Impure Systems and Ecological Models (I): Axiomatization

Abstract

Building models as a practical aspect of ecological theory has as a principal purpose the determination of relations in formal (mathematical) language. In this paper, the authors provide a formalization of ecological models based on impure systems theory. Impure systems contain objects and subjects: subjects are human beings. We can distinguish a person as an observer (subjectively outside the system) that by definition is the subject himself and part of the system. In this case he acquires the category of object. Objects (relative beings) are significances, which are the consequence of perceptual beliefs on the part of the subject about material or energetic objects (absolute beings) with certain characteristics. The impure system approach is as follows: objects are perceptual significances (relative beings) of material or energetic objects (absolute beings). The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. In this work we define measures which let us choose the more suitable variables to relate both the model with the ecosystem and with different models. In this way we define different comparison indexes.