a contribution to model theory

8/3/2019 A Contribution to Model Theory

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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

1

http://www.gcmarshall.bg/KP/2b/4.pdf





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

http://www.climateprediction.net/

http://www.wikipedia.com/



http://www.climateprediction.net/




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



• 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



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



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



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


Fig. 5 K-System



• 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



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



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


Higher-Level

K-System

AnticipationPerception

Motivation

Anticipation

Perception

Motivation

Anticipation

Perception

Motivation

Motivation


Higher-Level

K-System

Fig. 10 Aggregations of K-Systems

Fig. 11 Typical processes in a C2 staff organisation



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



Boyd-77 Boyd John R. Patterns of Conflict www.belisarius.com 1977

Bremer-87 Bremer Stuart A. The Globus Model Campus/Westview 1987

Emshoff-70 Emshoff

Sisson

James R.

Roger L.

Design and Use of Computer

Simulation Models

Macmillan Company 1970

Gelbmann-02 Gelbmann Gerhard An outline of pragmatologic modeltheory

Electronic document http://sammelpunkt.philo.at:8080/perl/user_eprints?

userid=51

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Hughes-84 Hughes Wayne P. Military Modeling MORS 1984

Meadows-72 Meadows Dennis L. The Limits to Growth: A Report for the

Club of Rome`’s Project on the

Predicament of Mankind

Universe Books 1972

Müller-06 Müller Roland History of Models in short, The

concept of model: Definitions and

Types

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NATO-98 NATO RTA NATO Modelling and Simulation

Master Plan

NATO Secretary General AC/323-WP/04 1998

NATO-99 NATO RTA Code of Best Practice on Assessment

of C2

Research and Technology

Organization

RTO-TR-9 1999

NiemeyerC-01 Niemeyer Jens C. Fluid Dynamics of Thermonuclear

White Dwarf Explosions and

Primordial Black Hole Collapse

Technische Universität

München

2001

NiemeyerC-02 Niemeyer Jens C. Three-dimensional Simulations of

Type Ia Supernovae

Astr.Astrophys.,391,1167 2002

NiemeyerK-71 Niemeyer Klaus H.A. Systemanalyse Moderne Industrie Management Enzyklopädie 1971

NiemeyerK-83 Niemeyer Klaus H.A. A Contribution to the Typology of

Games in: Operational Gaming

Pergamon Press 1983

NiemeyerK-03 Niemeyer Klaus H.A. Modelling and Simulation in Defence Information&Security,

ProCon

Advances in Modeling and

Simulation, Volume 12, Nr.1

2003

Riegler-01 Riegler Alexander Towards a Radical Constructivist

Understanding of Science

Foundations of Science 6,

(1-3), 1-30

2001

Stachowiak-73 Stachowiak Herbert Allgemeine Modelltheorie Springer 1973

Zeigler-84 Zeigler Bernard Multifacetted Modelling Academic Press 1984

13

a contribution to model theory

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