a contribution to model theory
TRANSCRIPT
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A Contribution to Model Theory
Klaus Niemeyer (In: Scientific Support for the Decision Making in the Security Sector , NATO Science for Peace and Security
Series, Vol.12, Ed: Kounchev,O., Willems,R., Shalamanov, V., Tsachev, T., IOS Press, Amsterdam, 2007)
The model phenomenon
Modelling and Simulation is an essential component for any intellectual behaviour. Human knowledge
and intellect is based on the ability to create and manipulate models either cognitive or concrete, as an
individual or in groups. The collection of information and the systematic creation of an image, model or
construction which represents a part of the real environment are fundamental for the development of
intellect. Only by experimenting or manipulating these representations in a goal oriented, more or less
systematic approach it is possible to determine those solutions, which are faulty, less effective or
negative. The intellectual search for best solutions is always based on the ‘trial and error’ application of
models. Learning is only possible by making mistakes but this should not be done with a real system of
high value. Therefore, only models which permit the necessary simulations and experiments are the
means for finding the best solutions.
With the quantum leap in the evolution characterised by digital computer technology modelling and
simulation is contributing and developing in high synergy with the information systems technology.
Although the principles of experimenting in knowledge gathering on the basis of replicas of real systems
are as old as human intellect, models and simulations with digital computers have developed during the
last few decades. The disciplines of natural sciences, in particular those with a quantitative and logic
approach to fact finding as well as the engineering disciplines developed a huge amount of numerical
and logic models which are operated on digital computers.
The kernel of simulation is the development and application of explicitly formulated models which are
executed on computers. These models enable reproducible results to be generated at anytime in so-
called computation experiments. These are achieved with many changing assumptions and constraints
and thus are accessible for discussion and change. The models are structured from mathematical and
logical relationships which are based on technical, physical or social insights and theories. A model can
be seen as a replica of an existing perceptible system or as a precursor of a foreseeable system in theplanning stages. The model enables the simulation of the system considered and the analysis of
parameters, assumptions and arguments. It enables insights into sensitive areas, trends and
interrelationships between parameters.
It can be assumed that models and simulations are indeed the most sophisticated method of information
processing and may be regarded as part of hybrid intelligence. Considering the possibilities of existing
computer technology, the performance of which has increased far beyond all expectations during the
last few years and has so far hardly been exploited, as well as the possibilities of associated software
and simulations, it becomes clear that models and simulations have an enormous potential with regard
to thinking processes. On account of the models, the simulations have a rational basis, on which a
profitable discussion may be carried out. Due to model structuring it is possible to define and control the
complex relations of the real world. In a superior way, human decision-making is still given an important
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arbitrary function; but irrationalities due to the limited human information processing capacity are
eliminated. Simulations offer the possibility of experimenting and analysing the systems of the future,
which might be introduced one day. On account of the direct decision-making activity in these simulated
systems, experimental games provide planners with information on the future. They are catalysts for
group intelligence, which can define, evaluate and manipulate complex system relationships. Only in this
manner the problems of the future are likely to be treated consciously and rationally.
Many examples exist that show the power of models and simulation in science, engineering, planning
and forecasting. In astrophysics the limits of human knowledge are considerably extended using models
simulating the explosion of stars or the processes during the first’s moments of the existence of the
universe.1 The future of the global climate is predicted with relatively high precision as consequence of
the burning of fossil energy.2 The limits of growth as calculated by even simple models indicated urgent
requirements to change traditional behaviour of humans.3 In the military area many models for the
simulation of military campaigns, battles and processes were developed, are continuously improved andadjusted to real world events. Also these models are increasingly used for the improvement of armed
forces, decision making in military headquarters, experimenting and training.4
The need for a theory of modelling
Due to the fact that the model paradigm has created such an avalanche of applications in almost all
disciplines the definition of what a model is all about is not yet commonly agreed and available. 5 In
literature many definitions exist, only a few provide some structure and the idea of deeper understanding
of the phenomena. Examples are:6
A model is a person who serves as a subject for artwork or fashion, usually in the medium of
photography but also for painting or drawing, or is a miniature representation of something, or is a style,
type, design, or is a simplified representation (usually mathematical) used to explain the workings of a
real world system or event, or is the structural design of a complex system.
