Is domain-specific reasoning in conditional reasoning tasks really domain-specific? The 2 nd London Reasoning Workshop 28-29/08/2007 Akira Nakagaki (Waseda University)

2 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)

3  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. How to Explain a “Sears” task （ D’Andrade cited in Rumelhart 1980 ） （ｐ）（￢ｐ）（ｑ） （￢ｑ）（￢ｑ） Four Receipts used in Sears Task by D’Andrade (adapted from Rumelhart 1980) signature ________ signature ________ Purchase Chair ＄ 40 Purchase Desk ＄ 150 Peter Wason （ｐ）（￢ｐ）（ｑ） （￢ｑ）（￢ｑ） Four Receipts used in Sears Task by D’Andrade (adapted from Rumelhart 1980) signature ________ signature ________ Purchase Chair ＄ 40 Purchase Desk ＄ 150 Peter Wason

4 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.

5  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. A Typical Task of PRS （ Cheng & Holyoak, 1985 ） （ｐ）（ｐ） （￢ｐ） （ｑ）（ｑ） （￢ｑ ）（￢ｑ ） Four forms presented in PRT （ Cheng & Holyoak, 1985 Experiment 1 ） typhoid hepatitis cholera typhoid hepatitis ENTERING （￢ｑ ）（￢ｑ ） typhoid hepatitis cholera TRANSIT ENTERING

6 Social Contract Theory (Cosmides, 1989)  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  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.

7  Rule １ (Standard Social Contract ） : ｐ ⇒ ｑ If you take the benefit, then you pay the cost.  Rule ２ (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. A Typical Task in Social Contract Context （ Cosmides,1985 ） （ｐ）（ｐ）（￢ｐ）（ｑ）（ｑ） （￢ｑ）（￢ｑ） Four Cards presented in SSC Benefit Accepted Cost Paid Benefit NOT Accepted Cost NOT Paid

8 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).

9  Rule given by the mother to her son : If you tidy your room, then you may go out to play. ( p ⇒ q )  Task in Case １ ( 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. A Typical Task in DRT （ Manktelow & Over, 1991 ） （ｐ）（￢ｐ） （ｑ） （￢ｑ）（￢ｑ） Four cards presented in DRT Tidied the room Went out to play Not tidied the room Not went out to play

10 Abstract Selection Tasks (Wason, 1966)  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?  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 ） Four Cards presented in AST （ｐ）（ｐ）（￢ｐ）（ｑ）（ｑ） （￢ｑ）（￢ｑ） 85EK

11  Statement Ⅰ : If a card has E on the face, then it has 8 on the back. (p ⇒ q)  Statement Ⅱ : If a card has E, it has not 8.(p ⇒ ￢ q)  Statement Ⅲ : 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? Abstract Selection Tasks with negative conditionals (Evans, 1972) Four cards presented in AST （ｐ）（ｐ）（￢ｐ）（ｑ）（ｑ） （￢ｑ）（￢ｑ） E8K5

12 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. StatementMatching Bias Logical Selection Statement Ⅰ p ⇒ qp，qp，qp， ￢qp， ￢q Statement Ⅱ p ⇒￢ qp，qp，qp，qp，q Statement Ⅲ ￢ p ⇒ qp，qp，q ￢ p ，￢ q

13 Comparison of effects between Reasoning by PRS and M Bias in p ⇒￢ q Matching Bias in p ⇒￢ q Statement Ⅱ Card Selection p ⇒￢ qp，qp，q Replace q with ￢ q → p ⇒ qp ，￢ 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. Reasoning by PRS Regulation Card Selection p ⇒ qp ，￢ q

14 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 StatementCard Selection p ⇒￢ qp，qp，q ￢ p ⇒ qp，qp，q Replace q with ￢ q, and then convert ￢ p ⇒￢ q → p ⇒ qp ，￢ q q ⇒ pp ，￢ q Reasoning in SCT RuleCard Selection Standard p ⇒ q p ，￢ q Switched q ⇒ p p ，￢ q

15 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. Two types of selections in AST StatementCard Selection ￢ p ⇒ qp ， q as the modal selection ￢ p ⇒ q ￢ p ，￢ q as the logical selection Replace p with ￢ p → p ⇒ q ￢ p， q￢ p， q p ，￢ q Reasoning in DRT RuleCard Selection p ⇒ q in agent’s perspective ￢p，q￢p，q p ⇒ q in actor’s perspective p ，￢ q

16 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 ASTReasoning in DRT StatementCard SelectionRuleCard Selection ￢ p ⇒ qp，qp，q p ⇒ q in agent’s perspective ￢p，q￢p，q p ⇒ ￢ qp，qp，q p ⇒ q in actor’s perspective p ，￢ q Replace p,q with ￢ p, ￢ q → p ⇒ ￢ q ￢ p， ￢q￢ p， ￢q Repeat as it is → p ⇒ ￢ q p ， q

17 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.

18  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. How to Explain a “Sears” task （ D’Andrade cited in Rumelhart 1980 ） （ｐ）（￢ｐ）（ｑ） （￢ｑ）（￢ｑ） Four Receipts used in Sears Task by D’Andrade (adapted from Rumelhart 1980) signature ________ signature ________ Purchase Chair ＄ 40 Purchase Desk ＄ 150 Peter Wason （ｐ）（￢ｐ）（ｑ） （￢ｑ）（￢ｑ） Four Receipts used in Sears Task by D’Andrade (adapted from Rumelhart 1980) signature ________ signature ________ Purchase Chair ＄ 40 Purchase Desk ＄ 150 Peter Wason Martin Braine