Knowledge Representation and ReasoningAbductionSlide 3Abduction examples (cont.)Comparing abduction, deduction, and inductionCharacteristics of abductive reasoningCharacteristics of abductive reasoning (cont.)Slide 8Sources of uncertaintyDecision making with uncertaintyBayesian reasoningOther uncertainty representationsUncertainty tradeoffsBayesian ReasoningOutlineSlide 16Slide 17Why probabilities anyway?Probability theoryProbability theory (cont.)Example: Inference from the jointExercise: Inference from the jointIndependenceExercise: IndependenceConditional independenceExercise: Conditional independenceBayes’s ruleBayesian inferenceSimple Bayesian diagnostic reasoningBayesian diagnostic reasoning IILimitations of simple Bayesian inferenceLimitations of simple Bayesian inference II1Knowledge Knowledge Representation and Representation and ReasoningReasoningChapter 10.1-10.2, 10.6CS 63CS 63Adapted from slides byTim Finin andMarie desJardins.Some material adopted from notes by Andreas Geyer-Schulz,and Chuck Dyer.2Abduction•Abduction is a reasoning process that tries to form plausible explanations for abnormal observations–Abduction is distinctly different from deduction and induction–Abduction is inherently uncertain•Uncertainty is an important issue in abductive reasoning•Some major formalisms for representing and reasoning about uncertainty–Mycin’s certainty factors (an early representative)–Probability theory (esp. Bayesian belief networks)–Dempster-Shafer theory–Fuzzy logic–Truth maintenance systems–Nonmonotonic reasoning3Abduction•Definition (Encyclopedia Britannica): reasoning that derives an explanatory hypothesis from a given set of facts–The inference result is a hypothesis that, if true, could explain the occurrence of the given facts•Examples–Dendral, an expert system to construct 3D structure of chemical compounds •Fact: mass spectrometer data of the compound and its chemical formula•KB: chemistry, esp. strength of different types of bounds•Reasoning: form a hypothetical 3D structure that satisfies the chemical formula, and that would most likely produce the given mass spectrum4–Medical diagnosis•Facts: symptoms, lab test results, and other observed findings (called manifestations)•KB: causal associations between diseases and manifestations•Reasoning: one or more diseases whose presence would causally explain the occurrence of the given manifestations–Many other reasoning processes (e.g., word sense disambiguation in natural language process, image understanding, criminal investigation) can also been seen as abductive reasoningAbduction examples (cont.)5Comparing abduction, deduction, and inductionDeduction: major premise: All balls in the box are black minor premise: These balls are from the box conclusion: These balls are blackAbduction: rule: All balls in the box are black observation: These balls are black explanation: These balls are from the boxInduction: case: These balls are from the box observation: These balls are black hypothesized rule: All ball in the box are black A => B A ---------BA => B B-------------Possibly AWhenever A then B-------------Possibly A => BDeduction reasons from causes to effectsAbduction reasons from effects to causesInduction reasons from specific cases to general rules6Characteristics of abductive reasoning•“Conclusions” are hypotheses, not theorems (may be false even if rules and facts are true) –E.g., misdiagnosis in medicine•There may be multiple plausible hypotheses–Given rules A => B and C => B, and fact B, both A and C are plausible hypotheses –Abduction is inherently uncertain–Hypotheses can be ranked by their plausibility (if it can be determined)7Characteristics of abductive reasoning (cont.)•Reasoning is often a hypothesize-and-test cycle –Hypothesize: Postulate possible hypotheses, any of which would explain the given facts (or at least most of the important facts)–Test: Test the plausibility of all or some of these hypotheses–One way to test a hypothesis H is to ask whether something that is currently unknown–but can be predicted from H–is actually true•If we also know A => D and C => E, then ask if D and E are true•If D is true and E is false, then hypothesis A becomes more plausible (support for A is increased; support for C is decreased)8Characteristics of abductive reasoning (cont.)•Reasoning is non-monotonic –That is, the plausibility of hypotheses can increase/decrease as new facts are collected –In contrast, deductive inference is monotonic: it never change a sentence’s truth value, once known–In abductive (and inductive) reasoning, some hypotheses may be discarded, and new ones formed, when new observations are made9Sources of uncertainty•Uncertain inputs–Missing data–Noisy data•Uncertain knowledge–Multiple causes lead to multiple effects–Incomplete enumeration of conditions or effects–Incomplete knowledge of causality in the domain–Probabilistic/stochastic effects•Uncertain outputs–Abduction and induction are inherently uncertain–Default reasoning, even in deductive fashion, is uncertain–Incomplete deductive inference may be uncertainProbabilistic reasoning only gives probabilistic results (summarizes uncertainty from various sources)10Decision making with uncertainty•Rational behavior:–For each possible action, identify the possible outcomes–Compute the probability of each outcome–Compute the utility of each outcome–Compute the probability-weighted (expected) utility over possible outcomes for each action–Select the action with the highest expected utility (principle of Maximum Expected Utility)11Bayesian reasoning•Probability theory•Bayesian inference–Use probability theory and information about independence –Reason diagnostically (from evidence (effects) to conclusions (causes)) or causally (from causes to effects)•Bayesian networks–Compact representation of probability distribution over a set of propositional random variables–Take advantage of independence relationships12Other uncertainty representations•Default reasoning–Nonmonotonic logic: Allow the retraction of default beliefs if they prove to be false•Rule-based methods–Certainty factors (Mycin): propagate simple models of belief through causal or diagnostic rules•Evidential