Mental representation of logical connectives

Logical connectives, such as “AND”, “OR”, “IF . . . THEN”, and “IF AND ONLY IF” are ubiquitous in both language and cognition; however, reasoning with logical connectives is error-prone. We argue that some of these errors may stem from people's tendency to minimize the number of possibilities compatible with logical connectives and to construct a “minimalist” one-possibility representation. As a result, connectives denoting a single possibility (e.g., conjunctions) are likely to be represented correctly, whereas connectives denoting multiple possibilities (e.g., disjunctions or conditionals) are likely to be erroneously represented as conjunctions. These predictions were tested and confirmed in three experiments using different paradigms. In Experiment 1, participants were presented with a multiple-choice task and asked to select all and only those possibilities that would indicate that compound verbal propositions were true versus false. In Experiment 2, a somewhat similar task was used, except that participants were asked later to perform a cued recall of verbal propositions. Finally, Experiment 3 used an old/new recognition paradigm to examine participants' ability to accurately recognize different logical connectives. The results of the three experiments are discussed in relation to theories of representation of possibilities and theories of reasoning.     

Reconnecting interpretation to reasoning through individual differences

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an “immediate inference” task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (Newstead, 1989, 1995; Roberts, Newstead, & Griggs, 2001). Narrow appeal to particular Gricean implicatures in this work fails to bridge the gap. Grice's theory taken as a broad framework for credulous discourse processing in which participants construct speakers' “intended models” of discourses can reconcile these results, purchasing continuity of interpretation through variety of logical treatments. We present exploratory experimental data on immediate inference and subsequent syllogistic reasoning. Systematic patterns of interpretation driven by two factors (whether the subject's model of the discourse is credulous, and their degree of reliance on information packaging) are shown to transcend particular quantifier inferences and to drive systematic differences in subjects' subsequent syllogistic reasoning. We conclude that most participants do not understand deductive tasks as experimenters intend, and just as there is no single logical model of reasoning, so there is no reason to expect a single “fundamental human reasoning mechanism”.     

A study of position habits induced by reward and “frustration”

Predictions from Maier's theory of “frustration”-instigated behaviour have been tested in an experimental situation differing significantly from that in which the theory was propounded yet containing the central element of “frustration”—the insoluble problem.

A water discrimination unit was employed in which the performance of rats would be observed during attacks on insoluble problems, position problems or symbol problems.

Two groups, each containing ten Wistar albino rats, served as subjects. The research design consisted of the following phases: preliminary training, development of position responses, exposure to a symbol-reward problem with 50 per cent, punishment and exposure to a symbol-reward problem with 100 per cent, punishment. The design differed for the two groups only at the phase in which the position responses were established. During this phase one group was exposed to a position-reward problem and the other to an insoluble problem.

Position responses were established as frequently under position-“frustration” (position stereotypes) as under position-reward (position habits) conditions. Position stereotypes were more rigid—more resistant to extinction—than position habits under conditions of 50 per cent, punishment. Position stereotypes were as readily extinguished under 100 per cent, punishment as were position habits under 30 per cent, punishment.

The first two observations conform to predictions made from Maier's theory. The third does not. That is to say, not all situations containing the basic elements of “frustration” give rise to stereotyped behaviour patterns which are as rigid or “fixated” as Maier's theory would predict. It is a reasonable hypothesis that the characteristics of stereotyped responses established in certain “frustration” situations may be described adequately in terms of conventional learning principles without the necessity of resorting to a distinction between “goal-motivated” and “frustration-instigated” behaviour.     

Mental models and temporal reasoning

We report five experiments investigating reasoning based on temporal relations, such as: “John takes a shower before he drinks coffee”. How individuals make temporal inferences has not been studied hitherto, but we conjectured that they construct mental models of events, and we developed a computer program that reasons in this way.As the program shows, a problem of the form:

1. a before b

2. b before c

3. d while b

4. e while c

What is the relation between d and e?

where a, b, c, etc. refer to everyday events, calls for just one model, whereas a problem in which the second premise is modified to c before b calls for multiple models because a may occur before c, after c, or at the same time as c.