Models are abstractions, concepts or software and are grouped into analogical models, business
models, software development process models, and abstract models. An abtract model is an abstract or
conceptual object used in the creation of a predictive formula. A model theory is the study of the
representation of mathematical concepts, a mental model is a person's cognitive representation of an
idea or thought process. The modelling is a process in neuro-linguistic programming, or a similitude inengineering, used in the scientific testing of physical models. A working model is just engineering
software.
An abstract model is seen as a causal model, or a mathematical model, or a scientific model which is
model driven engineering (software development technique based on abstract models). The
1 NiemeyerC-01; NiemeyerC-02
2 www.climateprediction.net ; many personal computers around the world participate and contribute via the internet to this climate
simulation
3Meadows-72, Bremer-87
4 NATO-98, NATO-99, Hughes-84, NiemeyerK-03
5 www.wikipedia.com; www.müllerscience.com;
6 Müller-06
2
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metamodelling is a model of the modelling, the molecular modelling is used to mimic the behaviour of
molecules. The Standard Model is the theory in particle physics which describes certain fundamental
forces and particles, and a computer model is a computer program which attempts to simulate an
abstract model of a particular system and usually builds upon a mathematical model.
Models are also seen as physical or representational objects, a model (physical) is a physical
representation of an object. Solid modelling is a study of unambiguous representations of the solid parts
of an object, and a scale model is a replica or prototype of an object. The model building is a hobby
centered around construction of material replicas. A 3D model is a three dimensional polygonal
representation of an object, usually displayed with a computer
In common understanding an art model is a person who poses for purposes of art, for example in art
school or a model is a person whose occupation is to function as a living prop, often to display products.
A promotional model is a person who promotes a product or service. A role model is a person who
serves as a behavioural or moral example to others. All this becomes even more difficult, if combined with other heavy words. Then we have "model ideas"
and "idea models" ´, or "system models" and "model systems“, or “model theories” and “theory models”,
or “model of models” and “meta models”.
The general impression is a lack of rigid systematic structuring of the model paradigm, a considerable
chaos in understanding and the need for further work on a theory of models, since the modelling is a
very fundamental process and important for the generation and management of knowledge.
In the philosophical literature the term model is used in close connotation with intelligent behaviour and
cognition.7 In the year 1868 the founder of pragmatism, Charles Sanders Peirce, formulated: „We have
no ability to think without signs”. One can see his theory of signs also as model theory.
In his famous book „The Logic of modern Physics” physicist Percy W. Bridgman wrote 1927: „I believe
that the model is a useful and indeed inescapable tool of thought, in that it enables us to think about the
unfamiliar in terms of the familiar”. With the advances in the area of information technology many
computer models have been developed and fundamentals to the model technique are discussed and
published.8
The philosopher Herbert Stachowiak9 postulated that all „cognition is cognition in models and by
models“. It means that any contact with the world, „being out – passive or active – for recognizing of
something”, is „relative to certain subjects, intentional selecting, focussing and in temporal limitation of
its relation to the original”. Stachowiak formulated the General Model Theory , which is also seen as the
Neopragmatic Conception of Model. Recent work in the area of Radical Constructivism by Riegler and
others 10 as well as work on a Pragmatologic Theory of Models by Gelbmann and others is a
continuation of philosophical thinking in this area and needs to be considered.
A most comprehensive and fundamental work towards a theory of models was published by Stachowiak.
Stachowiak proposes the following taxonomy of models and distinguishes between:
• Physical models (Fig.1)
7Müller-06
8 Emshoff-70, NiemeyerK-71, NiemeyerK-83, Zeigler-84, NATO-98
9Stachowiak-73
10 Riegler-01, Gelbmann-02
3
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• Semantic models (Fig.2)
While physical models are made out of material or have a physical content the semantic models are
mind models, interpretations, or knowledge which are owned and processed by an intelligent system.
