Is domain-specific
reasoning in conditional
reasoning tasks really
domain-specific?
The 2nd London Reasoning Workshop 28-29/08/2007
Akira Nakagaki (Waseda University)
Three theories of domainspecific 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)
2
How to Explain a “Sears” task
（D’Andrade 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.
Purchase
Purchase
signature
signature
Desk ＄150
Chair ＄40
Peter
Wason
________
________
（ｑ）
（￢ｑ）
（ｐ）
（￢ｐ）
Four Receipts used in Sears Task by
D’Andrade (adapted from Rumelhart 1980)
3
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.
4
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
（ｐ）
typhoid
TRANSIT
hepatitis
cholera
（￢ｐ）
（ｑ）
Four forms presented in PRT
（Cheng & Holyoak, 1985 Experiment 1）
typhoid
hepatitis
（￢ｑ ）
5
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.
The“look 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
6
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.
Benefit
Accepted
（ｐ）
Benefit NOT
Accepted
Cost Paid
（￢ｐ）
（ｑ）
Four Cards presented in SSC
Cost NOT
Paid
（￢ｑ）
7
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 (selfdenying actor).
 Case4: The actor does not make p true but makes q true (cheating
actor).
8
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( Actor’s perspective）:
Select only those cards which would show whether the
mother had broken the rule.
 Task in Case4 ( Agent’s perspective）:
Select only those cards which would show whether the boy
had broken the rule.

Tidied the
room
（ｐ）
Not tidied
the room
Went out
to play
（ｑ）
（￢ｐ）
Four cards presented in DRT
Not went
out to play
（￢ｑ）
9
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?

E
（ｐ）
K
8
（￢ｐ）
（ｑ）
Four Cards presented in AST
5
（￢ｑ）
10
Abstract Selection Tasks
with negative conditionals (Evans, 1972)
StatementⅠ: If a card has E on the face, then it has
8 on the back. (p ⇒ q)
 StatementⅡ: If a card has E, it has not 8.(p ⇒ ￢q)
 StatementⅢ: 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?

E
（ｐ）
K
8
（￢ｐ）
（ｑ）
Four cards presented in AST
5
（￢ｑ）
11
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
StatementⅠ p ⇒ q
Matching Bias Logical Selection
p，q
p， ￢q
StatementⅡ
p ⇒￢q
p，q
p，q
StatementⅢ
￢p ⇒ q
p，q
￢p ，￢q
12
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
Reasoning by PRS
StatementⅡ Card Selection
Regulation
Card Selection
p ⇒￢q
p⇒q
p ，￢q
p⇒q
p ，￢q
p，q
Replace q with ￢q
→
13
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
Reasoning in SCT
Statement
Card Selection
Rule
Card Selection
p ⇒￢q
p，q
Standard p ⇒ q
p，￢q
￢p ⇒q
p，q
Switched q ⇒ p
p，￢q
Replace q with ￢q, and then
convert ￢p ⇒￢q
→
p ⇒q
p，￢q
q⇒p
p，￢q
14
Comparison of effects between Reasoning
in DRT and in ￢p ⇒ q


What is happening in actor’s and agent’s 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 .
Reasoning in DRT
Two types of selections in AST
Statement
Card Selection
Rule
Card Selection
￢p ⇒ q
p，q as the
p ⇒q in agent’s
perspective
￢p，q
p ⇒q in actor’s
perspective
p，￢q
p⇒q
￢ p， q
p⇒q
p，￢ q
modal selection
￢p ⇒ q
￢p，￢q as the
logical selection
Replace p with ￢p
→
15
Comparison of effects between
Reasoning in DRT and M Bias in AST


What is happening in actor’s and agent’s 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
Reasoning in DRT
Statement
Card Selection
Rule
Card Selection
￢p ⇒ q
p，q
p ⇒q in agent’s
perspective
￢p，q
p ⇒ ￢q
p，q
p ⇒q in actor’s
perspective
p，￢q
Replace p ,q with ￢p , ￢q →
p ⇒ ￢q
￢ p， ￢q
Repeat as it is →
p ⇒ ￢q
p，
q 16
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.
17
How to Explain a “Sears” task
（D’Andrade 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.
Purchase
Purchase
signature
signature
Desk ＄150
Chair ＄40
Peter
Wason
________
Martin
Braine
________
（ｑ）
（￢ｑ）
（ｐ）
（￢ｐ）
Four Receipts used in Sears Task by
D’Andrade (adapted from Rumelhart 1980)
18