Disjunctive Rules Research Articles

Typicality in logically defined categories: Exemplar-similarity versus rule instantiation

A rule-instantiation model and a similarity-to-exemplars model were contrasted in terms of their predictions of typicality judgments and speeded classifications for members of logically defined categories. In Experiment 1, subjects learned a unidimensional rule based on the size of objects. It was assumed that items that maximally instantiated the rule were those farthest from the category boundary that separated small and large stimuli. In Experiment 2, subjects learned a disjunctive rule of the form "x or y or both". It was assumed that items that maximally instantiated the rule were those with both positive values (x and y). In both experiments, the frequency with which different exemplars were presented during classification learning was manipulated across conditions. These frequency manipulations exerted a major impact on subjects' postacquisition goodness-of-example judgments, and they also influenced reaction times in a speeded classification task. The results could not be predicted solely on the basis of the degree to which the rules were instantiated. The goodness judgments were predicted fairly well by a mixed exemplar model involving both relative-similarity and absolute-similarity components. It was concluded that even for logically defined concepts, stored exemplars may form a major component of the category representation.

An autosegmental approach to metathesis in Rotuman

Rotuman phonology is characterized by a complex system of rules involving the morphologically-conditioned metathesis of word-final vowels with the immediately preceding consonant, as well as umlauting, vowel shortening, and diphthongization, which apply disjunctively to the output of the metathesis rule. This paper shows that Autosegmental Phonoly provides a simpler account of these rules than previous descriptions. Positing Rotuman to have separate vowel and consonant tiers, this analysis shows that Rotuman phonology has a rule of V-truncation at the level of the CV skeleton, which triggers the leftward reassociation of the orphaned feature matrix to the preceding V-slot. The resulting double associations are resolved with the help of a series of disjunctive rules that refer to the featural conflicts between the two vocalic segments associated to the same V-slot. This account is superior to other accounts because of its simplicity and of the fact that it captures the anticipatory nature of what is traditionally described as metathesis.

An apparatus for the study of logical thinking in concept learning

An apparatus is described which allows the study of formal thought through concept learning tasks. The apparatus has two circuits: one has the logical structure of conjunctive/disjunctive concept learning rules; the other has the structure of biconditional/exclusive disjunctive rules. Eight push buttons representing four binary valued stimuli, are arranged in pairs. Only one button from each pair may be activated by the subject at any one time consequently combinations of up to four buttons may be operational at once. The subject is asked to learn the rule for predicting the onset of the two lights on the control panel. The subject may generate any combinations of buttons he wishes to test, which has the advantage of allowing subjects to manipulate variables individually and maximizes subject involvement in the task.

Stimulus-Rule Interactions in Concept Verification

The difficulty of learning a conceptual rule has been shown to depend upon the stimulus attributes which that rule conjoins. For what appear to be separable attributes, the disjunctive rule is easier than the conjunctive. In contrast, for what appear to be integrable attributes, the conjunctive rule is easier. This paper reports six experiments designed to determine whether the integrality of stimulus attributes affects the speed of verification of the stimulus, as positive or negative, with respect to a given conjunctive or disjunctive concept. The pattern of reaction times is not consistent with the result of rule-learning experiments and does not support an integrality hypothesis. Verification times seem to be more a function of the perceptual salience of the relevant attributes of the concept. Thus, a perceptual-integrality hypothesis is an unlikely explanation of rule learning results.

A study of disjunctive reasoning

Whilst it is currently fashionable to construct sequential models of reasoning, the results of recent experiments on conditional reasoning tasks are apparently incompatible with this notion. There is evidence of two orthogonal statistical components, one logical and the other non-logical. It has been suggested that non-logical tendencies are ‘response biases’ independent of the linguistic structure of the rule. However, certain results suggest that the ‘matching bias’ observed in conditional tasks may not occur with disjunctives. Two experiments are reported in which subjects generated ‘subjective truth tables’ for disjunctive rules, in which the presence and absence of negative components was varied. Experiment I provided a powerful test of the matching bias hypothesis and found no evidence of its presence. The presence of negative components did, however, systematically affect performance. Experiment II, with the aid of latency measurements, provided support for the hypothesis that negatives were affecting the ease of interpretation of the disjunctive sentences, with one negative component causing at least as much difficulty as two. In discussion, it is pointed out that the present results can be reconciled with those on conditional tasks, on the assumption that ‘matching bias’ is a special case of associational biases which are dependent on the linguistic form of the rule. It still appears necessary to retain the distinction between logical and non-logical components of the performance. However, this does not necessarily imply parallel processes underlying the data. A single muddled thought process, in which a rational sequential strategy fails to be consistently applied, could give rise to the type of data obtained.

