Transcript Model Based Reasoning and Qualitative Reasoning Yuhong Yan NRC-IIT
Model Based Reasoning and Qualitative Reasoning
Yuhong Yan NRC-IIT [email protected]
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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.
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 3
Begin with an example
2 3 Mult1 2 3 Mult2 2 3 Mult3 Add1 Add2 A B 4
Observation vs. Prediction
2 3 Mult1 2 3 Mult2 2 3 Mult3 Add1 Add2
10 (12)
A
12 (12)
B 5
What’s wrong
2 3 Mult1 2 3 Mult2 2 3 Mult3 Add1 Add2
10 (12)
A
12 (12)
B Diagnoses {Add1}, {Mult1}, {Mult2, Add2}, {Mult2, Mult2} 6
Model
7 2 3 Mult1 2 3 Mult2 2 3 Mult3 Add1 Add2 A Structural model: Multiplier(Mult1), Multiplier(Mult2), Multiplier(Mult3), Adder(Add1), Adder(Add2) out(Mult1) = inp1(Add1) out(Mult2) = inp2(Add1) = inp1(Add2) B out(Mult3) = inp2(Add2) Behavioral model of each type of component: Adder(X) inp2(X) not AB(X) Multiplier(X) inp2(X) out(X) = inp1(X) + not AB(X) out(X) = inp1(X) * ...
Prediction: A=12, B=12 2 3 2 3 Mult1 Mult2 Add1 Add2
12
A
10 12
B
12
Observation A=10, B=12 A=10 generates two conflicts: {Add1, Mult1, Mult2} {Add1, Mult1, Mult3, Add2} 2 3 Mult3 8 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
Diagnosis on models of structure and function
actual device design textbook first principles ....
model of the device observed behaviour diagnosis predicted behaviour
diagnosis = removing discrepancies between the nominal predicted behaviour and the observed one
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model of the structure of the device and of the (nominal) behaviour of each type of component
From Luca Console
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 10 From Luca Console
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The ‘70s: heuristic diagnosis
the ‘70s: the expert systems age diagnosis 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 symptoms faults (diseases) knowledge derives from experience knowledge can be elicited from domain experts and represented using suitable KR languages From Luca Console
Diagnostic expert systems: conceptual view
12 domain expert (and knowledge engineer) K.A. interface K.B
control K.B
.
inference engine work. mem.
user interface final user From Luca Console
Case study 1: Mycin [Stanford Univ. 72-79]
13 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
Critiques to the heuristic approach
14 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
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 16
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
• “knowledge level” view: design textbook first principles....
actual system
model of the system
observed behaviour predicted behaviour 18 diagnosis Different approaches different types of models different definitions of diagnosis From Luca Console
Two Different Evolutions
19 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
Diagnosis on causal models
actual system design textbook first principles ....
model of the system observed behaviour diagnosis
diagnosis = covering (explanation) of the observations via causal chains originated by the faulty behaviour
20 predicted behaviour
causal models of the behaviour (correct and/or faulty)
From Luca Console
Example
oil_cup normal holed oil_loss oil_level normal low radiator normal holed water_level Obs1 = {engine_temp(high)} Two minimal candidate explanations E1 = { oil_cup(holed) } E2 = {radiator(holed)} oil_gauge normal red water_temp normal high normal high engine_temp engine_on 21 From Luca Console
Example
oil_cup normal holed oil_loss oil_level normal low radiator normal holed water_level Obs2 = {oil_gauge(red), engine_temp(high)} One minimal candidate explanation E1 = { oil_cup(holed) } oil_gauge normal red water_temp normal high normal high engine_temp engine_on 22 From Luca Console
Defining and computing diagnoses
23 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
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 black Abduction: rule: All balls in the box are black observation: These balls are black explanation: These balls are from the box Induction: case: These balls are from the box observation: These balls are black hypothesized rule: All ball in the box are black A=>B A ------- B A=>B B ------- Possibly A Whenever A then B but not vice versa -------- Possibly A=>B 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) 24
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. 25
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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
Diagnosis on models of structure and function(II)
actual device design textbook first principles ....
model of the device observed behaviour diagnosis predicted behaviour
diagnosis = removing discrepancies between the nominal predicted behaviour and the observed one
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model of the structure of the device and of the (nominal) behaviour of each type of component
From Luca Console
Model
28 2 3 Mult1 2 3 Mult2 2 3 Mult3 Add1 Add2 A Structural model: Multiplier(Mult1), Multiplier(Mult2), Multiplier(Mult3), Adder(Add1), Adder(Add2) out(Mult1) = inp1(Add1) out(Mult2) = inp2(Add1) = inp1(Add2) B out(Mult3) = inp2(Add2) Behavioral model of each type of component: Adder(X) inp2(X) not AB(X) Multiplier(X) inp2(X) out(X) = inp1(X) + not AB(X) out(X) = inp1(X) * ...
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 29 From Luca Console
Dimensions in modeling (not exhaustive !) process oriented component oriented structural models ...
functional models ...
behavioural models teleological models causal models (similar to comp. oriented.) ...
process models crisp probabilistic correct behaviour fault models ....
intensional extensional static dynamic discrete state 30 change time varying quantitative qualitative derivatives landmarks intervals orders of magnitude ...
flat hierarchical From Luca Console
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 31
One Example on Qualitative Model
Exampel: qualitative sum f = f1 + f2 (notice that there are ambiguous cases) + neg 0 pos neg neg neg ??
0 neg 0 pos pos ??
pos pos Similar to define qualitative multiple * neg 0 pos neg pos 0 neg 0 0 0 0 pos neg 0 pos 32
Qualitative Modeling
Capture the fundamental aspects of a system or mechanism Suppress much of the detail Abstraction and Approximation Simulating (process) 33
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 34
Limitation of QR
Ambiguous Less accuracy More compact or more volume? 35
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 36
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 37
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 38
Application: distributed business application modeling and diagnosis
39 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
Workflow network
40 Pic from F.Laymann and D.Roller, “Workflow-based Applications”, IBM Systems Journal, Vol 36, No. 1, 1997
Workflow-based Application
WFMS Execution WFMS Execution 41
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 43
Prepare yourself to read the proofs
Deduction theorem, which is known to the ancient Greek For any sentences sentence ( and , => ) is valid |= if and only if the Reductio ad absurdum (proof by refutation, proof by contradiction) |= if and only if the sentence ( ¬ ) is unsatisfiable 44