Experiments 1–3 showed that problems requiring one mental model elicited more correct responses than problems requiring multiple models, which in turn elicited more correct answers than multiple model problems with no valid answers. Experiment 4 contrasted the predictions of the model theory with those based on formal rules of inference; its results corroborated the model theory. Experiment 5 confirmed that a premise leading to multiple models took longer to read than the corresponding premise in one-model problems, and that latency to respond correctly was greater for multiple-model problems than for one-model problems. We conclude that the experiments corroborate the mental model theory.     

Pragmatic schemas and conditional reasoning in children

Solving problems involving conditional relationships has been postulated to play a central role in the development of deductive reasoning, which itself underpins much cognitive developmental theory. The traditional Piagetian and “natural logic” approaches to this topic have more recently been challenged by findings that are more readily explained in terms of the concept of pragmatic schemas. On this basis it was predicted that even young “pre-formal” children would be able to succeed in a Reduced Array Selection Task if the test statement (referring to a previously told story about bees living in a hive) was couched in such a way as to evoke an authorization or permission schema. This proved to be the case in the present study involving 54 nine- and ten-year-old children: The permission condition elicited 70% globally correct solutions, compared to the 11% elicited by the formal control condition. Moreover, this facilitatory effect of the permission condition carried over to a second trial conducted in a standard way across all the conditions.     

Semantic distance in memory structure: The retrieval of conceptual relationships

Four experiments are described which aim to distinguish the relative contributions of measures of semantic distance based on formal and normative criteria. Experiment I replicates a previous finding by Collins and Quillian (1969) that sentence confirmation RTs support a hierarchically-organised memory model. Experiments II and III minimised the role of syntactic processes and examined the times taken to “see the relationship” between pairs of concepts. The results also supported a hierarchical model but cast doubt upon the formal distinction between superset and property relationships. Experiment IV showed similar results using only property relationships of the “has” form. Multiple regression analyses of the data indicate that “number of intervening links” is a more consistent predictor of RT than “associative” measures of semantic relatendness and confirm strong linearity effects consistent with a hierarchical model of storage.     

Driye-leyel and flexibility in paired-associate nonsense-syllable learning

“High-anxiety” and “low-anxiety” subjects, selected for extreme scores on the Taylor Anxiety Scale, learned a list of paired-associate nonsense syllables in the belief that they were undergoing an intelligence test. Both groups were then given a second list of paired associates to learn, the stimulus-items being the same as those of the first list but the responses being changed. Before the presentation of the second list, half the subjects in each group were given anxiety-increasing instructions and the remaining half were given reassuring instructions.

The results verified two predictions made from Hull's behaviour theory, using the concept of fear or anxiety as a secondary drive:—“high anxiety” subjects took more trials to master the second learning task than “low-anxiety” subjects; and there was a significant interaction between initial anxiety-level and type of instructions, such that “high-anxiety” subjects who received drive-increasing instructions had a worse performance in the second part than all other sub-groups. There was no indication that “low-anxiety” subjects were significantly affected by the type of instructions received. The “high-anxiety” group had greater difficulty than the “low-anxiety” group in learning the first list, but the difference was non-significant.     

Effects of content on inclusive disjunction reasoning

An experiment is reported which establishes that inclusive disjunction arguments embedded in concrete content are not always easier to reason with than those involving abstract content. The subjects had to assess conclusions drawn from pairs of premises such as “Either Joan is intelligent or she is rich (or both); Joan is intelligent” or “Either Joan is intelligent or she is rich (or both); Joan is not intelligent”. The terms in the disjunctive premise were varied systematically across three content dimensions (i.e. compatible, abstract and contradictory). An analysis of variance revealed significant differences according to both principle of inference and type of content, and a significant interaction between these factors. The results demonstrated that semantically incompatible premise content had a marked influence on comprehension of inclusive disjunction reasoning schemes. The response patterns suggest that these reasoning schemes invited erroneous judgments based on other logical connectives.     

The effects of externalization on syllogistic reasoning

An experiment is reported that investigated the effects of externalization of mental models in syllogistic reasoning. Although there was no evidence that the requirement to “externalize” mental models of syllogisms improved reasoning, an unexpected recognition test demonstrated that subjects' memory for the meaning of the premises was improved by externalization. In particular, where the correct conclusion had been deduced using the externalization procedure, responses in the recognition test reflected an appreciation of the relations between the end terms of the premises.     

