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Model Based Reasoning and

Qualitative Reasoning

Yuhong YanNRC-IIT

Yuhong.yan@nrc.gc.ca

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Overview About what?

MBR, MBD, QR History and state of art Examples: give you first feel

What is the content? Content of this part How to study this part? Reading papers,

reference books, assignments

I reference Luca Console’s slides in the first part. If most of the content of a slide is from his original one, I label his name on the slide.

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My Expectation in this Course Formal methods Only a few main important topics

Consistent-based diagnosis Multiple fault modes Select observation points ATM Qualitative modeling and reasoning

Examples More thinking, more pleasure, less

pressure

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Begin with an example

Mult1

Mult2

Mult3

Add2

2

3

23

23

Add1 A

B

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Observation vs. Prediction

Mult1

Mult2

Mult3

Add2

2

3

23

23

Add1 A

B(12)

(12)10

12

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What’s wrong

Mult1

Mult2

Mult3

Add2

2

3

23

23

Add1 A

B(12)

(12)10

12

Diagnoses

{Add1}, {Mult1}, {Mult2, Add2}, {Mult2, Mult2}

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Model

Behavioral model of each type of component:Adder(X) not AB(X) out(X) = inp1(X) + inp2(X)Multiplier(X) not AB(X) out(X) = inp1(X) * inp2(X)...

Structural model:

Multiplier(Mult1), Multiplier(Mult2),

Multiplier(Mult3), Adder(Add1),

Adder(Add2)

out(Mult1) = inp1(Add1)

out(Mult2) = inp2(Add1) = inp1(Add2)

out(Mult3) = inp2(Add2)

Mult1

Mult2

Mult3

Add2

23

23

23

Add1 A

B

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Mult1

Mult2

Mult3

Add2

23

23

23

Add1 A

B

Prediction: A=12, B=12

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12Observation A=10, B=12

10

12

A=10 generates two conflicts:{Add1, Mult1, Mult2}{Add1, Mult1, Mult3, Add2}

conflict = set of components involved in the discrepancy; they cannot be all working properly

diagnosis = (minimal) hitting set of the conflicts;intersection between the conflicts provides single-fault diagnoses

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Diagnosis on models of structure and function

actualdevice

observedbehaviour

modelof the device

predicted behaviour

diagnosis

design textbook first principles ....

model of the structureof the device and of the (nominal) behaviourof each type ofcomponent

diagnosis = removing discrepanciesbetween the nominal predicted behaviourand the observed one

From Luca Console

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A Little Bit on History The ‘70s: heuristic approaches to

diagnosis The ‘80s

critique to the heuristic approach model-based diagnosis: the beginnings and the

basic techniques The ‘90s: state of the art The ‘00: opportunities for the future

From Luca Console

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The ‘70s: heuristic diagnosis

the ‘70s: the expert systems agediagnosis is one of the main experimentation areas for expert systems a well-defined problem with definite boundaries

specific domain knowledge to be represented specific reasoning and problem solving strategies

Basic assumptions: diagnosis = heuristic process experts rely on associational knowledge of the form

symptomsfaults (diseases) knowledge derives from experience knowledge can be elicited from domain experts and

represented using suitable KR languages

From Luca Console

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Diagnostic expert systems: conceptual view

domain expert (and knowledge engineer)

K.B

K.A. interface

control K.B.

final user

user interface

work. mem.

inferenceengine

From Luca Console

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Case study 1: Mycin [Stanford Univ. 72-79]

Diagnosis and therapy of bacterial infections Knowledge base: production rules (original proposal)

if (1) the stain of the organism is gram-negative

(2) the morphology of the organisms is coccus(3) the growth configuration of the organism is chains

then there is a suggestive evidence (0.7)that the identity of the organisms is streptococcus

Inference strategy: backward chaining Approximate reasoning: ad-hoc heuristic approach Explanations: HOW, WHY, WHY-NOT ... Meta-rules for control from Mycin to Emycin and many other applications

From Luca Console

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Critiques to the heuristic approach

Some serious problems difficulties in acquiring and maintaining the

knowledge base experience knowledge

it is not easy to find experts who are usually not available

subjective knowledge dependent on the specific expert

it is impossible to deal with cases not considered a-priori

it is difficult to deal with multiple faults it is impossible to reuse knowledge in similar

devices or even in new versions of the same device

limited explanation capabilities

From Luca Console

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The ‘80s: model-based reasoning

New tendency (late 70s - beginning of the 80’s)experience heuristic knowledge model of the system to be diagnosed

“objective” model, not specific for diagnosis (task independent)

New approach to knowledge-based systems based on “deep knowledge” based on “first principles” second-generation expert systems “model-based”

From Luca Console

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What is model-based reasoning (MBR) an inferring process using models

abstracted from the reality of a system. MBR is the symbolic processing of an explicit representation of the internal working of a system in order to predict, simulate and explain the resultant behaviour of the system from the structure, causality, functional and behaviour of its components

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Model-based Diagnosis (MBD) A main application task for MBR MBD = finding malfunctions (faults,

diseases ...) in a system starting from a set of observations (measurements, tests, symptoms, examinations ...) and system description.

