Complexity Reduction A Pragmatic, Semantic Approach · 2011-10-16 · Complexity Reduction A Pragmatic, Semantic Approach Empowering Collaborative Intelligence Joseph J Simpson

SystemSystemSystemSystemConceptsConceptsConceptsConcepts

SM

Complexity ReductionA Pragmatic, Semantic Approach

Empowering Collaborative Intelligence

Joseph J SimpsonMary J Simpson

S t C t LLCSystem Concepts LLChttp://www.systemsconcept.org

August 17th, 2011

© 2011 Joseph J Simpson, Mary J Simpson


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Overview

Introduction and DefinitionsScientific Foundations• Scientific Method (Abduction Induction Deduction)Scientific Method (Abduction, Induction, Deduction)• Types of Truth• Types of Systems• Types of Complexityyp p y

Historical Systems Engineering (SE) Practices• SE Method, N Squared Chart (N2C)• SE Method Design Structure Matrix (DSM)SE Method, Design Structure Matrix (DSM)• SE Method, Interpretive Structural Modeling (ISM)

Recent Developments• Abstract Relation Type (ART)• Abstract Relation Type (ART)• ART for N2C• ART for DSM• Concept Cube SMConcept Cube

Summary and Questions© 2011 Joseph J Simpson, Mary J Simpson


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Introduction

• Primary goal is to enable group learning• Learning and discovery reduce cognitive

complexity• Groups are collections of intelligent agents both

human and non-human• Some systems engineering (SE) techniques

support structured group learning for humans• Other SE techniques include the use of intelligent

tagents• Evolutionary programming is used to add intelligent

t t l i l SE t h iagents to classical SE techniques



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Scientific

Foundations



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Scientific Method

InferenceReduces uncertainty and develops clear objective views of the world

AbductionGenerates theories, conjectures, hypotheses and explanations that have not yet been verified by induction or deduction

InductionGenerates conclusions based on observations or experimentalGenerates conclusions based on observations or experimental data

DeductionDeductionProcess of formal, mathematical reasoning that produces a conclusion based on a set of assumptions that are given as true


C.S. Peirce, Four Types of Inference SystemSystemSystemSystemConceptsConceptsConceptsConcepts

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“Every perceptual judgment shades into an abductive inference or hypothesis, and further elucidation of the meaning must involve phases corresponding to deduction and induction.”*p p g

P l

Deduction

Perceptual Judgment Abduction

Induction

‘Is more basic than’

© 2011 Joseph J Simpson, Mary J SimpsonFigure adapted from Chapter 2 Universal Priors to Science, A Science of Generic Design, Managing Complexity through Systems Design, John N Warfield, 2003.

Is more basic than

*Manley Thompson, The Pragmatic Philosophy of C S. Peirce, 1953, page 250.


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Peirce, Scope of Inference Structure

Inference

Perceptual J d t Ampliative DeductiveJudgment Ampliative Deductive

Inductive Abductive Syllogistic Non-syllogistic

Crude Quantita-tive Qualitative

‘Is a sub-category of’

© 2011 Joseph J Simpson, Mary J SimpsonFigure adapted from Chapter 2 Universal Priors to Science, A Science of Generic Design, Managing Complexity through Systems Design, John N Warfield, 2003.


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Scientific Method & Model Building, AD Hall

C

Theory

PredictionsC

C C

C CC

Deduction

P P′InductionModify

Confirm, Verify

CompareData,

ObservationsData,

Observations~

Error in Model,Theory

ConfidenceLimits of Model

or Theory

C = ConceptsWhere

© 2004 Joseph J Simpson, Mary J SimpsonFigure adapted from Chapter 4 The Basis of Systems Methodology in Scientific Method, Metasystems Methodology, Arthur D. Hall, 1989.


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Scientific Method-Evolutionary Computation, Fogel

Model Hypothesis

General Solution

Deductive ManipulationHypothesis SolutionManipulation

Inductive Generalization

Deductive Specialization

Measured Real World

Estimated Real World

Independent Verification

© 2011 Joseph J Simpson, Mary J SimpsonFigure adapted from Chapter 1 Defining Artificial Intelligence, Evolutionary

Computation, Toward a New Philosophy of Machine Intelligence, David B. Fogel, 2006.