The physical models are always connected with a semantic model, which provides the sense and
interpretation of the physical model to the creator, operator or user of the model.
General Model Theory
Stachowiak defined
<M, O, K, t, Z>
as a tupel of five parameters of which an object O and a model M representing the functional operation
F, M= F(O). The object M is a model of object O at time interval t and in reference to the objective Z for
a K-system K .
Models M are substitutes for the original O for defined, cognisant or perceiving and acting, model-using
subjects (intelligent systems) K within defined time frames t and by restrictions on given mental or real
goals Z. The symbol K is written for the operator who performs the functional operation F which models
O in M. This operator usually can be conceived of as a semiotic subject. With t we refer to a certain point
or span of time for the performance of the operator. And Z abbreviates the interests or aims, purposes,
targets, calibrating values which are to be accounted for by the operation of modelling O in M. Z just
says to which degree M is a satisfying model of O. i.e. which selection of essentially modelling attributes
is relevant.
4
Physical
Models
Two
dimensional
Three
dimensional
Picture/Image Script/Text/Drawing
Physical-Technical
Bio-Technical
Psycho-Technical
Socio-Technical
Mechanical Electro-mechanical Electronic Electro-chemical
Static Dynamic Analog Digital
Physical
Models
Two
dimensional
Three
dimensional
Picture/Image Script/Text/Drawing
Physical-Technical
Bio-Technical
Psycho-Technical
Socio-Technical
Mechanical Electro-mechanical Electronic Electro-chemical
Static Dynamic Analog Digital
Fig. 1 Physical Models
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Relationship between model and original (F)
Any model is by definition an image or representation of an original. Therefore models are always
“virtual”, which is not real , but may display the full qualities of the real. Any model is also a construct
developed or created by humans or more generally by an intelligent system for a given purpose or
motivation.
Either a model is seen as a representation of its original, or is seen to be a prototype for a future
construction. Thus there is a certain relationship between a model and its original in reality or between
the future construction and its model in reality. The generation of models is a directed process in time
hence the model-original relationship can be separated into:
• A model is the representation or mapping of the original (perception-model)—the past. (Fig.3)
• A model is the prototype or standard for a future construction (anticipation-model)—the future.
(Fig.4)
The representation characteristic of models only does not reflect the prototype-construction-relation and
is the reason for many misunderstandings. Models with the representation characteristic can be
classified as perception-models; models with the prototype characteristic can be classified as
anticipation-models. In other words a model is either a model of an existing object, entity or system,
which could also be a model, or a model for an object, entity or system, which has to be changed,
manipulated or generated in the future. The notation “perception” is introduced to describe the process
of describing something already existing while “anticipation” is introduced to look into the future, or plan
something, or engineer a new system and to indicate that this is a process oriented towards the future.
5
Semantic Models
Emotional Cognitive
Scientific PoeticMeta-Physical
FormalEmpirical
TheoreticalOperative-Prospective
Belief
Formal Non-Formal
Semantic Models
Emotional Cognitive
Scientific PoeticMeta-Physical
FormalEmpirical
TheoreticalOperative-Prospective
Belief
Formal Non-Formal
Fig. 2 Semantic Models
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Normally only a few attributes, elements
or parameters are taken into
consideration, those, which are
important or relevant for the desired
purpose. The many attributes, elements
or parameters, which have a noise
effect and decrease the clearness of
results or which have a small relevance,
are not taken into consideration. This
effects a reduction of complexity of the real object
within the model. It characterizes the fact, that
models simplify the original or the futureconstruction in order to systematize facts or to
transmit knowledge and information, etc.11 A
model is easier and less expensive to manipulate
as the original or a construction.
The model- original relationship can be
formulated using the set theory notation:
For the perception-model: (Fig.3)
With M = v U m and O = c U n the mapping P: c → v is defined.
For the anticipation-model: (Fig.4)
With P = p U e and R = r U a the mapping A: p → r is defined.
