Causation

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Causation

• Charles L. Ortiz, Jr.
• Artificial Intelligence Center
• SRI International

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Causal attribution

• Uses of causal knowledge
• Planning Explanation
• Prediction Diagnosis
• The problem of causal attribution
• Given partial descriptions of two events, a
  and b, determine the causal connection, if any,
  between the occurrence of a and the occurrence of
  b (singular causation).

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Opacity of causal reports

• Laws Particulars
• Causal reports
• Taking I-95 (a) caused him to be late for work
  (b).
• Driving to work in his buick caused him to be
  late for work.
• . The event subsumption problem

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Explanatory perspective

• Other causal relations prevents, enables,
  hinders, etc.
• John tried not to spill the coffee by holding
  the cup steady but failed.
• Rational action drawing causal connections
  between mind and action
• Negative events Non-movement events
• Attempts and failures Method-of relations

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A picture of causal reasoning

• Initial knowledge
• WD world description (objects, events,
  properties, mental states, etc).
• L precondition/effect rules
• D non-causal knowledge (constraints,
  explanatory, etc)

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Causal reduction hypothesis

• Whether a caused b is true or false can be
  reduced to determining whether the
  counterfactual, if a had not occurred then b
  would not have occurred, is true or false

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Example

• Taking I-95 caused him to be late for work
• Lewis semantics for counterfactuals pgtq iff q
  holds in closest p-worlds

Take US1 On time Walk Late Ride bike Late

Take I-95 Late to work
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Belief change

• Ramsey Test To evaluate p gt q given beliefs,
  S, add p to S, making minimal modifications to S
  to maintain consistency. If q holds in the
  resulting state, then p gt q is true.
• Preference problem for counterfactuals
• Which change operation?
• Revision, update (Winslett)
• Syntactic (Ginsberg), model-based

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Preference problem

• Situation 1 A falls
• Predictive counterfactuals and causal direction
• If C had not fallen, would B not have fallen
  either?
• If C had not fallen, would E not have fallen
  either?
• Explanatory counterfactuals
• If C had not fallen, it would have had to have
  been the case that A or B did not fall either.

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Preference problem (contd)

• Define trio_fall C,D,E
• fall at same time
• Event decomposition What if D had not fallen?
• Simultaneous causation
• Event naming Child disobeys if knocks down
  domino
• Explanatory knowledge If H falls, A must be down

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Preference problem (contd)

• Other relations Letting B fall by not grasping
  it
• Even though If I had grasped B I would have
  prevented it from falling I did not cause it to
  fall.
• Counterfactuals and ramifications suppose alarm
  rings when C falls. What if C had not fallen?

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Technical requirements

• Events and time represented at the object level
• Integrated with solution to frame problem
• Preferences must be articiulated
• Counterfactual preferences hyupothesis (CPH)
  preferences chosen so that application of CRH
  results in conclusions consistent with
  commonsense causal intuitions
• Some syntactic method for updating (ramifications)

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Explanatory Update Theory

• w holds(p,t) and w occurs(e,t)
• Event-type constructor, _at_
• occurs(put_at_agt(Harry)_at_obj(C)_at_on(A)_at_dur(5),1)
• Information state, s(w,t) assumptions plus
  inertial inferences
• Persistences, P, holds(p,t) gt holds(p,t1) given
  lowest lt-priority
• s(w,t) occurs(a,t) gt occurs(b,t)
• s(w,t) ?occurs(a,t) in some u ?s(w,t)

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Information update

• S ? T ? minT, __u

ue S
T-worlds t1 t2 t3 t4 t5
S-worlds s1 s2 s3 s4 s5
Update t2 t3
Partitioned (lt) set of beliefs according to
importance
Closer than
t2
t4
s2
s2
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Supported beliefs (frame problem)

• Beliefs are either epistemically supported or not
• True in all worlds, or
• Supported by some belief
• A belief set, A, supports some P iff some Q
  dissapears from A when P is removed
• Possible worlds are ordered according to an
  explanatory ordering, ltE, such that S ltE T iff
  S has more supported beliefs that T.
• Information state is set of minimal ltE - worlds

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Information state

• Assumptions/foundational beliefs A WD ? L
• s(w,t)minA, ltE

W1
A falls B falls C,E fall D,F fall G falls
H falls
W2
A falls F falls, C,E fall D,F
down
W3
A falls B falls D,F move
C,E fall
1 2 3 4
5 6 W1 preferred no unsupported
actions
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Counterfactual semantics

• s(w,t) occurs(a,t) gt occurs(b,t) iff
• mins(w,t) ? occurs(a,t), ltE
  occurs(b,t)
• Check that b occurs in all of the a-updated
  worlds that have been explained that is, that
  have the least number of unsupported beliefs
  (handles the frame problem).