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Model-based diagnosis

Different approaches different types of models different definitions of diagnosis

predictedbehaviour

actualsystem

observedbehaviour

diagnosis

modelof the system

design textbook first principles....

• “knowledge level” view:

From Luca Console

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Two Different Evolutions

Diagnosis on causal models “process centered” approach born in medical domains, then application to

diagnosis of industrial processes and devices model: causal description of the behavior of the

system, in normal and/or faulty conditions Diagnosis on models of structure and function

“component centered” approach born in technical domains, then other

applications model: description of the structure of a device

(components and their connections) and of the function of each type of component

From Luca Console

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Diagnosis on causal models

actualsystem

observedbehaviour

modelof the system

predicted behaviour

diagnosis

design textbook first principles ....

causal modelsof the behaviour(correct and/orfaulty)

diagnosis = covering (explanation)of the observations via causal chainsoriginated by the faulty behaviour

From Luca Console

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Example

Obs1 = {engine_temp(high)}Two minimal candidate explanations E1 = { oil_cup(holed) } E2 = {radiator(holed)}

oil_cup

normal holed

oil_level

normal low

oil_loss

oil_below_car

oil_gauge

normal red

radiatornormal holed

water_levelnormal low

water_tempnormal high

engine_tempnormal high

engine_on

From Luca Console

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Example

Obs2 = {oil_gauge(red), engine_temp(high)}

One minimal candidate explanation E1 = { oil_cup(holed) }

oil_cup

normal holed

oil_level

normal low

oil_loss

oil_below_car

oil_gauge

normal red

radiatornormal holed

water_levelnormal low

water_tempnormal high

engine_tempnormal high

engine_on

From Luca Console

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Defining and computing diagnoses

Diagnosis: Given a set of observations determine a (minimal) set of faults whose

consequences cover the observations “Knowledge level”: diagnosis = abductive process

determine an explanation of the observations using the model as the domain theory

Abduction: Given a theory T and a set Obs of observations to

be explained Determine a set E such that

T E |= Obs T E consistent

Diagnosis as set covering

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Comparing abduction, deduction and induction

Deduction: major premise: All balls in the box are black minor premise: These balls are from the box conclusion: These balls are blackAbduction: rule: All balls in the box are black observation: These balls are black explanation: These balls are from the boxInduction: case: These balls are from the box observation: These balls are black hypothesized rule: All ball in the box are black

Induction: from specific cases to general rules Abduction and deduction: both from part of a specific case to other part of the case using general rules (in different ways)

A=>BA--------B

A=>B B--------Possibly A

Whenever A then B but not vice versa---------PossiblyA=>B

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Abduction-based diagnosis Originally, diagnostic systems were

abductive ones and relied on fault models AB(c) => symptom B.

They are able to give explanations of symptoms from the diagnosis: if diagnosis AB(c) is inferred by abduction, it explains (in the sense implies or entails) symptom B.

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Diagnosis on models of structure and function

Models of structure and function Generating prediction starting from the

model of the correct behaviour (and the inputs)

Analysis of the discrepancies between predicted and observed behaviour; for each predicted value that differs from the observed one: conflict = set of components involved in the

discrepancy; they cannot be all working properly generating all conflicts (actually only the minimal

ones) at least one component in each conflict must be

faulty diagnosis = (minimal) hitting set of the conflicts

From Luca Console

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Diagnosis on models of structure and function(II)

actualdevice

observedbehaviour

modelof the device

predicted behaviour

diagnosis

design textbook first principles ....

model of the structureof the device and of the (nominal) behaviourof each type ofcomponent

diagnosis = removing discrepanciesbetween the nominal predicted behaviourand the observed one

From Luca Console

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Model

Behavioral model of each type of component:Adder(X) not AB(X) out(X) = inp1(X) + inp2(X)Multiplier(X) not AB(X) out(X) = inp1(X) * inp2(X)...

