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Consistency-Based Diagnosis Hal Lindsey CSCE 580

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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

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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

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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

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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

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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

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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

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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

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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)

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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

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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

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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}

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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

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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/ http://www-formal.stanford.edu/leora/kcourse/

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