A Contribution to the Model Theory Klaus Niemeyer

A Contribution to the Model Theory Klaus Niemeyer N-O-A

Harald Tribune 10/31/2020 N-O-A 2

What is a Model? • • • A person who serves as a subject for artwork or fashion, usually in the medium of photography but also for painting or drawing. A miniature representation of …. . A style, type, or design A simplified representation (usually mathematical) used to explain the workings of a real world system or event. The structural design of a complex system 10/31/2020 N-O-A 3

Abstractions, concepts or software • Analogical models • Business model • Software development process models • Model (abstract), an abstract or conceptual object used in the creation of a predictive formula • Model theory, study of the representation of mathematical concepts • Mental model, a person's cognitive representation of an idea or thought process • Modeling (NLP), a process in neuro-linguistic programming • Similitude (model), in engineering, used in the scientific testing of physical models • Working Model, engineering software. 10/31/2020 N-O-A 4

Model (abstract) • Causal model • Mathematical model • Scientific modeling – Model Driven Engineering, a software development technique based on abstract models – Metamodeling, a model of a model – Molecular modelling, used to mimic the behaviour of molecules – Geologic modelling – Morphological modelling – The Standard Model, theory in particle physics which describes certain fundamental forces and particles – Model building (particle physics) • Computer model, a computer program which attempts to simulate an abstract model of a particular system, usually builds upon a mathematical model 10/31/2020 N-O-A 5

Physical or representational objects • Model (physical), a physical representation of an object • Solid modelling, study of unambiguous representations of the solid parts of an object • Scale model, a replica or prototype of an object • Model building, a hobby centered around construction of material replicas • 3 D model, a 3 D polygonal representation of an object, usually displayed with a computer • Model (computer games), in 3 D computer graphics, a computer generated image of a character or an object 10/31/2020 N-O-A 6

Persons or occupations • Model (art), a person who poses for purposes of art, for example in art school (often known as an artist's model) • Model (person), a person whose occupation is to function as a living prop, often to display products, e. g. a fashion model • Supermodel, a person who attains celebrity status through fashion modeling • Promotional model, a person who promotes a product or service • Role model, a person who serves as a behavioural or moral example to others 10/31/2020 N-O-A 7

Proliferation of Model Definitions Probing models, phenomenological models, computational models, developmental models, explanatory models, impoverished models, testing models, idealized models, theoretical models, scale models, heuristic models, caricature models, didactic models, fantasy models, toy models, imaginary models, mathematical models, substitute models, iconic models, formal models, analogue models, instrumental models, etc. , 10/31/2020 N-O-A 8

Combinations • All this becomes even more difficult, if you combine two heavy words. Then you have "model ideas" and "idea models" ´, "system models" and "model systems“ or “model theories” and “theory models” • “model of models” and “meta models” 10/31/2020 N-O-A 9

Is all cognition „in models”? • 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. “ • The philosopher Herbert Stachowiak (1973) 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”. 10/31/2020 N-O-A 10

Philosophy • Pierce: Pragmatism • Popper: Critical Rationalism • Riegler: Radical Constructivism • Stachowiak: General Model Theory (Neopragmatic Conception of Model) • Gelbmann: Pragmatologic Theory Of Models See also: R. Mueller www. muellerscience. com 10/31/2020 N-O-A 11

Models Physical Models 10/31/2020 Semantic Models N-O-A 12

Physical Models Two dimensional Picture/Image Script/Text/ Drawing Mechanical Static 10/31/2020 Three dimensional Physico. Technical Bio. Technical Dynamic Analog N-O-A Socio. Technical Electro-chemical Electronic Electro-mechanical Psycho. Technical Digital 13

Semantic Models Emotional Cognitive Belief Scientific Meta-Physical Formal Empirical Theoretical Operative. Prospective Formal 10/31/2020 Poetic Non-Formal N-O-A 14

General Model Theory Stachowiak 1973: Mod (M, O, K, t, Z) 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 10/31/2020 N-O-A 15

K-system K = Kybiak (see: Steinbuch) (Cybernatic Organism, Intelligent Organism) K-System Motivator Perceptor Operator Effector Environment 10/31/2020 N-O-A 16

K-system K-System Motivation Perception Anticipation Environment 10/31/2020 N-O-A 17

Semantic Models Internal (K-System) 10/31/2020 External (Physical) N-O-A 18

Model Theory • Characteristics • Operator (k-system) • Purpose • Relationship model / original • Contraction 10/31/2020 N-O-A 19

Analyses / Perception Attributs Not Relevant Experimental Frame Attributs Reduction of Complexity Core 10/31/2020 Model N-O-A 20

Syntheses / Anticipation Experimental Frame Attributs Adding Complexity Model 10/31/2020 N-O-A Construct 21

Relationship Model / Original • A model is the representation or mapping of the original (perception-model)—the past • A model is the prototype or standard for a future construction (anticipation-model)—the future 10/31/2020 N-O-A 22

Operator / K-System Motivation Perception-models Anticipation-models Environment 10/31/2020 N-O-A 23