The model using operator or K-system (K)
Models are substitutes for the original/construct: For defined, cognizing or perceiving and acting model
using subjects (K-systems) and within defined time frames and by restrictions on given mental or real
actions.12
Models and in particular simulation models, are major elements of any intellectual system. On the basisof perception models, which are equivalent to the learning, memory, experience of the system, a goal
oriented motivation and a repertoire of anticipation models, equivalent to planning models, the K-system
is able to manipulate or anticipate the environment. In this view, the perception models and the
anticipation models are essential ingredients of any intellectual behaviour.
The K-system as discussed in this paper is simplified in order to describe and systematize the idea of
the generalization of intelligent systems based on perception-models, motivation and anticipation-
11 The process of model building is in any case a constructive activity, also valid for perception models as discussed in this paper.
On the other hand the term generation of a construction is used only in the context of the anticipation model. A construction in this
sense is only understood as a desired new object or entity of reality.
12 A K-system has been defined and introduced as an element of the model theory by Stachowiak-73. The K illustrates the
abbreviation of Cybernetics (In German: Kybernetik).
6
p: Model
Attributes
e: Experimental Frame Attributes
r: Construct
Attributes
Adding Complexity
P: Virtual,
PrototypeR: Reality,
Construction
a: Additional Attributes
Fig. 4 Anticipation Model
c: Core
Attributes
n: Noise, Attributes Not Relevant
v: Model
Attributes
m: Experimental Frame Attributes,
Additional Attributes
Reduction of ComplexityReduction of Complexity
O: Object in Reality M: Virtual, Model
Fig. 3 Perception Model
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models (Fig.5). In connection with a just interesting part of an external reality in relation to the K-system
we identify an information cycle, with a feedback of information via the environment of the k-system. The
K-system is in a simplified manner a repertoire of perception models, anticipation models and a
motivator to form an acting subject. The perception models are representations of the external reality in
the feedback-cycle; the anticipation models are prototypes for the external reality and produce guidance
for the change or manipulation of the external reality. In this context the primary goal of the perception
models is the best possible representation of the external environment and the generation of a pool of
knowledge which is available for the creation and execution of anticipation models.
The anticipation models are controlled by the motivator
and are based upon the set of relevant perception
models. The acting subject can be a human or any
capable biological structure, a computer or a compoundout of these elements, e.g. groups, organizations etc. The
motivator within the K-system produces the objectives for
the combination of the modular elements within the
repertoire of perception models, which results in the
anticipation models. The basic motivation is assumed to be a change of the external reality in a direction
that the stability of the cycle will be increased or the survivability of the K-system will be maximized. The
perception- and anticipation-models within the K-systems are called internal (endogenous) models. 13 A
K-system has the ability to increase the quality of the internal models with the tendency of an increasing
adaptation and approximation of the external reality (learning).
Purpose (Z)
The most determining principle is that models are developed and applied in order to fulfil given goals or
motivations. This reflects the pragmatic or neo-pragmatic school of philosophical thinking.
The dominating attribute of a model design and its simulation application is the objective or motivation
for this activity. Examples of the objectives are (Fig.6):
• Research, which creates new insights in the phenomena of the environment, including
organisations, operations, planning, procedures, technologies, etc.• Development and engineering which create new options for activity on the basis of the research
insights. This includes the assessment of options and the identification of the best solutions and
prototypes.
• Testing, this adds ‘flavour’, ‘noise’ or ‘dirt’ in order to test the functionality and robustness of
solutions and prototypes in stress conditions.
13 Exogenous (external) models are generated by the K-system for interaction with other K-systems to form K-systems on higher
levels as e.g. in organisations.
7
Environment
K-SystemMotivation
Perception Anticipation
Environment
K-SystemMotivation
Perception Anticipation
Fig. 5 K-System
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• Training/exercises, which enable humans to operate and control the developed and tested
solutions in quasi-real conditions.
The objectives cannot be seen in isolation. There is a clear direction or sequence of activities (Fig.6).
