Consistency-based diagnosis

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Consistency-based diagnosis. 1 Introduction 2 Diagnosis as constrain propagation plus register of dependencies 3 General Diagnostic En g ine:GDE 4 A theory of diagnosis from first principles 5 CBD without on-line dependency-recording: the possible conflict approach - PowerPoint PPT Presentation

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Consistency-based diagnosis

1 Introduction2 Diagnosis as constrain propagation plus register of dependencies3 General Diagnostic Engine:GDE4 A theory of diagnosis from first principles 5 CBD without on-line dependency-recording: the possible conflict approach6 Current research areas and open problems

Knowledge-BasedKnowledge-BasedSytemsSytems

component orientedcomponent oriented process orientedprocess oriented

causal modelscausal models process modelsprocess modelsfunctionalfunctionalmodelsmodels

behaviouralbehaviouralmodelsmodels

teleologicalteleologicalmodelsmodels

correctcorrectbehaviourbehaviour

faultfaultmodelsmodels

staticstatic dynamicdynamic time-time-varyingvarying

quantitativequantitative qualitativequalitative

discrete statediscrete state changechange

derivativesderivatives

intensionalintensionalextensionalextensional

landmarkslandmarksintervalsintervals orders oforders of

magnitudemagnitude......

.….…

...... ......

......

crispcrisp probabilisticprobabilistic

(similar to comp. oriented.)(similar to comp. oriented.)

hierarchicalhierarchicalflatflat

.….…

Model-based ReasoningModel-based Reasoning

structuralstructuralmodelsmodels

Case-BasedCase-BasedReasoningReasoning

Machine LearningMachine Learning

Automated DiagnosisAutomated Diagnosis

Application fieldsApplication fields

ProcessesProcesses MedicineMedicine DevicesDevices Software…Software…

Introduction

GDE 3

Control Theory / Engineering (FDI community) Robuts Fault Detection and Isolation (Global) Analytical Models, mainly Generation and Analysis of Residuals (discrepancy) Most commonly used techniques

State-observers Parity-equations (Analytical Redundancy Relations) Parameter Identification (or Estimation)

Artificial Inteligence (DX community) Fault Isolation and Identification

(assumption: robust fault detection is available) Qualitative Models (causal, constraints, semi-qualitative, etc.) Conflict detection and candidate (diagnosis) generation Diagnosis based on structure and behaviour

Consistency-based diagnosis Abductive diagnosis Consistency-based Diagnosis with fault models

BRIDGE (integration of DX and FDI)

Model-based diagnosis approaches

GDE 4

Historical background Second generation Expert Systems (Davis,

1982-84) First works in USA, late 70s – early 80s (@

MIT, Stanford Univ.) Solid theoretical theory (Reiter, 1987) Early results:

mid/late-80s: static systems late 80s, early 90s: dynamic systems late 90s (mature) large systems

Consistency Based DiagnosisIntroduction

GDE 5

Model-based diagnosis fundamental

RealSystem

ObservedBehaviour

Diagnosis

Discrepancy(symptom)

BehaviourModel

PredictedBehaviour

GDE 6

Consistency Based DiagnosisIntroduction

Main Model Based Diagnosis framework from DX community

Component oriented (ontology) May be extended to processes / constraints

Knowledge: structural + behavioural (local) models models of components

Only models of correct behaviour

GDE 7

Basic Assumptions (de Kleer 03)

Physical system Set of interconnected components Known desired function Design achieves function System is correct instance of design

All malfunctions caused by faulty component(s) Behavioural information

Only indirect evidence

GDE 8

Behavioural information: Behavioural models

Components are in some physical condition e.g. a wire

Different physical conditions result in different behaviours

Condition 1 Condition 2 Condition 3

v 0 + -

i 0 + -

Behaviour 1

v 0 + -

i 0 0 0

Behaviour 2

v 0 + + - -

i 0 0 + 0 -

Behaviour 3

GDE 9

Behavioural information: Ruling out behaviours

We cannot verify the presence of behaviours, but we can falsify them

After observing

We cannot infer behaviour 2, but we can reject behaviour 1

v 0 + -

i 0 0 0

GDE 10

Consistency Based Diagnosis Intuition

Search for the model that is “compliant” with the observations

RealSystem

ObservedBehaviour

Diagnosis

Discrepancy

BehaviourModel

PredictedBehaviour

GDE 11

General Diagnostic Engine

GDE, de Kleer and Williams, 87 First model based computational system

for multiple faults Main computational paradigm

Still in use! Still a reference to compare any model-

based proposal on DX community

GDE 12

A classic expository example:the polybox (de Kleer 87, 03)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