Contraction A model does not represent all attributes of the original or construction. A model represents only those attributes, which are relevant or suitable for the generator or user of the model. This effects a reduction of complexity of the real system (original/construct) within the model. 10/31/2020 N-O-A 24

Purpose • Models are substitutes for the original/construct: • For defined, cognizing or perceiving and acting model using subjects (k-systems) • Within defined time frames • By restrictions on given mental or real actions • Models are developed and applied in order to fulfill given goals or motivations of the k-system 10/31/2020 N-O-A 25

Purpose Examples • Research • Construction • Engineering • Planning • Test • Teaching • Demonstration • Training • Gaming • Communication 10/31/2020 N-O-A 26

Manipulation Reality Objects Real Life Experiment Model Simulation 10/31/2020 N-O-A Experimental Frame System Virtual Model and Experimental Frame 27

Evolution of Modelling and Simulation Reality Noise Analyses Reduction of Complexity Research Core Model Prototyping Engineering Construct Testing Adding Complexity Training Construct Syntheses Noise Construct Noise 10/31/2020 N-O-A 28

Cycle of Two K-Systems K-System A Object Of Consideration C K-System B Gaming, Interactive Simulation, Discussion, Dialectic, Co-operation, Litigation, etc. 10/31/2020 N-O-A 29

Cycle of Two K-Systems K-System B K-System A A-B A-A C M-A P-B P-A 10/31/2020 M-B N-O-A 30

Military Decision Cycle OODA loop Orient Observe Objective Decide (Motivation) ACT Situation (Perception) Mission Analysis of Objective Force Comparison Own Forces Environment -Terrain -Weather -Population Adversery Forces -Capability -Intention Development of Options Planning (Anticipation) Assessment of Options Decision Planning Situation 10/31/2020 N-O-A Execution 31

Definitions Objectives Command Control Sensors Effective System Environment Situation = Environment + Effective System 10/31/2020 N-O-A 32

Command Control (C 2 -) Model Endogenous Objectives M Motivation P Planning A „Anticipation“ Situation „Perception“ Effectors Sensors Environment 10/31/2020 Effective System Exogenous Objectives N-O-A 33

Hierarchy of Military Modelling Process Level Unit Of Time Environment Frame Elements High, Strategic Month, Weeks Continent Theatre Climate Armed Forces Major Formations Homogeneous Units Weapon Systems, Vehicles Medium, Operational Days Topography, Weather Combined Arms, Major Formations Low, Tactical Hours, Minutes Terrain, Local Visibility Homogeneous Units 10/31/2020 N-O-A 34

Military Hierarchie Motivation Strategic Planning Perceived Situation Motivation Operational Planning Perceived Situation Motivation Tactical Motivation Planning Perceived Situation 10/31/2020 Perceived Situation N-O-A 35

Specialization Motivation Anticipation Perception 10/31/2020 Anticipation N-O-A 36

Escher 10/31/2020 N-O-A 37

Characteristics of C 2 -Systems • Hybrid (Humans and IT Systems) • Goal oriented • Process oriented (feedback via environment, control) • Intelligent behaviour • Distinct from environment • Perceives the environment through sensors • Acts on the environment through effectors (command) • Hierarchical structure 10/31/2020 N-O-A 38

Characteristics of Agents (Newell, Wooldridge&Jennings, etc. . ) • Executes autonomously • Communicates with other agents • Monitors the state of its environment • Able to use symbols, abstractions, (models) • Able to exploit significant amounts of domain knowledge • Capable of adaptive goal-oriented behavior • Able to learn from the environment • Tolerant of errorful, unexpected, or wrong input • Real time, timely response • Natural language 10/31/2020 N-O-A 39

Characteristics of Agents (Hayes-Roth) • Perceive dynamic conditions in the environment • Take action to affect conditions in the environment • Reason to interpret • Perceptions • Solve problems • Draw inferences • Determine actions 10/31/2020 N-O-A 40

Characteristics of Agents An agent is a unique form of software abstraction with inherent capabilities: • Communicativity • Control • Decision making • Autonomous operation • Persistence 10/31/2020 N-O-A 41

Relations • Atomal Agent = Model(Human)= Model(Motivation, Perception, Anticipation, Sensors, Effectors) • Experimental Frame = Model(Input, Output, Environment) • Agent = Atomal Agent „or“ Atomal Agent + IT-Construct • C 2 -Model = Agent 10/31/2020 N-O-A 42

Hypotheses • Characteristics of C 2 -Models and agents are identical • The atomal object of the C 2 system is a human individual • The human can be represented (modeled) as an agent • An agent can be a structured, organised set of other agents, atomal agents, or IT components • The C 2 -Model is an agent • Agents and K-Systems are identical 10/31/2020 N-O-A 43

Centralized Command Arrangements 10/31/2020 N-O-A 44

Centralized Command Arrangements 10/31/2020 N-O-A 45

Decentralized Command Arrangments 10/31/2020 N-O-A 46

Decentralized Command Arrangements 10/31/2020 N-O-A 47

Future Work • Further reference and discussion of relevant paradigm in philosophy, psychology and natural science • Mathematical/logical explication and reasoning • Definition and Taxonomy of terms in the modelling area • Publication Please contribute and review 10/31/2020 N-O-A 48