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

Commonsense Reasoning and Argumentation 13/14HC 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 d1: if smoke machine on then smoke d2: if smoke then poor vision k1: smoke machine on Is ‘poor vision’ implied?

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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!

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)

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

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.

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

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

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