GDE 13

Model based approach to diagnosis

RealSystem

ObservedBehaviour

Diagnosis

Discrepancy

Model

PredictedBehaviour

Textbooks, design, first principles

GDE 14

Observed Behaviour

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

F[10]

[12]

GDE 15

Model based approach to diagnosis

RealSystem

ObservedBehaviour

Diagnosis

Discrepancy

Model

PredictedBehaviour

Textbooks, design, first principles

GDE 16

Local propagation (I)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

GDE 17

Local propagation (II)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

GDE 18

Local propagation (III)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F12

GDE 19

Local propagation (IV)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F12

6

GDE 20

Local propagation (V)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F12

6

12

GDE 21

Predicted Behaviour

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F12

6

12

GDE 22

Model based approach to diagnosis

RealSystem

ObservedBehaviour

Diagnosis

Discrepancy

Model

PredictedBehaviour

Textbooks, design, first principles

GDE 23

Candidates

Detect Symptoms: F=12 and F=10 Generate Candidates: {M1}, {A1}, {M2, S2},

{M2, M3}

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F[10]

6

[12]

12

12

GDE 24

Diagnosis for the polybox

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

4

6

F[10]

6

[12]

12

12

GDE 25

Diagnosis for the polybox

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F[10]

6

[12]

12

10

GDE 26

Diagnosis for the polybox

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

4

F[10]

6

[12]

12

12

GDE 27

Diagnosis for the polybox

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

4

F10

8

[12]

12

12

GDE 28

How GDE works?

1. Detecting every SYMPTOMPrediction: propagating on every direction (even

non causal!)

2. Identifying CONFLICTS3. Generating CANDIDATES

GDE 29

Prediction - Requirements

Modeling Structure Modeling component behaviour Predict overall behaviour

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F12

6

12

GDE 30

Modelling Structure - Requirements

Determine the structural elements and interconections Which entities can be the origin of

malfunction? Which parts can be replaced? Which variables can be observed? Reflect aspects and levels of (diagnostic)

reasoning about the device behaviour

GDE 31

Component-Oriented Modelling: Components and Connections

Systems: components linked by connections via terminals Components: Normally physical objects

Resistors, diodes, voltage sources, tanks, valves Terminals: unique comunication link Connections:ideal connections (but may be

modelled as components) No resistance wires, loadless pipes...

Possible faults: defect components, broken connection

GDE 32

Modelling Behaviour -Requirements

Describe behaviour of the structural elements: Locality

Goal: detecting discrepancies Consider aspecs like

Generality: which kind of devices are to be diagnosed?

Robustness: which type of failure are to be detected Reflect the diagnostic reasonig process (e.g.

simplifications) Which kind of information is (easily) available

(e. g. qualitative information)

GDE 33

Local behaviour models

Constrains / relations among Input/Output variables Internal parameters

Various directions No implicit reference to or implicit assumptions

about context (existence or state of other components)

Locality Necessary for diagnosis: different context because

something is broken; otherwise implicit hypothesys must be revised

Reusability: model library, compositionality

GDE 34

Local behaviour model - Example

Or-gate Variables: in1, in2,out Domaindom(in1)=dom(in2)=dom(out)={0,1} Relation{{0,0,0}, {1,0,1}, {0,1,1}, {1,1,1}} dom(in1) dom(in2) dom(out)

Inferences in1 = 1 out = 1 in2 = 1 out = 1 in1=0 in2=0 out = 1

out=0 in1=0 in2=0 out=1 in1=0 in2=1 out=1 in2=0 in1=1

causal direction

non causal direction

GDE 35

Behaviour model of a valve

Relation: f = k A Implicit assumption: pump is on and ok

Relation: IF on(B) and ok(B) THEN f= k A Implicit assumption: a pump exists and is connected as in the

diagram Better: f = k’ (p1 – p2) A

Principle: no function in structure

B

A f

p1 p2

GDE 36

Abstract model

Domain for each variable, vardom(var) = {OK, BAD, ?}

Model for each correct component, CIF for all input-variables, vari of C, vari = OK

THEN for each output-variable, varo of C, varo = OK To avoid masking of faults by correct components

IF there exists an input-variable, vari of C, vari = BAD

THEN for each output-variable, varo of C, varo = BAD

M1

M2

M3

A1

A2

F

G

A

B

D

E

C

F

GDE 37

Prediction - Principles

Infer the behaviour of the entire device from Observations Component models Structural description

