Systemic TOGA Encyclopedia

    eArticles based on the TOGA meta-theory observations &  interpretation

High-Intelligence & Decision Research Group


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Model  (Modeling)


   Shortest definition

  Model  is  every goal satisfying (goal-oriented) representation or description of a given    entity, such as an object, system, process  or property.


In other words (the recommended  TOGA's definition):


 Model is real or abstract system  which is the carrier of a function or property of another   pre-selected  system or process (s/p) with a requested or sufficient accuracy.  


- It is usually simpler than a  modelled object but it is not always simpler.


  Modeling is goal-oriented activity of intelligent agent, where its goal it to obtain a s/p which

  has requested by intelligent agent, properties of the modeled s/p with sufficient accuracy. 


   Descriptive  definition

A system/process Y (abstract/real) is called model of a system/process X (abstract/real) , if and only if it exhibits some properties of  X which are necessary, and with the precision sufficient for the achieving of a given goal G of an intelligent agent.

Between X and Y is a model-relation, i.e.:  Y  M  X |G,

where X is called modeled entity/object,
or, we also may express  Y as   Y = M (X | G),

were M denotes a model of  X under the condition of  satisfaction of a goal G .


In the attributes space: modeled entity X is recognized by a set of measured or uniquely observed N properties:  Xs= { x1, x2, ...xN}, i.e. these properties define the space XS.


The goal G  is described by another set of  attributes G s= { g1, g2, ...gJ} with the space GS.

In this case, M (X | G) depends on such subset  sX  of Xs   for which we may write: G (sX). It means,  the attributes space of  YS :  y1x y2, ...x yK,  has to be subspace of GS.


Modeling (definition)
Modeling is an activity of model building in frame (/using) of a given conceptualization factory system C.

                           MA:    I (X) --> M | (G, C)                                                           (1)                 


   I (X) - denotes  the information about X available for a modeler, an  intelligent agent (IA).

  C - conceptualization factory system is a couple:  (materials, tools) in a physical or abstract 


        In the case of an abstract system: C also is called conceptualization system,  where the 

        material set is called ontology, and tools are a set of possible/available operations on this

        material. For example,  TAO (the Theory of Abstract Objects) in TOGA is a C.


  G - goal (== objective/purpose), it denotes pre-selected  property of a state of  the couple

      (IA, its/his/her  Environment), which should be achieved when  M will be applied by IA.


Here we need to distinguish identification and specification activities. Both are a modeling, but  identification relates to an existing system, where specification relates to a system which does not exist yet and is designed/planed.


If the problem is sufficiently precisely and formally specified/identified,  the modeling can also be an automatic process, 



   Important remarks


1.  Model is a relative concept, the same system can be a model for an intelligent agent A but it is not a

     model for an intelligent agent B.

2.. Model describes a  function (in engineering sense) of a system/process (s/p) , because it includes the

     goal-oriented properties of  modeled  system.

     In this generalized sense,  "to be a  model" denotes function/use of a system/process, not necessarily its

     physical specific properties. The same system can be a model of many different modeled entities.

3.  Function model (model of function)  denotes a selected properties of a given function from the

     perspective of another, more specialized goal (application).

4.  The concept model does not exist without the concept goal (it can be expressed as a destination,

    application or  use of a model system/object).

5. The modeling of  same  s/p  for different goals/objectives produces different models.

6. The modeling of  same  s/p using different conceptualization system produces different models.



   Systemic generalization


Every perceived entity can be modeled as an abstract object by an intelligent agent acting in its domain-of activity.

Therefore a modeling depends on the properties of IA and its domain of observation D.


In the case of a rational modeling. IA  reasoning depends on its all  IPK (Information, Preferences, Knowledge), they include C and G.                


Hence we may write:


                      MA ( X(D), (IPK -> G, C) ):       I (X) --> M | (G, C)                                                  (2)


In the case  of a bounded rational modeling,  the rational modeling mechanism is  influenced/modified  or perturbed by emotional and physical properties of IA (denoted by e), frequently not conscious for it/him/her, therefore the expression (2) has to be rewritten as follows:


                      MA ( X(D), ( IPK -> G, C, e ):       I (X) --> M' | (G', C')                                          (3)


 At a consequence, the realistic modeling requires an iterative process focused on the minimizing of:


                                                || FG(G'(M')) - FG (G(M))|| 


 in the problem specific space,

 where FG  are a functional dependent on the models properties..


 In interdisciplinary sciences and engineering

 The problem of the congruence between necessary for the modeling common IPK  and the sufficient

 control and mitigation of  e are  the critical aspect  of consensus building  in the modern interdisciplinary

 research and development projects.





Modeling formalism and modeling paradigms (rules) development is a meta-modeling in the  meta-knowledge perspective .



  Categories: systemics, cognitive sciences and socio-cognitive engineering, meta-knowledge


 (the article in extension yet)


  Other links:

First version: 18 Feb. 2002, Copyright 2002-2007 Adam  Maria Gadomski, ENEA, CAMO,  HID Research Group