Computational General System Theory

A new formal system definition for the Bertylanffy-Program.  We now have to find formal concepts that base on our reductive levels and provide the basic for practical application development for general system theory applications. The motivation behind this is the same than in the Bertalanffy-Program: By drawing analogies “unnecessary duplication of labor” should be avoided.

Graphical representation of the CGST-System-Ontology.

 But in contrast to Bertalanffy and his colleagues we can access more than twenty years of computational intelligence development and therefore do not use mathematical sets of equality but concepts of well-defined structured fragments of mathematical logic within the World Wide Web, e.g. Semantic Web standards. And we also use an alternative way to draw near the goal of developing practical general system theory applications. This will lead us to a Quintuple (Γ, Δ, Θ, Q, F), where Γ is a set of classes, Δ is a set of properties, Θ is a relational set of assignments of types Δ ○ Γ ○ Γ or Δ ○ Γ, Q is a set of possible states for (Γ, Δ, Θ) and F is a set of (functional and logical) rules for (Γ, Δ, Θ, Q).

Set of classes Γ. A class is a concept that can be atomic or complex. It is atomic if there do not exist any subclasses and no other classes are needed to define this class. It is complex, if there exist subclasses or the class must be defined by using other (atomic or complex) classes. In practice we use classes to define objects of reality that have several attributes and where instances of the class appear in reality and therefore also in our application.

Example. To define the concept of a human being or a bacteria, we would use a class (Γ={HumanBeing, Bacteria}).

Set of properties Δ. Properties can either be attribute properties or object properties. An attribute property assigns an (atomic) attribute to class, while an attribute can have a value in an instance of a class but can not be a class itself. For relations between two classes we need object properties.

Example. For our classes from above we introduce the attributes body size, weight and genetic code. Note: At the moment we introduce these attributes in our application (Δ={bodySize, weight, geneticCode}) they are not assigned to any concept.

Relation set of assignments Θ. Only with relating classes to each other or to attributes by using object or attribute properties, in our model they get connected. Relations always have the form Δ ○ Γ ○ Γ (in case that Δ is an object property) or Δ ○ Γ (in case that Δ is an attribute property).

Example. Using relations to assign our example attributes and classes in the right way we get Θ={(weight, HumanBeing), (bodySize, HumanBeing), (geneticCode, HumanBeing), (weight, Bacteria), (geneticCode, Bacteria)}.

Using the Web Ontology Language (OWL) for Γ, Δ and Θ. Of course the definitions from above are not strictly formal. And we will not continue with developing a formal language for Γ, Δ and Θ because such a language that fulfils all our needs already exists as a world wide standard: In 2004 the World Wide Web consortium passed the so called Web Ontology Language (OWL) as a common standard for ontology descriptions in the Semantic Web. Although OWL as a standard is not without controversy, it includes all concepts we need for classes and properties and is used in a lot of applications already today.

Because of this reason we argue for OWL as a formal language for Γ, Δ and Θ. Furthermore doing so also prevents us from a lot of formal work proving the complexity and expressiveness of our model, because OWL can be related to Description Logics (structured fragments of predicate logic) and here a lot of scientific work according to these points has already been done. For an introduction into ontology modelling with OWL we recommend (Gomez-Perez 2005), for theoretical introduction and the most relevant facts of its logical background we recommend (Bader 2003).