Preserve dependencies on component models

Propagate the effects of local models along the interaction paths (connections)

Propagate not only in the causal direction

GDE 38

PropagationCausal direction (I)

[A]=3 [C]=2 X=6 (M1)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

GDE 39

PropagationCausal direction (II)

[B]=2 [D]=3 Y=6 (M2)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

GDE 40

PropagationCausal direction (III)

X=6 Y=6 F=12 (A1)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F12

GDE 41

Propagation“Backward” direction (II)

[F]=10 X=6 Y=4 (A1)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

4

F[10]

GDE 42

Candidate Generation

Detecting SYMPTOMS (DISCREPANCIES)

Identifying (minimal) CONFLICTS

Generating (minimal) CANDIDATES

GDE 43

Symptoms

Symptoms are contradictions that indicate an inconsistency between observations and correct behaviour

But other potential sources of contradictions Imprecise measurements Bugs in the model Bugs in propagation

RealSystem

ObservedBehaviour

Diagnosis

Discrepancy

Model

PredictedBehaviour

GDE 44

Symptoms Detection

Symptoms occurs as contradictory values for one variable

Predicted plus observed Predicted following two different paths

Discrete Variables Static x=val1 x=val2 val1 val2 Dynamic x=(val1, t1) x=(val2, t2) val1 val2 (t1 t2)

Continuous Variables

Quantitatives (static): Intervals: x=i1 x=i2 (i1 i2) Values: x=val1 x=val2 val1 val2 Relations: xval1 xval2

Qualitatives: distance,distance >Threshold

GDE 45

Some symptoms for the polybox (I)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F12

[10]

[12]

GDE 46

Some symptoms for the polybox (II)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

4

F[10]

[12]6

GDE 47

Some symptoms for the polybox (III)

M3

A1M1

M2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

4

F

10

6

[10]

[12]

X F6 FX

M2

A2

Y

ZG

6

GDE 48

Some symptoms for the polybox (IV)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

F[10]

[12]

12

10

6

6

6

4

4

8

GDE 49

Identify conflicts

Conflict (informal):set of correctness assumtions underlying discrepancies

Polybox (minimal) conflicts F=[10] F=12 {M1, M2, A1}, {M1, M3, A1, A2} X=6 X=4 {M1, M2, A1}, {M1, M3, A1, A2} Y=6 Y=4 {M1, M2, A1}, {M1, M3, A1, A2} Z=6 Z=8 {M1, M3, A1, A2} G=[12] G=10 {M1, M3, A1, A2}

By definition,any superset of a conflic set is a conflict {M1, M2, A1} {M1, M2, A1, A2} {M1,M2, M3, A1, A2}

Minimal conflict: conflict no proper subset of which is a conflict It is essential to represent the conflicts through the set of

minimal conflicts (to avoid combinatorial explosion)

GDE 50

Conflicts latice

[M1, M2, M3, A1, A2]

[M1, M2, M3, A1] [M1, M2, M3, A2] [M1, M2, A1, A2] [M1, M3, A1, A2] [M2, M3, A1, A2]

[M1, M2, M3][M1, M2, A1] [M1, M3, A1] [M2, M3 A1][M1, M3, A2][M1, M2, A2] [M1, A1, A2] [M2, A1, A2][M2, M3, A2] [ M3, A1, A2]

[M2, M3][M1, M3][M1, M2] [M2, A1][M1, A1] [ A1, A2][M1, A2] [ M3, A1] [ M3, A2][M2, A2]

[M1]

[ ]

[A2][A1][M3][M2]

GDE 51

Conflicts generation with ATMS

The problem solver performs inferences The ATMS records the dependencies between inferences

Introduce observations as facts Support each local propagation with a correcteness

assumption for the component Label of a node:(minimal) environments that entails the

prediction Records components that support prediction Avoids recomputation

Symptoms: produce NOGOODS

NOGOODS are the MINIMAL CONFLICTS

GDE 52

Conflicts generation, detailed model, first minimal conflict (I)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

{{M1}}

GDE 53

Conflicts generation, detailed model, first minimal conflict (II)

{{M1}}

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6{{M2}}

GDE 54

Conflicts generation, detailed model, first minimal conflict (III)

{{M1}}

{{M2}}

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F12

{{M1, M2, A1}}

GDE 55

Conflicts generation, detailed model, first minimal conflict (IV)