Natural and contrived experience in a reasoning problem

This study is concerned with the effects of prior experience on a deceptive reasoning problem. In the first experiment the subjects (students) were presented with the problem after they had experienced its logical structure. This experience was, on the whole, ineffective in allowing subsequent insight to be gained into the problem. In the second experiment the problem was presented in “thematic” form to one group, and in abstract form to the other group. Ten out of 16 subjects solved it in the thematic group, as opposed to 2 out of 16 in the abstract group. Three hypotheses are proposed to account for this result.     

Selective effects of an anaesthetic drug on cognitive behaviour

The prediction has been tested that under the influence of an anaesthetic drug, nitrous oxide, cognitive performances undergo differential impairment, the extent of which is positively correlated with the “complexity” of the task, Ten kinds of performance were investigated, ranging from speed of finger tapping to reasoning by analogy. The relative complexity of each task was determined, in accordance with conventional criteria, from its respective qualitative category or “level”—relational, associative, and motor—and within each category from qualitative analysis of the component processes involved in its execution. A simple group difference design was used, involving two groups of 50 subjects each, matched for age and sex.

Significant deterioration as a consequence of drug administration occurred in the performance of all tasks. On the whole, the more complex a task the more did it tend to be impaired. Motor performances were, however, impaired to a greater extent than had been predicted. The possible significance of these findings is discussed.     

Observing responses and discrimination learning

An operant response in the pigeon, whose performance results in exposure to the discriminative stimuli, is described and suggested as an experimental analogue for “observing.” Such an operant response is then used to explore the relationship between observing responses and discrimination learning in a variety of discrimination situations, of progressively increasing complexity. In general, the results support the contention that the development and maintainence of observing responses is closely related to the degree of differential behaviour manifested toward the discriminative stimuli. Certain modifications are suggested in the theoretical formulation underlying the concept of “observing responses.”     

A preliminary study of distinctive features in problem solving

The abstract logical structure of family relationship problems, such as, “What relationship to a man is his mother's father?” was described in terms of a “distinctive-feature-transition count (dft)”, where the answer to the problem was characterized in terms of the distinctive features of descendancy, co-linearity, and sex. On average, it proved possible to predict the difficulty of such problems from such a count; thus tending to support the idea of a relational rather than an associative memory structure.     

Children's syllogistic reasoning

Most theories of the development of deductive ability propose that children acquire formal rules of inference. An alternative theory assumes that reasoning consists of constructing a mental model of the situation described in the premises, scanning the model for an informative conclusion, and then searching for alternative models that refute this conclusion. Hence, performance should reflect two principal factors: the difficulty of constructing a model, which depends on the “figure” of the premises, and the number of models that have to be evaluated to respond correctly. In Experiment 1, two groups of children (9- to 10- and 11- to 12-year-olds) drew conclusions from 20 pairs of syllogistic premises. The results confirmed that children are affected both by figure and by number of models. Experiment 2 corroborated these findings for all 64 possible forms of syllogistic premises. The development of reasoning ability may therefore depend on the acquisition, not of formal rules of logic, but of procedures for manipulating models.     

Shorter articles and notes the interpretation of the passive voice

It was hypothesized that sentences in the passive voice emphasize the importance of the things referred to by their grammatical subjects to a greater extent than sentences in the active voice. Each subject had to produce simple diagrams to represent two sentences, one active and one passive, and it was assumed that the size of areas in these diagrams could be taken as an index of importance. In Group EQ, the sentences specified an equivalent arrangement of colours, e.g. “Red follows Blue,” “Blue is followed by Red”; in Group CO, they specified converse arrangements, e.g. “Red follows Blue,” “Red is followed by Blue.” The predictions, that (i) the subjects of all sentences would tend to be represented as larger than the objects, and that (ii) the subjects of passives would be represented as larger than those of actives, were confirmed.     