Structural model:

Multiplier(Mult1), Multiplier(Mult2),

Multiplier(Mult3), Adder(Add1),

Adder(Add2)

out(Mult1) = inp1(Add1)

out(Mult2) = inp2(Add1) = inp1(Add2)

out(Mult3) = inp2(Add2)

Mult1

Mult2

Mult3

Add2

23

23

23

Add1 A

B

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Modeling Modeling is the critical aspect of model-based diagnosis Each model is an abstraction of the actual physical system

different choices and assumption in modeling different dimensions (aspects) are captured by different types

of models choosing the models depend on many factors

which pieces of information are available which are the goals of diagnosis which observations (and in which form) can be available which repair and test action can be made temporal constraints on the behavior of the device and on

the diagnostic process ....

Different dimensions in modeling

From Luca Console

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Dimensions in modeling (not exhaustive !)

component orientedprocess oriented

causal models process modelsstructuralmodels

functionalmodels

behaviouralmodels

teleologicalmodels

correctbehaviour

faultmodels

static dynamic time-varying

quantitative qualitative

discrete state change derivatives

intensional extensional

landmarksintervals

orders ofmagnitude

...

....

... ...

... ...

crisp probabilistic

(similar to comp. oriented.)

hierarchicalflat

From Luca Console

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Qualitative Model Quantitative (numeric) models: based on

mathematical equations in some cases they are derived from physical laws but usually

they are difficult to use they are not what people use to solve problems

Qualitative models abstract models they need a “new mathematics”, that is “common-

sense” forms of reasoning to solve qualitative equations closer than numeric models to the way we reason problem: being more abstract they are less accurate and

can be ambiguous

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One Example on Qualitative Model Exampel: qualitative sum

f = f1 + f2 (notice that there are ambiguous cases)

+ neg 0 posneg neg neg ??0 neg 0 pospos ?? pos pos

* neg 0 posneg pos 0 neg0 0 0 0pos neg 0 pos

Similar to define qualitative multiple

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Qualitative Modeling Capture the fundamental aspects of a

system or mechanism Suppress much of the detail Abstraction and Approximation Simulating (process)

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Qualitative Reasoning An inferring technique using qualitative

model to derive new knowledge of, and gain insight into a system

An approach used by human being’s thinking and reasoning

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Limitation of QR Ambiguous Less accuracy More compact or more volume?

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Research topics in MBD and QR Modeling:

New modeling methods Model reuse Model checking, verification

Diagnosis methods on: Hybrid system Dynamic system On-board system

New application areas: Biometrics Ecology E-business

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The ’00: Who in this area Crucial Missions: satellites, nuclear plants,

chemistry plants, space shuttle, Rockets E.g. NASA, Thales, Ontario power

Manufacturing: automobile E.g. all car makers, Bosch

Technique suppliers for the above two Academic and research institutes Other areas:

Biomedical Education Business

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Application: Business system modeling and performance analysis Causal-effect relation modeling and

reasoning Explanation on the reasons of one

performance indicator Hybrid system: both qualitative and

quantitative relation

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Application: distributed business application modeling and diagnosis B to B applications:

supply chain management; vendor matching on marketplaces; cooperative project; virtual organizations/enterprises

B to C applications: through web services distributed business process modeling:

Workflow network Business description language Communication protocol and semantic management Knowledge management (inside/outside)

Features: Dynamic environment; Distributed environment

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Workflow network

Pic from F.Laymann and D.Roller, “Workflow-based Applications”, IBM Systems Journal, Vol 36, No. 1, 1997

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Workflow-based Application

WFMS

Execution

WFMS

Execution

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Research issues How to model: design phase Features of the model

Deadlock Loop Resources sharing

Diagnosis: executing phase If the performance is abnormal, where is the

fault? Inside/outside? Recovery actions? Distributed diagnosis?

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Application: Logic in NBON Initial: logic expression to describe vendor Review: manually check false positive, false

negative Adjust: more accurate logic expression

Not a typical diagnostic problem The constraints are independent No constraint propagation, no deduction No cause-effect relation if don’t exploit business pattern Need to modify the “model”, not deduce from the model Can solve with simple algorithm

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Prepare yourself to read the proofs Deduction theorem, which is known to the

ancient GreekFor any sentences and , |= if and only if the

sentence ( =>) is valid

Reductio ad absurdum (proof by refutation, proof by contradiction)

|= if and only if the sentence (¬) is unsatisfiable