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Types of Truth

Three types of statements (or sentences) are considered in this discussion: formal, factual and value.

FormalTruth of formal sentences depends only on the form of the logical connectives in the sentence.

FactualTruth of factual sentences depends on the state of the real world, and how well the synthetic statement describes the real world.

ValueTruth of a value sentence is determined in a number of waysTruth of a value sentence is determined in a number of ways, including the methods applied to formal and factual sentences.Value sentence truth expands to ethics, culture, & prediction.



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Types of Truth

Formal Factual ValueExamples(a)(b)

A is BA is not B

John is a man.John is not a man.

John is a good man.John ought to pay five dollars.

(c) If A then B All swans are white. John values gold.

These sentences tell us:

What is possible or impossible

What is true or false in the world.

What ought orought not to be.

us:

Evidence relevant to their truth:

Meaning of words, esp.“is”, “not”, “and”, “if then”.

Meanings and observations.

Meanings, observations and value/ethical systems.

Known by experience?

No Yes Some types yes,some types no.

Are they certain?

Yes No No

Required to A proof is necessary & Observational data No one kind of argument;

© 2011 Joseph J Simpson, Mary J Simpson Adapted from “Metasystems Methodology” A.D. Hall. III

Required to validate inferences:

A proof is necessary &sufficient.

Observational data and predictive success.

No one kind of argument; many desired things.

Types of SystemsSystemSystemSystemSystem

ConceptsConceptsConceptsConcepts

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II. UnorganizedComplexity

(aggregates)

Statistical Analysis Word Frequency Agent Behavior

ss

(aggregates) Agent Behavior

ando

mne

s

III. OrganizedComplexity(systems)

Logic Rules Language Structure Operational Rules

Ra (systems) Operational Rules

“too complex for analysis; too organized for statistics”

I. Organizedsimplicity(machines)

Complexity

(machines)

Adapted from “Introduction to General Systems Thinking” G.M. Weinberg© 2011 Joseph J Simpson, Mary J Simpson


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Types of Complexity

Complexity is defined as the measure of the difficulty, effort and/or resources required for one system to effectively observe, communicate and/or interoperate with, another , p ,system.

Range of Complexity Types

C iti /Cognitive/Perceptual ComputationalBehavioral Organic

[Everything Else]



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Types of Complexity

Cognitive Complexity“… is that sensation experienced in the human mind when, in observing or considering a system frustration arises from lackobserving or considering a system, frustration arises from lack of comprehension of what is being explored.” [Warfield]

Relativistic View of ComplexityRelativistic View of Complexity“… the complexity of a given system is always determined by some other system with which the given system operates.” [Casti]

Computational ComplexityComputational complexity is generally associated with well defined algorithmic problems and the efficient solutions for these stated algorithmic problems.g p



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Observations re. Types of Complexity

HumanCognitive Complexity

ComputerComputational Complexity

Communication in common context (Law 1)

Communication with common syntax (Symbols)

Can communicate with nonsense symbols (Law 2)

Cannot communicate with nonsense symbols

Limited by short-term memory Limited by computation time andLimited by short-term memory recall

Limited by computation time and memory size

Three types of language Single language component:components:

• Prose• Mathematics

Graphics

• Symbols (0,1) (binary logic)

• Graphics



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Historical

Systems Engineering (SE)

PracticesPractices



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SE Method: N-Squared Charts

Initially developed as a systems analysis and interface communication tool for software design and development.Proved to be well suited for the grouping of alternative system• Proved to be well suited for the grouping of alternative system configurations

• Mostly used to communicate system structurey y

• Based on analysis by human experts• Analyze and define interfaces• Present dependency, interdependency and sequence • Evaluate clustering and parallelism• Address interrelationships inherently without biasAddress interrelationships inherently without bias

• Recognize interface patterns and signatures (functionally-bound blocks, nodes, supported nodes, disjoints, etc.) thru use of human pattern recognition



