Expert Systems. A knowledge-based approach to intelligent systems. Intelligent System. Motivation. Approaches & Ingredients. Terminology.

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1 Motivation Expert Systems A knowledge-based approach to intelligent systems Intelligent System Peter Lucas Department of Information and Knowledge Systems Institute for Computing and Information Sciences University of Nijmegen, The Netherlands Machine Learning no data small datasets missing data large search space knowledge-based approach (i.e., via knowledge acquisition) Knowledge Acquisition Expert system Knowledge-based system Knowledge system Intelligent system Intelligent agent Terminology Sometimes used as synonyms, sometimes used to stress differences w.r.t.: Acquisition of knowledge (data or human expertise) Approaches & Ingredients Approach: knowledge modelling at different levels (get a grip on the knowledge): Problem-solving method (PSM): diagnostic PSM planning and scheduling PSM design and configuration PSM decision-making PSM implemented in a reasoning method Amount of expertise (expert or not) Content of system versus Architecture of system Knowledge base specified in a knowledge-representation formalism

2 Logical Approach Example: Model-based Diagnosis Knowledge base (KB) Horn clauses: x 1 x m ((A 1 A n ) B) PSMs with findings F and solution S: Deductive solution (S follows from KB and F ): KB F S real system model of structure/ obser vation pre diction observed predicted comparison and KB F. Abductive/inductive solution (S explains F ): KB S K F where K stands for contextual knowledge. Consistency-based solution (S and F are consistent): KB S F Model: representation of normal or abnormal, possibly also of the internal structure Formalisation: consistency-based diagnosis, and abductive diagnosis Consistency-based Diagnosis Normal Behaviour M 1 real system obser vation observed A 1 model of normal structure/ pre diction predicted discrepancy M 2 M 3 A 2 SYStem specification SYS = (SD, COMPS): SD (System Description): Discrepancy between predicted and observed fault (defect)! R. Reiter, A Theory of diagnosis from first principles, Artificial Intelligence, vol. 32, 57 95, J. de Kleer, A.K. Macworth, and R. Reiter, Characterising diagnoses and systems, Artificial Intelligence, vol. 52, , MUL(M 1 ), MUL(M 2 ), MUL(M 3 ), ADD(A 1 ), ADD(A 2 ) in 1 (A 1 ) = out(m 1 ), in 2 (A 1 ) = out(m 2 ) in 1 (A 2 ) = out(m 2 ), in 2 (A 2 ) = out(m 3 ) x(mul(x) in 1 (x) in 2 (x) = out(x)) x(add(x) in 1 (x) + in 2 (x) = out(x)) COMPS = {M 1, M 2, M 3, A 1, A 2 }

3 AB Predicate AB(c): component c is abnormal Abnormality Assumptions M 1 AB(c): component c is normal Example (Inverter I): M 2 A 1 A 2 1 I 0 [1] SD = { x((inv(x) AB(x)) (out(x) = in(x))), INV(I)} Input: in(i) = 1 Observed output: out(i) = 1} SD {in(i) = 1, out(i) = 1} { AB(I)} (assumption that I is normal is inconsistent) SD {in(i) = 1, out(i) = 1} {AB(I)} (assumption that I is abnormal is consistent) M 3 SYStem specification SYS = (SD, COMPS): SD (System Description): x((mul(x) Ab(x)) in 1 (x) in 2 (x) = out(x)) x((add(x) Ab(x)) in 1 (x) + in 2 (x) = out(x)) (Ab)normality assumptions D = { Ab(c) c COMPS } {Ab(c) c }, {M 1, M 2, M 3, A 1, A 2 } Which Components are Faulty? Abductive Diagnosis M 1 M 2 A 1 12 [10] observed real system obser vation observed match 2 3 M 3 A 2 12 model ofabnormal structure/ pre diction predicted Possible diagnoses (faulty componenten) : = {A 1 }, {M 1 }, {M 2, M 3 }, {A 2, M 2 }, since SD D OBS where D = { Ab(c) c COMPS } {Ab(c) c D} is always a smallest set, since = COMPS would also be a diagnosis otherwise Correspondence between predicted abnormal and observed defect! Originator: L. Console, D. Theseider Dupré and P. Torasso, A theory of diagnosis for incomplete causal models, In: IJ- CAI 89, , 1989

4 Causal Models Weak and Strong Causality Example: Causality: combination of Causes have particular Effects Strong causality: C E If C is present, then E must be present as well Logical representation: Cause 1 Cause n Effect Example: Weak causality: C α E If C is present, then E may be present as well (α: incompleteness assumption) Prediction Diagnostic Problem Diagnostic problem P = (Σ, F ), with:, with: : possible causes and incompleteness assumptions Φ: observable facts (Actually) observed facts: F, for example F = {, } R: causal model Diagnosis D? Prediction V : R V E, with E Φ (E is observable) (1) Prediction which explains F : R D F (2) but should not explain too much

5 Diagnostic Problem Don t Explain too Much Diagnostic problem P = (Σ, F ), with: (Actually) observed facts: F, for example F = {, } Examples of diagnoses: D = {, }, D = {, }, and is D = {, } a diagnosis? Observed facts: F = {, } Facts which should not be explained: C = { } Formally: D is a diagnosis, iff: (1) R D F (covering condition) (2) R D C (consistency condition) Consistency Condition Abduction: Abduction = Anticausal Reasoning Effect, Cause Effect Cause Idea: Reversal of causal relationship Observed facts: F = {, } Facts which should not be explained: C = { } Example: results in: Now: {, } R {,, } { } D = {,, } is no diagnosis Conclusion: Abduction = deduction with implication reversal

6 Cost-based Abduction Manual Construction of Bayesian Networks Express likelihood by means of a cost function: c : ( ) R often: c(d) = c({d}) d D D is a diagnosis with cost c(d), iff: (1) R D F (covering condition) (2) R D C (consistency condition) Qualitative modelling: Colonisation by Colonisation by bacterium A bacterium B Body response Body response to A to B Infection Colonisation by bacterium C Body response to C Eugene Charniak: cost function c equal to log, then 1 1 mapping cost-based abduction to Bayesian networks Fever WBC ESR People become colonised by bacteria when entering a hospital, which may give rise to infection Bayesian-network Modelling Problem Solving Qualitative causal modelling Cause Effect Quantitative interaction modelling Pr(Inf BR A, BR B, BR C ) As logic, Bayesian networks are declarative, i.e.: mathematical basis problem to be solved determined by (1) entered findings F (may include decisions); (2) given hypothesis H: Pr(H F ) (cf. KB F H) BR A BR B BR C Inf BR A t f BR B BR B t f t f BR C BR C BR C BR C Inf t f t f t f t f t f Examples: Classification and diagnosis: D = arg max H Pr(H F ) Temporal reasoning, prediction, what-if scenarios Decision-making based on decision theory MEU(D F ) = max u(x) Pr(x d, F ) d D x X π(u)

7 Conclusions Knowledge-based approach: need for handles for knowledge modelling Model-based approaches support using detailed qualitative models Logic can be replaced by set-theoretical or algebraic methods Interesting relationships between probabilistic reasoning and qualitative reasoning in model-based systems (e.g., cost-based abduction)

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