Predicting the difficulty of predicate-logic inference problems: An empirical examination of a predicate-logic model
The present work empirically examined a model of mental predicate logic proposed by Braine (in press), and focused on (a) establishing that the inferences predicted by the model are in fact made routinely, and (b) predicting the relative degree of difficulty of predicate-logic inference problems. The core part of the model, consisting of 10 direct reasoning schemas, is examined. Two sets of test problems were constructed: One of 64 monadic predicate inference problems (Set A), another of 64 dyadic predicate problems (Set B) that were constructed in one-to-one correspondence with those of Set A. An additional Set C combined the 128 problems in Sets A and B. One set of analyses developed a parametric model for monadic predicate problems using problem Set A. A second set of analyses developed a parametric model for dyadic predicate problems using problem Set B. A third set of analyses assesses whether a single model for both monadic and dyadic predicate problems could be developed, or whether two separate models are required. These analyses used a combined Problem Set C. On each problem the subjects evaluated the truth of a conclusion given a set of premises, and then rated the perceived difficulty of the problem on a 7-point scale. Thus, nine sets of perceived difficulty ratings were obtained, and from them nine respective sets of predicted difficulties were generated. The data satisfied three general predictions: (a) few errors were made in judging the truth value of conclusions given to each problem; this shows that the inferences of the 10 direct reasoning schemas are generally available; (b) The difficulty of problems correlated with the number of inference steps required to solve them, as defined by the reasoning routine associated with the inferences; (c) Problem difficulty was even more closely correlated with the summed difficulties of those inferences. Of these, (c) was examined by both cross-sample and cross-model validations. Finally, a parsimonious model was developed which reduces the ten parameters to three parameters, corresponding to three subsets of schemas.
0633: Cognitive therapy