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Commonsense Reasoning and Argumentation 13/14 HC 12: Reasoning with causal information

Commonsense Reasoning and Argumentation 13/14 HC 12: Reasoning with causal information. Henry Prakken 24 March 2014 (with thanks to Annette Ten Teije). Overview. Reasoning with causal and evidential defaults Abduction (Combining abduction and argumentation). Causal vs. evidential defaults.

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Commonsense Reasoning and Argumentation 13/14 HC 12: Reasoning with causal information

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  1. Commonsense Reasoning and Argumentation 13/14HC 12: Reasoning with causal information Henry Prakken 24 March 2014 (with thanks to Annette Ten Teije)

  2. Overview • Reasoning with causal and evidential defaults • Abduction • (Combining abduction and argumentation)

  3. Causal vs. evidential defaults d1: if smoke machine on then smoke d2: if smoke then poor vision k1: smoke machine on Is ‘poor vision’ implied?

  4. Causal vs. evidential defaults /Prediction vs. explanation d1: if smoke machine on then smoke d2: if smoke then poor vision k1: smoke machine on Is ‘poor vision’ implied? d1: if smoke machine on then smoke d3: if smoke then fire k1: smoke machine on Is ‘fire’ implied? Relevant whether a conditional is causal or evidential! And whether we want to predict or explain

  5. Representing causal relations: three methods Admit only one type of rule: Only evidential (e.g. MYCIN) Only causal (e.g. abduction) Admit both types of rules and regulate their interaction: Pearl’s C-E ‘system’ (Bex & van den Braak)

  6. Pearl’s C-E `system’ Two kinds of default conditionals: P  c Q = causal P  e Q = evidential Two source labels for propositions C(P) = causally derived E(P) = evidentially derived

  7. Reasoning with default conditionals: what is allowed? Allowed: P  c Q C(P) C(Q) P  c Q E(P) C(Q) P  e Q E(P) E(Q) Not allowed: P  e Q C(P) Q

  8. Reasoning with causal defaults • Prediction: sprinkler on: what will happen? • Modelling: ‘deduction’ (M.P.) • Explanation: grass wet: why? • Modelling: abduction • Invalid! Sprinkler on  Grass wet

  9. Abduction: what is it? • Finding the best explanation for a set of observations • What is the best explanation for the wet grass? Sprinkler on  Grass wet Rain  Grass wet

  10. Abduction: application areas • Commonsense reasoning • Diagnosis • Legal proof • Mental state abduction • Scientific theory formation • …

  11. Abduction in AI • Part of “Model-based diagnosis” • Model based reasoning: • Build a formal model of a system • Reason about the system’s behaviour by reasoning with the model • Applied to diagnosis: • Build causal model of the system’s abnormal behaviour • Observe behaviour • Find explanation of abnormal behaviour by reasoning with the causal model

  12. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing

  13. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing

  14. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing

  15. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing

  16. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing

  17. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing

  18. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing

  19. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing

  20. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing + headache

  21. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing + headache Abduction is nonmonotonic!

  22. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing + headache

  23. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing + headache

  24. Causal network (1) flu cold hangover smoke allergy fever coughing headache observed: coughing + headache

  25. piston-rings used oil-cup holed old-spark-plugs 1 lubric-oil burning oil-below-car oil loss spark-plugs used-up irreg-oil consumpt oil lack stack smoke 3 dirty-spark-plugs high-engine temp burnout irreg- ignition ignition problems 2 4 temp-indic red power decrease coolant evaporation mumbling engine vapour 5 lack-of-accel melting melted pistons 6 smoke-from engine

  26. piston-rings used oil-cup holed old-spark-plugs 1 lubric-oil burning oil-below-car oil loss spark-plugs used-up irreg-oil consumpt oil lack stack smoke 3 dirty-spark-plugs high-engine temp burnout irreg- ignition ignition problems 2 4 temp-indic red power decrease coolant evaporation mumbling engine vapour 5 lack-of-accel melting melted pistons 6 smoke-from engine

  27. piston-rings used oil-cup holed old-spark-plugs 1 lubric-oil burning oil-below-car oil loss spark-plugs used-up irreg-oil consumpt oil lack stack smoke 3 dirty-spark-plugs high-engine temp burnout irreg- ignition ignition problems 2 4 temp-indic red power decrease coolant evaporation mumbling engine vapour 5 lack-of-accel melting melted pistons 6 smoke-from engine

  28. piston-rings used oil-cup holed old-spark-plugs 1 lubric-oil burning oil-below-car oil loss spark-plugs used-up irreg-oil consumpt oil lack stack smoke 3 dirty-spark-plugs high-engine temp burnout irreg- ignition ignition problems 2 4 temp-indic red power decrease coolant evaporation mumbling engine vapour 5 lack-of-accel melting melted pistons 6 smoke-from engine

  29. Logical model of abduction: idea • Given • a causal model CM • a set of observations O • Find explanations for O, i.e. hypotheses H such that • H  CM |- O • H  CM is consistent • Compare the explanations

  30. Logical model of abduction(with strict causality) • Causal specification = (DFS,OBS,CM) • DFS = {d1, …, dn} (di literals) • possible defects • OBS = {o1, …, om} (oi literals) • possible observations • CM = set of causal rules • d1 …  dm  dn • d1 …  dj  ok • Abductive Causal Problem = (C,O) • C is a causal specification • O  OBS • Solution = an explanation for O in terms of C with H  DFS

  31. Example theory H1  H2 S1 H2  S2 H3  S3 S1  Obs1 S2  Obs1 S2  Obs2 S3  S4 S4  Obs2 observed behaviour: Obs1  Obs2 H1 H2 H3 S1 S2 S3 S4 Obs1 Obs2

  32. Negative observations flu cold hangover smoke allergy fever coughing headache - observed: coughing, headache, fever. - An explanation only needs to be consistent with the negative observations!

  33. Revised definition ‘solution’ • H  DFS is a solution of (C,O) iff • H  CM |- O • H  CM  Ocis consistent • Oc is the set of negative observations • Oc {o|o  OBS/O and o is a positive literal} • (Further constraints are possible)

  34. Weak causality flu cold hangover smoke allergy may may may fever coughing headache - coughing O; headache Oc - Problem: {smoke allergy} is no explanation! - Solution: allow weak causal rules

  35. Weak causality logically • DFS also contains “assumption literals” i • A  i  B = “A may cause B” • Definitions remain unchanged; • Explanations can now also contain assumption literals.

  36. flu cold hangover smoke-all. may may may fever coughing headache flu  fever flu  1  coughing flu  headache cold  coughing hangover  headache smoke-all.  2  coughing smoke-all.  3  headache O = {coughing} Oc = {headache} CM U {smoke-all., 2 } |-- {coughing} CM U {smoke-all., 2 } U Oc is consistent

  37. Preference criteria for explanations • subset minimal • number minimal (cardinality) • Variations: • Ignore assumption literals • Only consider ‘initial causes’ • Consider only designated defect literals • Add probabilities • …

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