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Function1

F1

F2

F1

F3

F1

F4

F1

F5

F1

F6

FeedForward

Functions, elements are placed on the diagonal

F2 F3 F4 F5 F6

F1

F2

Function2

F2

F3

F2

F4

F2

F5

F2

F6 Feed Forward i i di t d t F1

F3

F2

F3

Function3

F3

F4

F3

F5

F3

F6

F1 F2 F3 Function F4 F4

is indicated to the right and

downFeed-Back is indicated

F4 F4 F4 4 F5 F6

F1

F5

F2

F5

F3

F5

F4

F5

Function5

F5

F6

to the left and up

F1

F6

F2

F6

F3

F6

F4

F6

F5

F6

Function6 Feed-Back

Interactions or interdependencies between functions, elements are indicated in the remaining squares



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F1

F2 Critical Element or Function

F3

F4

F5

F6Tightly related

Simple Flow (no feedback)

Control Loops

F7

F8

Tightly related functional group

(a ‘natural’ module)

Nodal Point

Loops

F9

F10

Nodal Point

F11Complex

Interactions

Adapted from “The N2 Chart, R. Lano, Copyright 1977, TRW Inc.© 2011 Joseph J Simpson, Mary J Simpson


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Nine Functions and Twenty-Three Nodes Five Functions and

Eight NodesF1

F2

F3

F4

Where:FA = F1FB = F2, F3 AND F44

F5

F6

F7

FC = F5FD = F6, F7 AND F8FE = F9

F9

F8

FA

FB

FD

FC

FB


FE


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SE Method: Design Structure Matrix (DSM)

First developed to address the reduction of computational complexity in sets of linear equations.

• Recognized as a powerful graphical tool to communicate large amounts of detailed information to groups of diverse individuals

• Developed to facilitate the solution of large-scale systems problems p g y pusing graphical communication techniques coupled with a set of computational rules and techniques

• Designed to identify system clusters and the highest value systemDesigned to identify system clusters and the highest value system configurations

• Has developed into a number of different, varying techniques each ith i t d tiwith unique syntax and semantics

Identification of feasible, alternative system configurations has proven highly complex and remains the highesthas proven highly complex, and remains the highest barrier to effective implementation



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SE Method: Directional DSM

Item1

Items are placed on the diagonal Rows with no ‘local’ interaction

are allowed

Item2 “Feed-Back” is minimized

X

Item3

Item4

“Feed Forward” is maximized

Direction differs from

Direction differs from

one technique to another

X X

X

Item5

differs from one technique

to another

Output

InputX

X

Item6X X X XX


Interactions or interdependencies between items are indicated in the remaining squares


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SE Method: Balanced DSM

Items are placed on the diagonal Rows with no ‘local’ interaction

are allowedItem1

Item2

Li k

X XX

Links are

Item3

Item4

Links are balancedXX

X X XXbalanced

Item5X

X X

X

XX

Item6X X


Interactions or interdependencies between items are indicated in the remaining squares


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SE Method: Interpretive Structural Modeling

Developed by John N Warfield, to address the reduction of cognitive complexity found in socio-technical systems. Warfield’s science encompasses:p

Behavioral pathologies of individuals, groups, organizations

Logic and language (formal logic, mathematics of structure, og c a d a guage ( o a og c, at e at cs o st uctu e,structural modeling, and languages)

Collaborative abduction (generation of structural hypotheses; bd i h h i i i )group abduction or hypothesis generation in a group process)

Adds intelligent computer-based agent to process

Applies to ideas and concept development



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SE Method: ISM

Logical Structure of the Problem(s)

Computer determines logically feasible set of concepts

Human experts reason, and

make a decision

p

make a decision

Humans focus on the remaining logically feasible concepts in the problem space to solve the problem(s)concepts in the problem space to solve the problem(s)


Problem and/or Set of Problems


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SE Method: ISM, Law of Triadic Compatibility

Quantifies the limitations of short-term memory as they relate to human decision makingThe human mind can recall and operate with seven concepts:The human mind can recall and operate with seven concepts:

• Three elements• The four combinations associated with three elements

{1,2,3}

The human mind is compatible with the need

{1,2} {1,3} {2,3}p

to explore interactions among a set of three elements

1 2 3elements

Capacity cannot be presumed for a set that both has four


Capacity cannot be presumed for a set that both has four members, and for which those members interact


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SE Method: ISM, Principle of Division by Threes

Iterative division of a concept as a means of analysis is mind compatible if each division produces at most three components, thereby creating a ‘tree’ withp , y g• One element at the top• At most three elements at the second level• At most nine elements at the third level• And so on…

Fi t l lFirst level

Second level


Third level


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Recent

Developments



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Abstract Relation Type (ART)

Based on the Abstract Data Type concept• Similar structure

• Similar behavior

• Programming language independent

Abstract Relation Types• Focused on global system organizing relationship

• Similar structure

• Similar semantics

• Specific system type independent

Used as basic components of a pattern language



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Has three main parts:

Prose Description (text, words)• Formal pattern• Informal prose

G hi R t tiFormal Prose

Graphic Representation(directed graphs)

• Must have formal graphsInformal Prose

g p• Can also have informal graphs

Mathematics & ComputerGraphs Math

Representation• Math equations

C t d


• Computer codes• One or both


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Abstract Relation Type, Setting the Context

Focus on system organizing relationship• Natural language relationship (meta-language)

Relationship typesRelationship types• Definitive• Competitive• InfluenceInfluence• Temporal• Spatial• Mathematical

• Mathematical relation (object language)Relation types

Universal• Universal• Reflexive• Transitive• Symmetric


• Symmetric• Hybrid


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Abstract Relation Type (ART) Example

Marking Space

Represents system structure

Value Space

Represents system value configuration(s)Represents system value configuration(s)

Outcome Space

Represents aggregation of system structure and system value(s)

Evolutionary algorithms are used to search the Outcome Space to find the best-fit solution



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Outcome Space (OS1)

. .

Marking Space (MS1)

. . ..

.

Value Space (VS1)

Abstract Relation Type (ART) ≡ Ƒ [ MS, OS ]


Outcome Space (OS) ≡ Ƒ [ VS1, VS2, …VSn, VSn+1, … ]


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Abstract Relation Type (ART), Example

A B C D E FA 0 0 0 0 0 1 0 1 2 3 4 50 1 2 3 4 5

Marking SpaceValue Matrix

Number Field

BCD

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reflects the same properties as the

organizing relationshipxD

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Outcome SpaceRepresents the System Structure [for each

object through , a one in the cell shows

A F Reflects the l ti l0

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o e t e ce s o slocation of an interface] =

relative value of the system

structure


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ART for N2C

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No Obvious Pattern;

Unordered1

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Unordered

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Ordered;


1 1

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Ordered;Obvious Patterns


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ART for N2C, Evolutionary Algorithm Applied

2 61 0 1 2 3 4 5

1 70 1 2 3 4 5 6

0 81 2 3 4 5 6 7

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4 43 2 1 0 1 2 3

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Unordered Marking Space; No Obvious

6 25 4 3 2 1 0 1

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5 34 3 2 1 0 1 21

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Space; No Obvious Pattern

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Ordered Marking Space;


1 1 00 0 00 0 0 1 1 00 0 00 0 0 1 1 00 0 00 0 0Obvious Patterns


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ART for DSM

• System structure is separated from system value

• Marking space is based on Warfield’s Mathematics of Structure – augmented Boolean mathematics

• Value space is based on Hitchins’ Automated N S d hSquared chart

• Evolutionary algorithm ART method generates did t l ti t ti ll d i th t fcandidate solutions automatically, reducing the cost of

human systems analysis and creating solutions not seen by the human analystseen by the human analyst



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ART for DSM

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Initial ART Marking Space

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0 Final ART Marking Space001