Visual pattern recognition: Size preprocessing re-examined

Template theories of visual pattern recognition assume the operation of preprocessing routines to deal with irrelevancies such as discrepancies in stimulus size. In three experiments where size was an irrelevant dimension, observers classified pairs of forms as either “same” or “different”. In Experiment I, the classification “different” was required when the stimuli shared the same form but a different orientation, and “same” when the stimuli shared the same form and orientation. Under these conditions RT was an increasing function of the magnitude of the size disparity between stimuli with equal slopes for “same” and “different” judgements. In Experiment II, “different” classifications were made to stimuli that had different forms, and “same” to figures with the same form. This stimulus set produced a size disparity function that interacted with response type; “different” responses had a shallower slope. Experiment III consisted of a mixed stimulus set drawn from both Experiment I and II. Stimuli that produced additive effects of size disparity and response type in Experiment I now produced an interaction between these two factors similar to the one observed in Experiment II. The results of these experiments are interpreted as evidence that previous contradictory results reported in the literature stem from differences in the way the stimulus set is constructed, and that size transformations can not be a necessary operation, at least when “different” judgements are made. The results are problematic for the view that size disparity effects in matching tasks are easily interpretable in terms of a primitive size normalization stage that precedes any comparison operations.     

The twelfth Bartlett memorial lecture: The role of single neurons in the psychology of perception

I feel deeply honoured by your invitation to give the Bartlett lecture, and am especially glad to do so in Holland, the home of so many distinguished psychologists of sensation and perception. And there is a third reason why it has given me much pleasure, for Sir Frederick Bartlett was one of those who had an important influence on the direction of my career some 40 years ago. I had to decide whether to spend my last year at Cambridge reading psychology or physiology, so I attended a short course of introductory lectures he gave in July. About half a dozen of us sat on upright wooden chairs circled around him as he sat in an armchair, smiling benignly. The first thing he did was to tell us to close our notebooks, for he was not going to say anything that would help us to pass any exams. And I believe the very last words of his last lecture were, “So you see it is all very difficult”. I was very glad he said that, for I had in fact found it all very heavy going: my brain seemed always to be lost in clouds of uncertainty when “remembering”, “thinking”, or “perceiving” were mentioned, because there was no conceptual framework for these processes except the words themselves and others spun around them. What I was looking for were the definable quantities of physics, chemistry and even physiology, these I could handle conceptually in their geometric and functional interactions, whereas I always find a purely verbal argument about abstractions difficult to follow and impossible to believe. So this lack of any nonverbal conceptual framework was very painful.

There was one phrase I think I recall him using that particularly aroused my interest-“the effort after meaning”; intuitively this seemed to be very important, but however much effort I made the meaning never quite emerged. I had almost decided that my mistrust of words made me unsuited to a career in psychology, but all the same I put my problem about “physiology or psychology” directly to Bartlett. After finding out that I was mainly interested in problems of sensation and perception, he said he thought that E. D. Adrian's research over the last 20 years had made more difference to that subject than any results obtained from within psychology itself.     

Group play therapy and tangible reinforcers used to modify the behavior of 8-yr-old boys

Eleven third-grade boys were randomly assigned to three play therapy groups. The boys had been referred by their teachers because of shy, withdrawn behavior. The Token Group met in a play group (4 Ss), had a therapist, and received tangible reinforcements for social approach behavior. The Verbal Group (4 Ss) was treated similarly to the Token Group except that no tangible reinforcements were used. The Control Group (3 Ss) met in a play group without a therapist present. Fourteen play sessions were held for each group. The Token Group changed more than the Verbal Group; the Verbal Group changed more than the Control Group; the Control Group showed no change on the objective measures used. The Token Group exhibited an increase in social approach behavior and a decrease in discrete, problem behavior. The Verbal Group increased slightly in social approach behavior. All groups failed to demonstrate changes in “productivity”, “anxiety” and “general psychological adjustment”.     

Assertive training: An adjunct to fluency shaping

“Assertive Training” has been utilized as an adjunct therapy in a six week residential program at Walter Reed Army Medical Center. The speech pathology staff in conjunction with the psychology staff determined that a persistent problem with long term success after patients were dismissed from therapy was largely due to a “behavioral deficit” in their interpersonal verbal confrontations. The anxiety resulting from such communication failure simply chips away at the self confidence needed to maintain a working level of fluency, resulting in a “snowballing” effect back to dysfluency.

Thus, the goals and procedures of assertive training for stutterers are discussed as a means to shape more effective skills in relating to others in difficult situations. Pre, post and six month follow-up data are presented.