Is domain-specific reasoning in conditional reasoning tasks really domain-specific?

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Is domain-specific reasoning in conditional
reasoning tasks really domain-specific?

• The 2nd London Reasoning Workshop 28-29/08/2007

Akira Nakagaki (Waseda University)
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Three theories of domain-specific conditional
reasoning

• Theory of Pragmatic Reasoning Schemas (Cheng
  Holyoak, 1985 Cheng, Holyoak et al., 1986)
• Social Contract Theory (Cosmides, 1989)
• Deontic Reasoning Theory (Manktelow Over, 1991,
  1995)

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How to Explain a Sears task(DAndrade cited in
Rumelhart 1980)

• Rule If any purchase exceeds 100, then the
  receipt must have the signature of the
  departmental manager on the back (The manager is
  called Peter Wason) .
• Task Which card or cards do you have to turn
  over in order to check whether they obey or
  violate the rule.

Peter Wason
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Theory of Pragmatic Reasoning Schemas(Cheng
Hollyoak, 1985, Cheng, Hollyoak et al., 1986)

• People reason using pragmatic reasoning schemas
  which are abstract knowledge structures induced
  from ordinary life experiences such as
  permission, causation, etc.
• PRS consists of a set of generalized,
  context-sensitive rules defined and evoked in
  terms of goals of actions and their relationships.

• The permission schema describes a type of
  regulation in which taking a particular action
  requires satisfaction of a certain precondition.
• Rule1 If the action is to be taken, then the
  precondition must be satisfied.
• Rule2 not to be taken, need not be
  satisfied.
• Rule3 If the precondition is satisfied, then the
  action may be taken.
• Rule4 is not satisfied, must not be taken.

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A Typical Task of PRS(Cheng Holyoak, 1985)

• Regulation If a form says, ENTERING on one
  side, then the other side includes cholera among
  the list of diseases.
• Rationale The form lists any inoculations the
  passenger has had in the past 6 months. This is
  to ensure that entering passengers are protected
  against the disease.
• Task In order to check if the regulation is
  being followed, which of the forms below would
  you need to turn over.

ENTERING
typhoid hepatitis cholera
TRANSIT
(?q )
ENTERING
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Social Contract Theory (Cosmides, 1989)

• In order to successfully engage in social
  exchange, humans have the built-in algorithms
  that govern how humans reason about social
  exchange.
• These algorithms in human reasoning are evolved
  through natural selection and produce and operate
  on cost-benefit representations of exchange
  interactions.

• Thelook for cheaters" algorithm is one of the
  built-in algorithms, evoked in social contract
  context and urges humans to detect cheaters in
  cost-benefit representations

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A Typical Task in Social Contract
Context(Cosmides,1985)

• Rule1(Standard Social Contract) p ? q
• If you take the benefit, then you pay the cost.
• Rule2(Switched Social Contract) q ? p
• If you pay the cost, then you take the benefit.
• Task Indicate only those card(s) you definitely
  need to turn over to see if any of these people
  are breaking this law.

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Deontic Reasoning Theory(Manktelow Over,
1991,1995)

• Deontic reasoning is what we are doing when we
  are trying to decide which action we must or may
  perform.
• It is different from deductive reasoning and
  highly dependent on social, pragmatic and
  subjective factors including subjective utilities
  or probabilities.
• What subjects do in deontic selection tasks is to
  look for possible violations or failures to
  conform to the rule.

• Four possible outcomes in which there can be a
  failure to conform to the rule in some sense
• Case1 The agent sees p is true but does not
  allow q (unfair agent).
• Case2 The agent does not see p is true but allow
  q (weak agent).
• Case3 The actor makes p true but does not make q
  true (self-denying actor).
• Case4 The actor does not make p true but makes q
  true (cheating actor).

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A Typical Task in DRT(Manktelow Over, 1991)

• Rule given by the mother to her son If you tidy
  your room, then you may go out to play. (p ?q)
• Task in Case1( Actors perspective)
• Select only those cards which would show whether
  the mother had broken the rule.
• Task in Case4 ( Agents perspective)
• Select only those cards which would show whether
  the boy had broken the rule.

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Abstract Selection Tasks(Wason, 1966)

• Hypothetico-deductive reasoning
• Very difficult task (usually around 10 correct)
• Selection patterns selection p, q (46),
  selection p (33), selection p, q, ?q (7),
  selection p, ?q (4) (Johnson-Laird Wason 1970)

• Statement If a card has E on the face, then it
  has 8 on the back. (p ? q)
• Task Which card or cards do you have to turn
  over in order to decide whether the statement is
  true or false?