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SE Method: Concept Cube SM

A Generic Concept Cube Approach• Designed to organize any given concept so that human

experts can recognize and evaluate a conceptexperts can recognize and evaluate a concept• Adapts basic aspects of Formal Concept Analysis• Incorporates Warfield’s “Law of Triadic Compatibility”Incorporates Warfield s Law of Triadic Compatibility

(LTC) and “Principle of Division by Threes” (PDT)• Main concept assigned as Level 0 (L0)• Three sub-concepts assigned as Level 1 (L1)• Standard numbering scheme (level, parent, local):

L0 > C0 0L0 -> C0.0L1 -> SC1.1; SC1.2; SC1.3L2 -> SC2.1.1; SC2.1.2; SC2.1.3

SC2.2.1; SC2.2.2; SC2.2.3SC2.3.1; SC2.3.2; SC2.3.3


The Concept


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The Concept Cube SM

Sub-Concept

1.1

The Concept Cube SM

Sub-Concept

1.2

Sub-Concept

1.3Highest Level of

Abstraction Level 1

Sub-Concept

2.1.1

Sub-Concept

2.3.1

Abstraction - Level 1

Abstraction Level 2

Sub-Concept

2.2.1

Sub-Concept

2.1.2

Sub-Concept

2.1.3

Sub-Concept

2.3.2

Sub-Concept

2.3.3

Sub-Concept

2.2.2

Sub-Concept

2.2.3Sub-Concept

1.3 CubeSub-Concept

1.1 Cube

Sub-Concept 1.2 Cube © 2011 Joseph J Simpson, Mary J Simpson



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Concept Cube Example, The Asset Cube

Specification

ProgramType

The Asset Cube

The System

SpProg

Action

Exposure

Eff figur

atio

n

Valu

e

Prot

ectio

n

Process

nmentProduct

Mechanism

torActor

Effect

Con

fi

The Threat

The TargetExposure Type

Pr

Environm

Requirements

Function

Architectur

Cos

t

Sced

ule

Tech

nica

l

Storage

ocessingTransmission

C s

MecVector

Event

Pre-Event

Post-Event Imm

edia

te

Nea

r-Te

rm

Long

-Ter

m

Configuration

tureProce

Integrity

Confidentiality

Availability Tech

nolo

gy

Polic

y, P

ract

ices

Hum

an F

acto

rs

ent

The System Cube

The Threat Cube

Action Effect

V l P t ti

Specification Program


y

The Target Cube[Information Assurance]

Value Protection


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Example, The Asset Cube – Level 1 Interfaces

ThreatThreat-Target

InterfaceSystem-Threat

Interface

SystemTarget

Target-SystemInterface



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Example, The Asset Cube – Level 2 Interfaces

Threat Interfaces

System Interfaces

Expo.

Exposure-Action

Effect-Exposure

Type

Type-Specification

Program-Type

EffectAction

Action-Effect

ProgramSpec.

Specification-Program

Config.

Configuration- Protection-

Protect.Value

gValue

ProtectionConfiguration

V lTarget


Value-Protection

gInterfaces


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Summary and

Questions



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Summary

ART approach facilitates reduction of cognitive complexity • Encodes typical systems engineering techniques in clearly defined

processes and patternsp p• Supports the application of computing resources to evaluate

alternative system representations• Separates system structure from system value and system semantics• Separates system structure from system value and system semantics,

& supports detailed communication of both the system organizing structural relationship, and system interface value relationships

• Connects these relationships to mathematical relations that are the• Connects these relationships to mathematical relations that are the basis for the computation and analytical portions of the cognitive complexity reduction

• Contributes to greater relative density of information transfer due to its• Contributes to greater relative density of information transfer due to its use of a formal approach to prose, mathematics, and structural graphics

E l i di ti h ART l ti t ti t h i ill


Early indications show ART evolutionary computation techniques will directly reduce computational complexity associated with the solution of complex system problems


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Discussion

• Questions?

• Comments?


Documents

Complexity Reduction A Pragmatic, Semantic Approach · 2011-10-16 · Complexity Reduction A Pragmatic, Semantic Approach Empowering Collaborative Intelligence Joseph J Simpson