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 PresentationTRANSCRIPT
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