It may be helpful to the reader, in following the specific examples in the text, to have a brief description of the problem-solving task involving logic expressions that was designed by O. K. Moore and Scarvia B. Anderson.
A logic expression is a sequence of symbols of two types: (1) variables--P, Q, R, and so on--and (2) connectives--not (-), and (•), or (v), and implies (⊃). An example from the text is R • (-P ⊃ Q), which may be interpreted as "R and (not P implies Q)." The subjects are not provided with this interpretation, however, but are told that the expressions are code messages and that the connectives are named "tilde" (-). "dot" (•), "wedge" (v), and "horseshoe" (⊃).
The following rules are provided for transforming one or two given logic expressions into a new expression (recoding expressions). We will state them here only approximately, omitting certain necessary qualifications.
|1.||A v B ⇔ B v A|
A • B ⇔ B • A
|2.||A ⊃ B ⇔ -B ⊃ -A|
|3.||A v A ⇔ A|
A • A ⇔ A
|4.||A v (B v C) ⇔ (A v B) v C|
A • (B • C) ⇔ (A • B) • C
|5.||A v B = - (-A • -B)|
A • B = - (-A v -B)
|6.||A ⊃ B ⇔ -A v B|
A v B ⇔ -A ⊃ B
|7.||A v (B • C) ⇔ (A v B) • (A v C)|
A • (B v C) ⇔ (A • B) v (A • C)
|8.||A • B ⇒ A|
A • B ⇒ B
|9.||A ⇒ A v X, where X is any expression|
The rules can be applied to complete expressions, or (except rule 8) to subexpressions. Double tildes cancel--i.e., - - A ⇔ A, but this cancellation is not stated in a separate rule.
|10.||If A and B are given, they can be recoded into A • B.|
|11.||If A and A ⊃ B are given, they can be recoded into B.|
|12.||If A ⊃ B and B ⊃ C are given, they can be recoded into A ⊃ C.|
Subjects were instructed in the use of these rules, then were given problems like those described in the text. They were asked to think aloud while working on the problems, and each time they applied a rule to recode one or two given expressions, the new expression was written on the blackboard by the experimenter, together with the numbers of the expressions and rule used to obtain it.