Model Based Reasoning and Qualitative Reasoning Yuhong Yan

Model Based Reasoning and Qualitative Reasoning Yuhong Yan NRC-IIT Yuhong. yan@nrc. gc. ca 1

Overview p About what? n n n MBR, MBD, QR History and state of art Examples: give you first feel What is the content? Content of this part p How to study this part? Reading papers, reference books, assignments p 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 2 slide.

My Expectation in this Course Formal methods p Only a few main important topics p n n n Consistent-based diagnosis Multiple fault modes Select observation points ATM Qualitative modeling and reasoning Examples p More thinking, more pleasure, less pressure p 3

Begin with an example 2 3 2 3 4 Mult 1 Add 1 A Add 2 B Mult 2 Mult 3

Observation vs. Prediction 2 3 Mult 1 10 (12) Add 1 2 3 Mult 2 12 (12) Add 2 2 3 5 Mult 3 A B

What’s wrong 2 3 Mult 1 10 (12) Add 1 2 3 Mult 2 12 (12) Add 2 2 3 A B Mult 3 Diagnoses 6 {Add 1}, {Mult 2, Add 2}, {Mult 2, Mult 2}

Model 2 3 2 3 Mult 1 Add 1 Mult 2 Add 2 Structural model: Multiplier(Mult 1), Multiplier(Mult 2), Multiplier(Mult 3), Adder(Add 1), Adder(Add 2) A out(Mult 1) = inp 1(Add 1) out(Mult 2) = inp 2(Add 1) = inp 1(Add 2) B out(Mult 3) = inp 2(Add 2) Mult 3 Behavioral model of each type of component: 7 Adder(X) not AB(X) out(X) = inp 1(X) + inp 2(X) Multiplier(X) not AB(X) out(X) = inp 1(X) * inp 2(X). . .

Prediction: A=12, B=12 2 3 Mult 1 Add 1 2 3 Mult 2 Add 2 2 3 Mult 3 12 A 10 12 B Observation A=10, B=12 A=10 generates two conflicts: {Add 1, Mult 2} {Add 1, Mult 3, Add 2} 12 conflict = set of components involved in the discrepancy; they cannot be all working properly 8 diagnosis = (minimal) hitting set of the conflicts; intersection between the conflicts provides singlefault diagnoses

Diagnosis on models of structure and function design textbook first principles. . actual device observed behaviour model of the device predicted behaviour diagnosis model of the structure of the device and of the (nominal) behaviour of each type of component diagnosis = removing discrepancies between the nominal predicted behaviour and the observed one 9 From Luca Console

A Little Bit on History The ‘ 70 s: heuristic approaches to diagnosis p The ‘ 80 s p n n critique to the heuristic approach model-based diagnosis: the beginnings and the basic techniques The ‘ 90 s: state of the art p The ‘ 00: opportunities for the future p 10 From Luca Console

The ‘ 70 s: heuristic diagnosis p the ‘ 70 s: the expert systems age diagnosis is one of the main experimentation areas for expert systems n p Basic assumptions: diagnosis = heuristic process n n n 11 a well-defined problem with definite boundaries p specific domain knowledge to be represented p specific reasoning and problem solving strategies 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 domain expert (and knowledge engineer) K. A. interface K. B control K. B. inference engine work. mem. user interface final user 12 From Luca Console

Case study 1: Mycin [Stanford Univ. 72 -79] p p 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 p p p 13 Inference strategy: backward chaining Approximate reasoning: ad-hoc heuristic approach Explanations: HOW, WHY-NOT. . . Meta-rules for control from Mycin to Emycin and many other applications From Luca Console

Critiques to the heuristic approach p Some serious problems n n n 14 difficulties in acquiring and maintaining the knowledge base experience knowledge p it is not easy to find experts who are usually not available p subjective knowledge dependent on the specific expert p it is impossible to deal with cases not considered a -priori p it is difficult to deal with multiple faults p it is impossible to reuse knowledge in similar devices or even in new versions of the same device limited explanation capabilities From Luca Console

The ‘ 80 s: model-based reasoning p p p New tendency (late 70 s - 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 n n 15 based on “deep knowledge” based on “first principles” second-generation expert systems “model-based” From Luca Console

What is model-based reasoning (MBR) p 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 p MBD = finding malfunctions (faults, diseases. . . ) in a system starting from a set of observations (measurements, tests, symptoms, examinations. . . ) and system description. p 17

Model-based diagnosis • “knowledge level” view: design textbook first principles. . actual system model of the system observed behaviour predicted behaviour diagnosis p Different approaches n 18 n different types of models different definitions of diagnosis From Luca Console

Two Different Evolutions p p 19 Diagnosis on causal models n “process centered” approach n born in medical domains, then application to diagnosis of industrial processes and devices n model: causal description of the behavior of the system, in normal and/or faulty conditions Diagnosis on models of structure and function n “component centered” approach n born in technical domains, then other applications n 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 design textbook first principles. . actual system model of the system observed behaviour predicted behaviour diagnosis causal models of the behaviour (correct and/or faulty) diagnosis = covering (explanation) of the observations via causal chains originated by the faulty behaviour 20 From Luca Console

Example oil_cup normal holed oil_loss radiator normal holed oil_level water_level normal low oil_below_car normal low oil_gauge normal red p Obs 1 = {engine_temp(high)} Two minimal candidate explanations n E 1 = { oil_cup(holed) } n E 2 = {radiator(holed)} water_temp normal high engine_on normal high engine_temp 21 From Luca Console

