Models & Modeling

As the complexity of information systems, enterprises, and software architectures raises steadily, human beings are forced to use abstraction in order to retain an overview of the investigated or designed sub-area of the real world. It is common practice to create models when analyzing complex real world or artificial systems. A model is “a representation of either reality or vi- sion“ (WHITTEN ET AL., 2004, p. 187). In some domains, the investigated system is referred to as a system under study (SEIDEWITZ, 2013). Stachowiak introduced these three criteria to

describe the nature of modeling on a theoretical basis (STACHOWIAK, 1973, p. 131-133): Omitted Attributes

Pre-Mapping

Area Post-Mapping _Area

Abundant Attributes

Attribute Mapping

Original Model

Figure 4: Theoretical definition of modeling (STACHOWIAK, 1973, p. 157)

• Mapping

Models always represent something, i.e., they rely on a concrete real or artificial artifact which itself can be a model. Models therefore act as a mapping or representation of this artifact (in the following related to as “original“). Stachowiak defines both, model and original as attribute classes. The mapping relation between an original artifact and a model can therefore be regarded as the mapping between attributes of the original to the model (in the sense of a mathematical mapping in set theory).

• Reduction

Models generally do not include all attributes of the original artifact, i.e., they include only a subset of attributes that is dedicated to the need of the modeler and/or the model user. Therefore models provide a certain level of abstraction.

• Pragmatism

The last criteria specifies, that during the description of what constitutes a model, multiple questions should be considered: what is the model built of (i.e., the original); when is it being built; for whom is it built; and which purpose does it serve.

The mapping of some part of the real world by means of creating a model of this part needs to be discussed in more detail. As mentioned earlier, Stachowiak describes both, original and model as attribute classes. During the mapping process, those attributes play an important role as they (1) can be integrated in the mapping, (2) can be omitted in the mapping as they don’t matter according to the current pragmatism of the model (omitted attributes), or (3) they are added to the model although they have no corresponding attribute in the original, i.e., because of technical or economic issues, or because of some limitations of the mapping relation according to the pragmatism of the model (abundant attributes). Figure 4 illustrates the mapping between the original and the model.

A more formal definition of the term model and modeling is given by Ferstl and Sinz. The au- thors define a model informally as “a system, that represents an other system by a goal-oriented manner“ (FERSTL AND SINZ, 2013, p. 137ff.). A model therefore consists of three con- stituents: an Object System SO, a Model System SM, and a Mapping Function f : VO > VM. The mapping function relates system components VO of the object system SO to the system components VM of the model system SM. Structural and behavioral conformance between SO and SM depend on whether the mapping function f is homomorphous or isomorphous, respec- tively. The Object System determines an excerpt of the reality the modeler is currently interested in, e.g., the business processes of an enterprise if a business process model is to be created. The Model Systemis a formal specification of the Object System, e.g., a data model, a business pro- cess model, an organizational model, created using the concepts formally defined in the Meta Model. Figure 5 illustrates the definition of modeling by Ferstl and Sinz.

Model

Object System

S

Model System

S

f: V

→ V

Meta

Model

Figure 5: Formal definition of modeling (FERSTL AND SINZ, 2013, p. 129)

Summarizing the definitions above, modeling can be stated as describing some aspects of the reality in more detail while ignoring and abstracting from others, thereby serving the purpose of the modeler and/or model user. Modeling can be used in order to break down the complexity of the reality and therefore provides a basis for an inter-subjectively understandable knowledge base. The definitions of model and modeling do concentrate on the mapping (function) between some real world phenomenon and a model. However they do not consider one vital aspect that is the basis for each modeled artifact: the modeler who perceives the real world, delimits the parts of the real world to be considered, and finally creates the model of that part of the real world by instantiating the mapping function. Ferstl and Sinz therefore introduce a complementary definition by reverting to a constructivist understanding of modeling (FERSTL ANDSINZ, 2013, p. 138f). Figure 6 illustrates this constructivist understanding of modeling.

Model System

S

Mapping

Subject

Model

Goals

Reality

Contextual

Relationship

Object

System S

Figure 6: Constructivist understanding of modeling (FERSTL ANDSINZ, 2013, p. 130)

In the center of the constructivist understanding of modeling stands a Subject i.e., a human being in the role of a modeler who is driven by certain goals while building models. B´ezivin also emphasized on the goal-driven aspect by stating, “A model is a simplification of a system built with an intended goal in mind“(B ´EZIVIN AND GERBE´, 2001, p. 274). The subject also stays in a contextual relationship to the reality, causing a subjective perception of the reality and interpretation of the object system. This perception and interpretation, driven by the goals pursuit, results in the models created by a human being.

Consequently, the process of modeling is always a very subjective matter, it is therefore worthwhile to reduce the subjective influence in modeling (e.g., by providing meta models, metaphors, process models) and providing an inter-subjective understandable model. The inter- subjective aspect comes with the usage of a commonly agreed modeling language, defining the general way of investigating the reality and building a model according to a modeling language. The comprehensive specification of a modeling language together with its application in order to build valid models are subsumed under the terminology of a modeling method, which will be introduced in the following.