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 Need a way to figure out which components are misbehaving

What is Diagnosis? Definition Goal of diagnosis Two main approaches 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

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

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

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

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

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

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)

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

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

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}

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

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/