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Epistemic preferences

• Causal Direction I Causal inferences preferred
• Future computed after updating present and past
• Motivation Not all beliefs are supported by some
  causal history some represent given information

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Epistemic preference II

• Causal direction II Locality of action
• Causal laws now take the form
• occurs(b,t) ? holds(ab(b,a,f),t) ? occurs(a,t) ?
  F
• Prefer some localized abnormality

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Preemption

• Strongest antecedent condition
• Taking rook causes game to be won
• but if hadnt taken rook, could hav advanced
  pawn and still won
• Let occurs(a,t1) ? occurs(b,t2) iff there is some
  occurs(g1,t1) ? ? occurs(gn,t1) which is the
  strongest condition entailed by occurs(a,t1)
  that is counterfactually related to b

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Semantics of causation

• Want to block non-causal counterfactual
  dependencies
• I ran home quickly. If I had not run home then I
  would not have run home quickly.
• You didnt grasp domino B. If you had, C would
  not have fallen.
• I played the C chord. If I had not played the E
  not I would not have played the C chord.
• I opened the door by pulling it. If I had not
  pulledthe door I would not have opened it.

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Semantics of causation

• occurs(a,t1) causes occurs(b,t2) ?
• a ? b ? t1 ? t2
• ? augmentation(a,b),t1)
• ? occurs(a,t1) instrumental occurs(b,t2)
• ? (occurs(a,t1) method occurs(b,t2))
• ? holds(part_of(a,b),t1)
• ? occurs(a,t1) ? occurs(b,t2)

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Instrumentality and methods

• Instrumentality a is instrumetal to b iff if we
  imagine the agent of a not existing, then b would
  not have occurred
• a is a method for b iff a?b, they are not
  augementations of each other, the agent is the
  same and they are counterfactually related (Ortiz
  99 see also Pollack 86)
• Handles branching acts, negative actions

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Causal relations and act-types

• Enables b b is possible after a
• Causes b b is necessary after a
• Forces b More resources to cause b
• Prevents b b never occurs after a
• Maintains p a process prevents p
• Helps b a reduces resources for b
• Hinders b a helps increase resources for b
• Lets b b not prevented, not instrumental

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Example helping

• I helped him pick up the sofa
• You can tell by the fact that its a little
  easier if we turn the whole thing upside down
  (Balkanski)
• Removing the benches helped the marchers cross
  the plaza (Talmy)
• Intuition Reduce the number of resources that
  would otherwise have been required

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Helping

• occurs(a,t1) enables occurs(b,t2) ?
• a?b ? t1 ? t2
• ? ?tgtt2. occurs(a,t1) ? ?occurs(b,t)
• occurs(a,t1) helps occurs(b,t2) ?
• ?x?y.b x_at_resource(R)_at_y
• ? occurs(a,t1) enables
• occurs(x_at_y_at_resources(R),t2)

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Rational act-types

• Act-type Description
• Agentive Grounded in basic act
• Intentional Aware of relation to basic and
  intended
• Accident Ends act wouldnt have done
  otherwise
• Mistake Means act wrong choice in ends
• Attempt Intended to b by some a a-ed
• Failure Attempt with wrong a or belief

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Applications

• Ascriptions of action roles and agent
  responsibility (accidental, failed, etc)
  important to analysis of collaboration
• see Ortiz, C.L., Introspective and Elaborative
  Processes in Rational Agents, Annals of
  Mathematics and Artificial Intelligence, 1999.
• Causal relations compact means of expressing
  supporting information in negotiations (viewed in
  terms of the exchange of useful information)

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Semantics of intentions-that
SharedPlans theory of collaboration (Grosz
Kraus) Intentions-that f commitment to group
helpful behavior
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Related work

• Situation calculus and branching time logics
  requires notion of closest branch
• cause predicate (Lin Thielscher)
• Pearl local surgery
• Narayanan rich event descriptions
• Varieties of causation Riger 76, Schank 77,
  McDermott 82, Allen 84, Talmy 88.
• Informal representations or unclear semantics
  (Rieger, Schank, Allen) incomplete coverage of
  causal terms (Rieger, Schank) hypothetical
  forces (Talmy)

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Summary

• Stratified view of causal reasoning
• Time and events represented explicitly express
  counterfactuals involving arbitrary event
  descriptions
• Solution to preference problem
• EUT extends MAT of Morgenstern, Stein
• Semantics for commonsense causal languaage

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Summary (contd)

• Semantics for causal terms can accommodate
  negative event descriptions in reports
• Analysis of many commonsense causal terms used in
  reporting (non)intentional acts attempts,
  failures, accidents,..
• Distinguishes causation from method-of and blocks
  spurious causation