An important feature of CML is its ability to expression partial knowledge of functions in a modular way. The relations described in this section are members of a general class of partial constraints called composable equations which allow influences on a quantity to be stated separately, in a modular fashion in the domain theory. These are n-ary functions of arbitrary n (e.g., summation) that are declared piecemeal through membership assertions (e.g., (C+ y x) approximately states that y is a summation of a number of quantities including x). Formulating the aggregate function (and fixing the value of n) requires all of the elements of the set to be known. It is difficult to construct theories in which all of the elements of a set can be derived in an effective manner. Thus, implementations of CML are expected to make a closed world assumption on each set which states that all of its elements are known. This can occur once the artifact and phenomena to be analyzed are identified.
For example, the law ``the change in a container's fluid is equal to the sum
of all the flows into and out of the container'' cannot be stated as a
well-formed equation until all flows into and out of the container are known.
Still, we would like to state how the flow of liquid out a container's portal
affects the amount of liquid in the container once, as a generally
applicable law, independently of what other flows may be occurring in a
specific instance.
CML provides the following set of composable equations.
The semantics of these composable equations may be jointly defined as follows:
Let be a set of pairs consisting of one of the above relation constants (an influence) and an influencing variable (the second argument).
Let F be the set of n-ary functions such that
Finally, there exists some such that
Note that there are some additional restrictions on the functions in F which are specified in [8].