{{M1}}

{{M2}}

{{M1, M2, A1}}

F=[10] F=12 {M1, M2, A1}

M2

M1A1

M3A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F[10]

6

12X F6 F

6

X

{ }

GDE 56

Conflicts generation, detailed model, second minimal conflict (I)

M3

A1M1

M2

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F

6

12

X F6 F

6

X

M2

A2

Y

ZG

6

[12]

{{M1, M3, A1, A2}}

GDE 57

Conflicts generation, detailed model, second minimal conflict (II)

F=[10] F=12 {M1, M3, A1, A2}

M3

A1M1

M2

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

6

6

F[10]

6

12X F6 F

6

X

M2

A2

Y

ZG

6

[12]

{{M1, M3, A1, A2}}

{ }

GDE 58

Conflicts generation, abstract model, first minimal conflict (I)

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[ok]

[ok]

[ok]

[ok]

[ok]

ok

{{M1}}

GDE 59

Conflicts generation, abstract model, first minimal conflict (II)

[ok]

[ok]

[ok]

[ok]

[ok]

{{M1}}

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

ok

ok{{M2}}

GDE 60

Conflicts generation, abstract model, first minimal conflict (III)

[ok]

[ok]

[ok]

[ok]

[ok]

{{M1}}

{{M2}}

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

ok

ok

Fok

{{M1, M2, A1}}

GDE 61

Conflicts generation, abstract model, first minimal conflict (IV)

[ok]

[ok]

[ok]

[ok]

[ok]

{{M1}}

{{M2}}

{{M1, M2, A1}}

M2

M1A1

M3A2

X

Y

Z

F

G

A

B

D

E

C

ok

ok

F[bad]

6

okX FFX

{ }

F=[bad] F=ok {M1, M2, A1}

GDE 62

Conflicts generation, abstract model, second minimal conflict (I)

[ok]

[ok]

[ok]

[ok]

[ok]

{{M1}}

{{M1, A1}}M2

M1A1

M3A2

X

Y

Z

F

G

A

B

D

E

C

ok F[bad]

6

X FFX

bad

bad

{{M1, A1, A2}}

GDE 63

Conflicts generation, abstract model, second minimal conflict (II)

[ok]

[ok]

[ok]

[ok]

[ok]

{{M1}}

{{M1, A1}}M2

M1A1

M3A2

X

Y

Z

F

G

A

B

D

E

C

ok F[bad]

6

X FFX

bad

[ok]

{{M1, A1, A2}}

bad{ }

G=[bad] G=ok {M1, A1, A2}

GDE 64

Candidates

Candidate: hypothesis of how the device differs from model

Represented as a set of assumptions Assumptions included: false Assumptions not included: false

Diagnosis: identify every candidate consistent with observations

Candidate example: {M2, A2}

Meaning: M2, A2 are faultyM1, M3, A1 are correct

GDE 65

Candidate generation

Each candidate has to account for all conflicts Each candidate has to retract at least one

correctness assumption out of each conflict Construct candidates as Hitting Set of (minimal)

conflicts Ca candidate, Ci conflict, Ca Ci Ci Ca, Ca i Ci

Each superset of a candidate is also a candidate:Minimal candidates:minimal hitting set of minimal conflicts

GDE 66

Candidate generation example

Minimal conflicts

Minimal candidates

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[3]

[2]

[2]

[3]

[3]

F[10]

[12]

12

10

6

6

6

4

4

8

{ M1, A1, M2 }

{ M1, A1, M3, A2 }

{M1}, {A1}, {M2, M3}, {M2, A2}

GDE 67

Conflict Directed Search

1. Let M be the set of putative minimal diagnoses, initially containing only [].

2. If no more minimal conflicts, the M is the set of minimal diagnoses

3. For every new minimal conflict C

1. For every diagnosis D in M

1. If D identifies one component in C as faulted, do nothing. 2. Else remove D from M and add to M all D’ which have some

component of C faulted.

