
different modules to connections among members of those different modules 4. A
description of the semantics of those connections (what they actually do) 5. A
"padding" of the modules chosen in step 2 to allow for the action of the
connections (step 3), as described in step 4. The formalism is completely
hierarchical -- in other words, the formalism works equally for the system as a
whole, for each of the modules, and for any larger system in which the original
system is a component. As it turns out, for whatever reason -- perhaps
evolutionary advantage optimization at the right level of abstraction -- many
biological systems are hierarchically modular, with the modules communicating
via various pathways. Thus, a formalism such as the one presented here could
have application to questions in biology.