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Abstract Selection Tasks with negative
conditionals (Evans, 1972)

• Statement? If a card has E on the face, then it
  has 8 on the back. (p ? q)
• Statement? If a card has E, it has not 8.(p ?
  ?q)
• Statement? If a card has not E, it has 8.(?p ?
  q)
• Task Which card or cards do you have to turn
  over in order to decide whether the statement is
  true or false?

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Matching Bias in Abstract Selection Tasks (Evans,
1972)

• Participants tend to select the cards whose
  symbols correspond to those mentioned in the
  statement irrespective of the position of
  negation.

Statement Statement Matching Bias Logical Selection
Statement? p ? q p,q p, ?q
Statement? p ??q p,q p,q
Statement? ?p ? q p,q ?p ,?q
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Comparison of effects between Reasoning by PRS
and M Bias in p??q

• What is happening in PRS is structurally the same
  as the matching bias in p ??q .
• Card selection is guided by attention to a
  violator of the rule in PRS,whereas it is guided
  by attention to a counterexample in p??q. Both
  phenomena are an effect of cognitive prégnance.

Matching Bias in p ??q Matching Bias in p ??q
Statement? Card Selection
p ??q p,q
Replace q with ?q ? Replace q with ?q ? p ? q p ,?q
Reasoning by PRS Reasoning by PRS
Regulation Card Selection
p ? q p ,?q
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Comparison of effects between Reasoning in SCT
and M Bias in AST

• What is happening in standard and switched
  versions of SCT is structurally the same as M
  bias in p ??q and ? p ? q .
• Unchanging selection is caused by constancy of
  the violator in the rules of SCT in spite of
  exchanging p and q,whereas it is caused by
  constancy of prégnance in both statements of AST
  in spite of shifting negation.

Matching bias in AST Matching bias in AST
Statement Card Selection
p ??q p,q
?p ?q p,q
Replace q with ?q, and then convert ?p ??q ? Replace q with ?q, and then convert ?p ??q ? p ?q p,?q
Replace q with ?q, and then convert ?p ??q ? Replace q with ?q, and then convert ?p ??q ? q ? p p,?q
Reasoning in SCT Reasoning in SCT
Rule Card Selection
Standard p ? q p,?q
Switched q ? p p,?q
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Comparison of effects between Reasoning in DRT
and in ?p ? q

• What is happening in actors and agents versions
  of DRT is structurally the same as two types of
  selection in ? p ? q .
• Mutually exclusive selection is caused by
  shifting perspective in DRT,whereas it is caused
  by shifting phase between the modal selection and
  the logical selection in ? p ? q .

Two types of selections in AST Two types of selections in AST
Statement Card Selection
?p ? q p,q as the modal selection
?p ? q ?p,?q as the logical selection
Replace p with ?p ? Replace p with ?p ? p ? q ? p, q
Replace p with ?p ? Replace p with ?p ? p ? q p,? q
Reasoning in DRT Reasoning in DRT
Rule Card Selection
p ?q in agents perspective ?p,q
p ?q in actors perspective p,?q
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Comparison of effects between Reasoning in DRT
and M Bias in AST

• What is happening in actors and agents versions
  of DRT is structurally the same as M bias in p
  ??q and ? p ? q .
• Shifting perspective in the same deontic rule
  produces mutually exclusive selection,in this
  case, reciprocal selection, whereas shifting
  negation in p ??q and ? p ? q, that is,
  reciprocal conditionals produce the same
  selection.

Matching Bias in AST Matching Bias in AST Reasoning in DRT Reasoning in DRT
Statement Card Selection Rule Card Selection
?p ? q p,q p ?q in agents perspective ?p,q
p ? ?q p,q p ?q in actors perspective p,?q
Replace p ,q with ?p , ?q ? Replace p ,q with ?p , ?q ? p ? ?q ? p, ?q
Repeat as it is ? Repeat as it is ? p ? ?q p, q
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Conclusion

• From the structural point of view, major findings
  in domain-specific (or thematic) conditional
  reasoning are the same as phenomena
  characteristic of abstract conditional reasoning.
• Domain-specific reasoning is not domain-specific
  but one of the various manifestations of
  domain-general reasoning.
• The cognitive system in charge of conditional
  reasoning does not consist of a heterogeneous
  mixture of logical elements, but of an
  interrelated structure which transforms itself as
  a whole.

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How to Explain a Sears task(DAndrade cited in
Rumelhart 1980)

• Rule If any purchase exceeds 100, then the
  receipt must have the signature of the
  departmental manager on the back (The manager is
  called Peter Wason) .
• Task Which card or cards do you have to turn
  over in order to check whether they obey or
  violate the rule.

Peter Wason
Martin Braine