2. Remove duplicates from M

4. Go to 2.

Candidate latice: parsimonious representation (I)

[M1, M2, M3, A1, A2]

[M1, M2, M3, A1] [M1, M2, M3, A2] [M1, M2, A1, A2] [M1, M3, A1, A2] [M2, M3, A1, A2]

[M1, M2, M3] [M1, M2, A1] [M1, M3, A1] [M2, M3 A1][M1, M3, A2][M1, M2, A2] [M1, A1, A2] [M2, A1, A2][M2, M3, A2] [ M3, A1, A2]

[M2, M3][M1, M3][M1, M2] [M2, A1][M1, A1] [ A1, A2][M1, A2] [ M3, A1] [ M3, A2][M2, A2]

[M1]

[ ]

[A2][A1][M3][M2]

C1:[M1, M2, A1]

Candidate latice: parsimonious representation (II)

[M1, M2, M3, A1, A2]

[M1, M2, M3, A1] [M1, M2, M3, A2] [M1, M2, A1, A2] [M1, M3, A1, A2] [M2, M3, A1, A2]

[M1, M2, M3] [M1, M2, A1] [M1, M3, A1] [M2, M3 A1][M1, M3, A2][M1, M2, A2] [M1, A1, A2] [M2, A1, A2][M2, M3, A2] [ M3, A1, A2]

[M2, M3][M1, M3][M1, M2] [M2, A1][M1, A1] [ A1, A2][M1, A2] [ M3, A1] [ M3, A2][M2, A2]

[M1]

[ ]

[A2][A1][M3][M2]

C1:[M1, M2, A1]

C2 :[M1, M3, A1, A2]

Candidate latice: parsimonious representation (III)

[M1, M2, M3, A1, A2]

[M1, M2, M3, A1] [M1, M2, M3, A2] [M1, M2, A1, A2] [M1, M3, A1, A2] [M2, M3, A1, A2]

[M1, M2, M3] [M1, M2, A1] [M1, M3, A1] [M2, M3 A1][M1, M3, A2][M1, M2, A2] [M1, A1, A2] [M2, A1, A2][M2, M3, A2] [ M3, A1, A2]

[M2, M3][M1, M3][M1, M2] [M2, A1][M1, A1] [ A1, A2][M1, A2] [ M3, A1] [ M3, A2][M2, A2]

[M1]

[ ]

[A2][A1][M3][M2]

C1:[M1, M2, A1]

C2 :[M1, M3, A1, A2]

Candidate latice: parsimonious representation (IV)

[M1, M2, M3, A1, A2]

[M1, M2, M3, A1] [M1, M2, M3, A2] [M1, M2, A1, A2] [M1, M3, A1, A2] [M2, M3, A1, A2]

[M1, M2, M3] [M1, M2, A1] [M1, M3, A1] [M2, M3 A1][M1, M3, A2][M1, M2, A2] [M1, A1, A2] [M2, A1, A2][M2, M3, A2] [ M3, A1, A2]

[M2, M3][M1, M3][M1, M2] [M2, A1][M1, A1] [ A1, A2][M1, A2] [ M3, A1] [ M3, A2][M2, A2]

[M1]

[ ]

[A2][A1][M3][M2]

C1:[M1, M2, A1]

C2 :[M1, M3, A1, A2]

C1 & C2

GDE 72

Candidate generation abstract model

Minimal conflicts

Minimal candidates

M1

M2

M3

A1

A2

X

Y

Z

F

G

A

B

D

E

C

[ok]

[ok]

[ok]

[ok]

[ok]

F[bad]

[ok]

ok

bad

ok

ok

bad

{ M1, A1, M2 }

{ M1, A1, A2 }

{M1}, {A1}, {M2, A2}

GDE 73

Candidate generation:problems

Undetected symptoms Insufficient observations

Imprecise Not available

Insufficient models Quantitative accuracy Qualitative ambiguity

Limitations of conflict generation Inherent in the prediction algorithm Inherent in the model

GDE 74

Conflict generation: limitations due to local propagation

Conflicts: {I, X1, X2, X3} Candidates: {I }, {X1}, {X2}, {X3}

{I} should not be a candidate {X1, X2, X3} ought to be a conflict

A

B

C

F

[1]

[1]

[1]

[1]I

X1

X2

X3

GDE 75

Conflict generation: limitations due to the model (I)

Observations: B1, B2 OFF,B3 ON Minimal conflicts

{S, W1, B1, W2}, {S, W1, W3, B2, W4, W2}, {B3, W5, B2, W6}, {B3,W5, W3, B1, W4, W6}

¡22 minimal candidates! {B1, B2}, {S, B3}, {W1, W5} (?)

B-1S

B-2 B-3

W-1

W-2

W-3

W-4

W-5

W-6

GDE 76

Conflict generation: limitations due to the model (II)

Observations: B1, B2 OFF,B3 ON Candidate {S, B3}

Logically possible Phisically impossible

Due to the absence of information about faulty behaviour (only models of correct behaviour)

B-1S

B-2 B-3

W-1

W-2

W-3

W-4

W-5

W-6

GDE 77