Consistency and Completeness in Model Systems

Abstract

In this research, we have shown that the goal of reducing the ecological system to a mathematical model cannot be achieved. Each mathematical model that is built has one of these two drawbacks: either some admissible outputs are not produced or some inadmissible outputs are produced. In this article, the authors aim to clarify to what point natural systems can be represented by formal languages. To this end, the concepts of consistent system and complete system are defined, from which it is demonstrated that the model system can be consistent and not complete. Initially, the authors define an axiomatic in which the inputs and outputs of natural systems and complex systems in general are classified, but from the point of view of the influence of objects from the system to the environment and vice versa. For each mathematical model that is generated, either of the two statements occurs: either some acceptable outputs are not produced, or some inadmissible outputs are produced. Finally, it is shown that if the set of inputs of the system is acceptable then the system is not complete or inconsistent.