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Consistency-Based Diagnosis

Consistency-Based Diagnosis. Hal Lindsey CSCE 580. Introduction. The Idea of consistency-based diagnosis stemmed from work done by Raymon Reiter and Johan de Kleer Developed to diagnose physical devices Main idea is that when a device doesn’t work, some components will be misbehaving

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Consistency-Based Diagnosis

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  1. Consistency-Based Diagnosis Hal Lindsey CSCE 580

  2. Introduction • The Idea of consistency-based diagnosis stemmed from work done by Raymon Reiter and Johan de Kleer • Developed to diagnose physical devices • Main idea is that when a device doesn’t work, some components will be misbehaving • Need a way to figure out which components are misbehaving

  3. What is Diagnosis? • Definition • Diagnosis in artificial intelligence relates to the development of algorithms and techniques that are able to determine whether the behavior of a system is correct • Goal of diagnosis • Given a description of some system and observations about the system, be able to determine what parts of the system are malfunctioning given unexpected behavior • Two main approaches • Expert • Model-based

  4. Expert Diagnosis • Also referred to as heuristic diagnosis • Based on experience from experts of the system; Experts determine diagnostic criteria • Examples • Rules of thumb • Statistical intuitions • Past experiences • Main Drawbacks from this approach • Difficulty acquiring the expertise • Complexity of the learning • Lack of robustness • Consistency/Completeness

  5. Model-based Diagnosis • Also known as diagnosis from first principles • Construct a causal model of the system, if things go wrong try to figure out what in the model isn’t working • Flow Diagram

  6. Model-based Diagnosis (Cont.) • Benefits of this approach • More precise modeling • System formalization • Expertise not required • Reiter decided this was the best approach for diagnosis • He developed a general theoretical foundation based on first principles

  7. Problem Formulation • Formulation of system and observation • Need a general formulation to cover variety of domains • Define a domain-independent concept of a system • A system is a pair (SD, COMP) where: • (1) SD, the system description, is a set of first-order sentences • (2) COMP, the system components, is a finite set of constant

  8. System Formulation Example • The system below can be described as: • COMP = {A1, A2, X1, X2, O1} • ANDG(X) & ~AB(X) D out(x) = and(in1(x), in2(x)) , • XORG(X) & ~AB(X) D out(x) = xor(in1(x), in2(x)) , • ORG(X) & ~AB(X) D out(x) = or(in1(x), in2(x)) , • ANDG(A1), ANDG(A2) , • XORG(X1 ), XORG(X2 ), • ORG(O1) • out(X1 ) = in2(A2), • out(X1) = in1(X2), • out(A2) = in1(O1), • in1(A2) = in2(X2) , • in1(X1) = in1(A1), • in2(X1) = in2(A1), • out(A1) = in2(O1) • Plus axioms that circuit inputs are binary and of boolean algebra

  9. Observations of Systems • Real world diagnostic settings involve observations • Without observations, we have no way of determining whether something is wrong and hence whether a diagnosis is called for • An observation of a system is a finite set of first-order sentences denoted OBS • A diagnosis will comprise: • (SD,COMP,OBS)

  10. Observation Formulation Example • The following observations of the system could be observed: • in1(X1) = 1, • in2(X1) = 0, • in1(A2) = 1, • out(X2) = 1, • out(O1) = 0 • Thus, circuit is faulty • Formally, the system if faulty if SD union {~Ab(c)| c in COMP} union OBS is inconsistent

  11. Formal Diagnosis • Diagnosis is the conjecture that certain components are faulty and the rest are normal • Principle of Parsimony • Diagnosis is a conjecture that some minimal set of components are faulty • Formal diagnosis for (SD,COMP,OBS) is a minimal set D subset of COMP such that SD union OBS union {Ab(c) | c in D} union {~Ab(c)| c in COMP – D} is consistent • Turns out D is determined by COMP – D, so Diagnosis is minimal D subset of COMP such that SD union {~Ab(c)| c in COMP – D} is consistent

  12. Computing Diagnoses • Generate Diagnosis from our Previous Example: • in1(X1) = 1, • in2(X1) = 0, • in1(A2) = 1, • out(X2) = 1, • out(O1) = 0 • In this example, there are 3 possible diagnoses: • {X1}, {X2, O1}, {X2, A2}

  13. Computing Diagnoses (Cont.) • How D is computed: • Generate all subsets of COMP • Check for inconsistency • Very inefficient • More efficient: • Formalize the notion of conflict set whereby you choose D such that COMP – D is not a conflict set for (SD, COMP, OBS) • Formalize notion of hitting set • Get minimal hitting set • Tree-labeling algorithm given by Reiter

  14. References • Reiter, Raymond. A Theory of Diagnosis from First Principles. Artifical Intelligence, Vol 32, No. 1. (April 1987), pp 57-95. • Peischl & Wotawa. Model-Based Diagnosis or Reasoning from First Principles. Intelligent Systems, Vol 18, No. 3. (May/June 2003), pp 32-37. • Morgenstern, Leora. Knowledge Representation. http://www-formal.stanford.edu/leora/kcourse/

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