Stimulus-Rule Interaction in Concept Learning

The acquisition and use of conceptual or categorical rules has heretofore been treated theoretically as a stimulus-independent process, involving the establishment of mental procedures that are equally applicable to any collection of stimulus attributes or within any stimulus population. The results of two experiments are inconsistent with this principle, at least for subjects who are relatively naive in the use of logical rules. The procedures that subjects employ initially, and therefore the relative difficulty of conjunctive and disjunctive rules, depend on the pair of attributes integrated by the rule in any concrete concept problem. The differences among attribute pairs reflect an underlying variable identified as local integrality. Integrable attributes conduce to conjunctive procedures, and separable attributes conduce to disjunctive procedures.

Child performance on discrimination tasks: Effects of amount of stimulus variation

Two independently conducted studies investigated stimulus variation effects on children's discrimination learning. The stimuli in the first study were generated by a conjunctive rule and were presented in pairs. Mean trials to criterion was significantly lower for the single-feature change treatment (17.4) than for the multiple-feature change treatment (29.9). Single-feature change-treatment transfer scores were significantly higher only for stimuli that differed in terms of one of the features. The second study not only replicated the initial finding concerning the single-feature change treatment but also found that students made more errors in reaching criterion when stimuli were generated by an exclusive disjunctive rule and were presented singly. For all tasks, the single-feature change treatment with stimuli presented in pairs was accompanied by fewer errors to criterion than the other treatments.

The Influence of Formal Education on Rule Learning and Attribute Identification in a West African Society

Groups of formally educated and of uneducated rural Kpelle tribesmen and children of Liberia, West Africa were given rule learning and attribute identification problems. On a wide variety of measures, rule learning proved easier than attribute identification for a conjunctive rule but not for a disjunctive rule. Education proved to have no significant effect on rule learning for either a conjunctive or a disjunctive rule. The influence of formal education was restricted to the superior performance of the educated subjects on the conjunctive attribute identification problems. These findings were interpreted as indicating that formal education exerts its influence primarily on the way in which known conceptual rules are used in a testing situation, exerting little (if any) influence on the actual learning of such rules.

Model and Observer Learning of Low, Medium, and High Level Concepts

Low (conjunctive), medium (disjunctive), and high (biconditional) level concept attainment problems were used to assess whether high level versus low and/or medium difficulty concept rules yield less positive transfer for observers than models. Direct learning and transfer of models were compared with vicarious learning and transfer of observers. 30 subjects in the latter condition observed 30 yoked models solve the initial problem before solving the intrarule-transfer task themselves. Conjunctive results were similar for models and observers with efficient solution occurring for both. However, greater positive transfer was apparent for models than observers in the biconditional task. Significant positive transfer occurred for both models and observers attaining the disjunctive rule.

Labels for Response Categories: Do Neutral Labels Make Conjunctive and Inclusive Disjunctive Concepts Equally Difficult

Four groups of 6 or 7 Ss each worked one problem involving a different concept rule where directional labels for response categories were used. The concept rules were conjunction, alternate denial, inclusive disjunction, and joint denial. Two groups of 8 Ss each worked one problem involving a different concept-rule problem with a neutral pair of labels. The concept rules were conjunction/alternate denial and inclusive disjunction/joint denial. A complete learning task was used. Significant rule effects were found within directional and neutral labels. In addition, conjunction/alternate denial with neutral labels was intermediate in difficulty between conjunction and alternate denial rule with directional labels. Likewise, the inclusive disjunction/joint denial rule was intermediate in difficulty between the inclusive disjunction and joint denial rules. The evidence also suggested that the first neutral label seen and/or the neutral label of lesser frequency acted strongly to determine the label upon which S focused attention.

Conjunctive and disjunctive rule learning as a function of age and forced verbalization

Six-, nine-, and twelve-year-old girls were presented with either two conjunctive or two disjunctive rule-learning problems. Older children made fewer errors than younger ones. On the first problem, disjunctive rules were more difficult than conjunctive ones, and forced verbalization facilitated performance. On the second problem, neither rules nor verbalization significantly affected performance. The data were interpreted as reflecting hypothesis-testing processes at all ages, although there was some evidence suggesting that 6-year-olds differed from the older children.

Proving a Disjunctive Rule

This experiment was designed to determine whether individuals reason correctly about disjunctive rules. The task consisted in the selection of appropriate instances either to prove, or to disprove, a given disjunctive rule. When the first component of the rule was negated, i.e. when the rule was logically equivalent to implication (p v q), the selection of appropriate instances was significantly more difficult than when the first component was not negated. The majority of subjects, however, revealed patterns of reasoning which were unstable and labile. The results are discussed in relation to those of previous experiments in which subjects had to reason about conditional sentences.