The training/exercises only make sense after ‘verification’ of the solutions (prototypes, structures,
organisations, procedures, technologies, systems, and operations) in testing frameworks. The testing
can only be done after the selection of the best developed and engineered solutions, which in turn is
only possible on the basis of research insights. It is impossible to turn these sequences around, e.g. a
training/exercise activity and framework is not a valid and useful approach for the research. The
intention for research is the identification of systematic insights, which can only be done by elimination of
real-life noise and dirt-effects. On the other hand in training/exercises these effects are essential
ingredients for the human trainees, since they represent reality in the human environment. The
objectives of the simulations are therefore leading to and determining different model constructs.
A simulation is an experiment on the basis of a suitable model and experimental frame (Fig.7). The
methods and principles of scientific experimentation in the implementation, application, and evaluation
phases are fully applied in the case of research and analysis. The credibility and/or acceptability of the
results are determined by the experimental frame, the purpose of the investigation, the model used, and
the reproducibility of results. Time is the independent parameter in a simulation From an initial state or
situation, the time and state of the model are changed and advanced either continuously or in time
steps or at events until a final state has been reached . A simulation is a stochastic simulation if relevant
processes are based on random events in the simulation. Based on identical initial states, the random
events produce significant different final states within the reproduced simulations. A sample of simulation
runs results in a probability distribution of the final states. A simulation is deterministic if no relevant
random events influence the processes. In this case, reproduced simulation runs should result in
identical final states.
8
Reduction of
Complexity
Research
Engineering
Test
Environment
Training
Environment
Noise
Testing
Reality
Core
Construct
Analyses
Syntheses
Adding
Complexity
Model
Construct
Construct
Prototyping
Reduction of
Complexity
Research
Engineering
Test
Environment
Training
Environment
Noise
Testing
Reality
Core
Construct
Analyses
Syntheses
Adding
Complexity
Model
Construct
Construct
Prototyping
Fig. 6 Model Evolutions
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Interactive Simulations are open to
human operators, who are able to
interact with the model while the
simulation is progressing and to change
parameters. For analysis purposes or
the testing of plans and procedures this
simulation is also known as
experimental gaming. For training
purposes in command and control settings it is known as CAX (Computer Assisted Exercise).14
Grouping of K-systems
Any organisational system requires steady adaptation like any other complex living system or organism.
To this end, potential improvement options need to be continuously tested and compared with a view to
their feasibility, effectiveness and robustness in a wide range of possible scenarios and taking into
account all of the sensitive factors and their inter-dependence. However, as the human brain may only
consider a limited number of system entities and interrelations simultaneously, modelling and simulation
tools and methods become necessary to support the planning and structuring of large organizations and
social systems. Since models permit account to be taken of the complex interactions of modern day
combined elements of organizations and its synergistic effects, simulation approaches do provide the
requisite basic instruments. Yet it must be borne in mind that any analysis does have its limitations due
to very practical reasons such as, for example, the availability of data, time, and skilled personnel.
14
The use of catchwords in some literature creates confusion and misleading connotations. Nowadays practically all exercises areassisted by computers, therefore the term CAX has no meaning. Other misleading catchwords are for example “virtual simulation”,
“constructive simulation”, or “life simulation”. These ill defined terms indicate a missing understanding of the model and simulation
phenomena, since any simulation has the virtual attribute, any simulation applies a constructed model and any simulation is living.
9
Planning
Perceived Situation
Motivation
PlanningPerceived Situation
Motivation
Planning
PerceivedPerceived SituationSituation
Motivation
Planning
Perceived Situation
Motivation
Strategic
Operational
ctical
Planning
Perceived Situation
Motivation
PlanningPerceived Situation
Motivation
Planning
PerceivedPerceived SituationSituation
Motivation
Planning
Perceived Situation
Motivation
Strategic
Operational
ctical
System
R e a l i t y
V i r t u a
lModel
Manipulation
Objects
Simulation
Application
Use
E x p e r i m e n t a l F r a m eReal Life Experiment
System
R e a l i t y
V i r t u a
lModel
Manipulation
Objects
Simulation
Application
Use
E x p e r i m e n t a l F r a m eReal Life Experiment
Fig. 7 Models and Simulation
8: Hierarchy of K-systems
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In case the K-systems organize a work specialization in the sense of the functions perception,
anticipation and motivation, the overall system can be seen as a K-system on the next higher level
Fig.10). The elements of this system are the participating K-systems and their external models, which
now become internal models for the superimposed K-system. An external model is an element of a K-
System on the next higher level.
