Dependency, Function, System, Model

Until now the following concepts have been introduced: parameter, dependency, and function. The function has been understood as a way to represent dependencies. There was an additional distinction between an abstract format of a function -giving only some structure without concrete meaning (otherwise often called a template- and a concrete function where the function is identified with concrete operations which can directly compute some values.

Turning the abstract function $f1 : POP \times ChR \longmapsto POP$ into a concrete function $f1 = add(POP, mul(POP, ChR))$ which corresponds in OKSIMO to the f1-box with two input parameters $POP, ChR$ and one output parameter $POP$ allows many more interpretations. One very common equivalent concept is that of an input-output system or simply a system. Thus by establishing a function one establishes also a system. There are many more mathematical concepts (automaton, graphs, grammars, etc.) which are equivalent to functions and systems. During this introduction we stay with the concepts function and system.

Insofar functions as well as systems have input and output parameters which can change their values we can think of functions and systems as a way to model behavior. In this sense we can say that a function -or a system- like $f1$ is a model of the observed behavior of a population represented by the parameters $POP$ and $ChR$.

If one wants to know whether a model is correct in the sense that the behavior of the model is sufficient similar with the observable behavior of the empirical world then one has to arrange a test of the model.