Example radiator p Obs 2 = {oil_gauge(red), engine_temp(high)} normal holed oil_loss normal holed One minimal candidate explanation oil_level water_level n E 1 = { oil_cup(holed) } normal low oil_below_car normal low oil_cup oil_gauge normal red water_temp normal high engine_on normal high engine_temp 22 From Luca Console

Defining and computing diagnoses p Diagnosis: n n p “Knowledge level”: diagnosis = abductive process n n n 23 Given a set of observations determine a (minimal) set of faults whose consequences cover the observations determine an explanation of the observations using the model as the domain theory Abduction: p Given a theory T and a set Obs of observations to be explained p 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 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 A=>B A -------B A=>B B -------Possibly A Whenever A then B but not vice versa ----Possibly A=>B

Abduction-based diagnosis Originally, diagnostic systems were abductive ones and relied on fault models AB(c) => symptom B. p 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. p 25

Diagnosis on models of structure and function p p p 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: n n 26 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) design textbook first principles. . actual device observed behaviour model of the device predicted behaviour diagnosis model of the structure of the device and of the (nominal) behaviour of each type of component diagnosis = removing discrepancies between the nominal predicted behaviour and the observed one 27 From Luca Console

Model 2 3 2 3 Mult 1 Add 1 Mult 2 Add 2 Structural model: Multiplier(Mult 1), Multiplier(Mult 2), Multiplier(Mult 3), Adder(Add 1), Adder(Add 2) A out(Mult 1) = inp 1(Add 1) out(Mult 2) = inp 2(Add 1) = inp 1(Add 2) B out(Mult 3) = inp 2(Add 2) Mult 3 Behavioral model of each type of component: 28 Adder(X) not AB(X) out(X) = inp 1(X) + inp 2(X) Multiplier(X) not AB(X) out(X) = inp 1(X) * inp 2(X). . .

Modeling p p Modeling is the critical aspect of model-based diagnosis Each model is an abstraction of the actual physical system n n n p different choices and assumption in modeling different dimensions (aspects) are captured by different types of models choosing the models depend on many factors p which pieces of information are available p which are the goals of diagnosis p which observations (and in which form) can be available p which repair and test action can be made p temporal constraints on the behavior of the device and on the diagnostic process p. . Different dimensions in modeling 29 From Luca Console

Dimensions in modeling (not exhaustive !) process oriented component oriented structural models . . . functional behavioural models causal models process models teleological (similar to comp. oriented. ). . . models . . . correct behaviour crisp fault models probabilistic . . intensional extensional static dynamic discrete state change timequantitative qualitative varying derivatives landmarks intervals orders of magnitude flat hierarchical . . . 30 From Luca Console

Qualitative Model p Quantitative (numeric) models: based on mathematical equations n n in some cases they are derived from physical laws but usually p p p they are difficult to use they are not what people use to solve problems Qualitative models n n 31 abstract models they need a “new mathematics”, that is “commonsense” 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

One Example on Qualitative Model p p Exampel: qualitative sum f = f 1 + f 2 (notice that there ambiguous cases) + neg 0 pos p neg neg ? ? 0 neg 0 pos ? ? pos Similar to define qualitative multiple * neg 0 pos 32 neg pos 0 neg 0 0 pos neg 0 pos

Qualitative Modeling Capture the fundamental aspects of a system or mechanism p Suppress much of the detail p Abstraction and Approximation p Simulating (process) p 33

Qualitative Reasoning An inferring technique using qualitative model to derive new knowledge of, and gain insight into a system p An approach used by human being’s thinking and reasoning p 34

Limitation of QR Ambiguous p Less accuracy p More compact or more volume? p 35

Research topics in MBD and QR p Modeling: n n n p Diagnosis methods on: n n n p New modeling methods Model reuse Model checking, verification Hybrid system Dynamic system On-board system New application areas: n n n 36 Biometrics Ecology E-business

The ’ 00: Who in this area p Crucial Missions: satellites, nuclear plants, chemistry plants, space shuttle, Rockets n p Manufacturing: automobile n p p p E. g. NASA, Thales, Ontario power E. g. all car makers, Bosch Technique suppliers for the above two Academic and research institutes Other areas: n n n 37 Biomedical Education Business

Application: Business system modeling and performance analysis Causal-effect relation modeling and reasoning p Explanation on the reasons of one performance indicator p Hybrid system: both qualitative and quantitative relation p 38

Application: distributed business application modeling and diagnosis p B to B applications: n n p p B to C applications: through web services distributed business process modeling: n n p supply chain management; vendor matching on marketplaces; cooperative project; virtual organizations/enterprises Workflow network Business description language Communication protocol and semantic management Knowledge management (inside/outside) Features: n n 39 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 41

Research issues How to model: design phase p Features of the model p n n n p Deadlock Loop Resources sharing Diagnosis: executing phase n n 42 If the performance is abnormal, where is the fault? Inside/outside? Recovery actions? Distributed diagnosis?

Application: Logic in NBON p p p Initial: logic expression to describe vendor Review: manually check false positive, false negative Adjust: more accurate logic expression Not a typical diagnostic problem n n n 43 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

Prepare yourself to read the proofs p Deduction theorem, which is known to the ancient Greek For any sentences and , |= if and only if the sentence ( => ) is valid p Reductio ad absurdum (proof by refutation, proof by contradiction) |= if and only if the sentence ( ¬ ) is unsatisfiable 44