Activities within an operations centre follow a pattern equivalent to the traditional staff process in any
organisation (Fig.11). The pattern starts with situation analyses collecting empirical information of
environment elements. This information is aggregated, systematised, structured, and combined with an
existing knowledge base. The situation perception is in consequence used to develop operational
options and to perform “look=ahead” analyses addressing “what-ifs”. These processes fall within the
domain of modelling, and, properly used, can improve the quality and timeliness of the development of
alternative options, assessment, decision and subsequently option implementation and execution
management.
11
Analysis of Objective
Objective
Development of Options
Assessment of Options
DecisionPlanning
Execution
Empirical InformationCollection
Aggregation
Structuring
Situation
Planning
(Anticipation)
SituationSituation
(Perception)
(Motivation)
Knowledge Base
Analysis of Objective
Objective
Development of Options
Assessment of Options
DecisionPlanning
Execution
Empirical InformationCollection
Aggregation
Structuring
Situation
Planning
(Anticipation)
SituationSituation
(Perception)
(Motivation)
Knowledge Base
AnticipationPerception
Motivation
Anticipation
Perception
Motivation
Anticipation
Perception
Motivation
Motivation
Perception Anticipation
Higher-Level
K-System
AnticipationPerception
Motivation
Anticipation
Perception
Motivation
Anticipation
Perception
Motivation
Motivation
Perception Anticipation
Higher-Level
K-System
Fig. 10 Aggregations of K-Systems
Fig. 11 Typical processes in a C2 staff organisation
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This leads to the modelling of command and control (C2) systems. Typical characteristics of C2-systems
are the mix of human operators and systems of advanced information techniques. C2-systems are goal
and process oriented (feedback via environment, control). They are performing intelligent behaviour, are
distinct from environment and perceive the environment through sensors. They are acting on the
environment through effectors (command), and have a hierarchical structure.15
Within the research area and domain of artificial intelligence and software development the notion of
agents was generated. Typical characteristics of agents are the autonomous execution, the
communication with other agents, the monitoring of the state of its environment, the ability to use
symbols and abstractions, the ability to exploit significant amounts of domain knowledge, the capability
of adaptive goal-oriented behaviour, the ability to learn from the environment, the tolerance of error,
unexpected, or wrong input, the timely response in real time, and the use of natural language.
In this sense a K-system and an agent are identical based on the description of these characteristics. If
assumed that a human is equivalent to the K-system or agent, the model of a human can be defined asan atomic agent within the context of modelling the hierarchical process or the C2-system. In a recursive
definition any agent or K-system is an atomic agent, or an atomic agent plus an agent, or an agent plus
constructs of the information technology in order to form a hierarchy within the C2 process.
Conclusions
The systematic formulation of a model theory and further work in this area will provide a considerable
improvement of the understanding the intelligent behaviour of humans and the decision making
processes of higher level human organisations including advanced constructs of information technology
like simulation models and decision support tools. If the agent technology and the combination of
knowledge bases with goal oriented manipulation of decision support tools in hybrid (human-computer),
systems is accepted and used, based on systematic model theoretic approaches, an improved decision
making of mankind for the obvious problems of the future should be possible. The phenomenon of
modelling seems very fundamental and should get high attention in the research and academic area,
since it is a bases in many disciplines ranking from philosophy to the pragmatic development and
engineering of software.
In consequence the intention of this paper is to propose an academic discipline dealing with the
phenomenon of modelling and to generate systematic structures for the understanding and work in thisarea in the future.
List of references
15 Boyd-77; The C2 process as feedback loop is described in many military staff papers and fundamental for operational concepts.
12
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