Model

Model has many different meanings, depending on the context.

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t==Models as abstractions or representations==

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• abstract model — theoretical representation of a phenomenon, e.g., Mathematical model.
• computer model — a computer program which attempts to simulate an abstract model of a particular system. A good example of this is the models used for weather forecasting.
• mental model — a person's cognitive representation of an idea or thought process.
• model theory — study of the representation of mathematical concepts.
• In neuro-linguistic programming, a model is a systematic unpacking and sequencing of the conscious and unconscious processes.
• Solid modelling — study of unambiguous representations of the solid parts of an object.
• The Standard Model — the theory in particle physics which describes certain fundamental forces and particles.
• An integrating aproach;

I. Models are usually man-constituted. That justifies talking about their purpose prior to talking about their consistency. Models are used as substitutes for originals because properties of the latter are of interest and the originals are not going to be investigated themselves. There may be a number of reasons for that such as taboos preventing from studying the original itself, or inability, the involved cost in terms of resources or moral damage being intolerable, or similar. For an investigator I it makes only sense to consider an entity M as a substitute of an entity O, if I can

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(1) establish an analogy, similarity, or similar relation between M and O that permits the substitution of O by M with respect to purpose and means, time-horizon etc., and

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(2) I can actually investigate M in the required way.

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That implies firstly that M does not have the properties of O that prevent I from investigating O. Also other properties of O may not be properties of M. In that sense a model is more abstract than its original. Secondly, a model M will in general have properties that O does not have and that actually aid I in investigating M.

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What the investigator I does in modeling is formulating a problem P in terms of the original O, translate that problem into a problem P' in terms of M, obtain a solution S' of P' and translate S' into a solution candidate S of P in terms of O. If S is actually a solution of P then the modeling process was successful and can be terminated. If, however, that is not the case then the investigator I can start over with a different problem, model, means of investigation, or relation between model and original. It is worth noting that the concept of solution to a problem depends on the investigator, its purpose, intended means of investigation, time-horizon of that investigation and so forth.

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What has been presented here so far essentially is due to Stachowiak, . To understand how then models are used in more detail one needs to distinguish from each other the various reference modes in which the investigator puts the model with respect to the original. The reference modes that perhaps are most important in computing are:

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(1) descriptive, i.e., the model describes the original. If the deviation from model to original cannot be tolerated then the model has to be changed. Analysis models are in a descriptive reference mode to their originals.

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(2) prescriptive, i.e., the the model prescribes the original. If the deviation from model to original cannot be tolerated then the original has to be changed. Design models are in a prescriptive reference mode to their originals, i.e., the implementation.

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(3) idealizing, i.e., the model is supposed to deviate from the original and as long as there is a good reason for that one doesn't worry. Software process models are in an idealizing reference mode to the actually realized software process. As the software process model describes how software shall be developed under ideal conditions there is no reason to be worried if one deviates from the model because the real conditions are not ideal.

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(4) constituting, i.e., the original is constituted by the model and that makes devations from model to original imposible. On ontology is in constituting reference mode to the domain it constitutes.

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The distinction between descriptive and prescriptive reference mode goes at least back to Wieringa, . More detail and references regarding models and modeling can be found, e.g., in .

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II. The consistency of models may be conceptual or physical. In many areas of research conceptual models have become the dominating species, as conceptual models, more easily than physical ones, can be investigated by means of computing. For conceptual models to be the shared property of a research community the concepts they involve must be capable of being shared. That is the case when a consensual understanding of these concepts has been achieved or can be achieved by means of definition, examples, etc.

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With respect to what is shown by a conceptual model there are differences at least with respect to computer science, mathematics and logic. Mathematical models in one way or another establish a functional cohesion between entities such as input values and output values. Logical models establish an interpretation relationship between formulae and structures. Models in Computer Science are largely organizational in that they show how data, a cooperation between agents, the process of creating a response to an external stimulus, an algorithm, or similar is structured. The emphasis of organization that is apparent in many models of computer science appears to be a consequence of either of the following:

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(1) complexity issues need to be dealt with such that a functional cohesion actually can be evaluated.

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(2) a domain of individuals or universe of discourse has to be established and the individuals within that domain are supposed to be capable of being distinguished from each other by means of their condition in that organization or particular handles available to a user of that model.

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III. The original of a model may itself be physical or conceptual. It may be so, independently of the consistency of the model. The model in the arts for example can be understood as an individual that functions as a proxy for certain aspects of a concept such as man, men, woman, child, etc. or as one of these under particular conditions. The original temporally or causally may be a predecessor of the original or a successor of it depending on the case at hand. Often it will be such that historically there can be found an iteration of sequences of model constitution and original constitution. One should not miss out the point that the original as well must be constituted in some way so it becomes accessible to the modeling individual I.

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IV. The term model is used in many communities with quite different traditions, commonly perceived problems, and purposes. To use the term properly therefore requires it being put into the right context. While this entry attempts to provide a general framework for talking about models it is not very likely that all communities would accept and use that framework.

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V. References

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Stachowiak, H.; "Modell" (In German); In: Seiffert, H.Handlexikon zur Wissenschaftstheorie; Deutscher Taschenbuch Verlag; 1989; pp. 219 - 222.

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Wieringa, R. J.; "Algebraic foundations for dynamic conceptual models"; PhD dissertation Free University of Amsterdam; 17 May 1990.

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Kaschek, R.; "Modeling ontology use for information systems"; In:

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Althoff, K.-D. & Dengel, A. & Bergmann, R. & Nick, M. & Roth-Berghofer, Th.

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(Eds.) Professional knowledge management; LNCS 3782 Springer Verlag; 2005.

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