Conjunctive bias in memory representations of logical connectivesa

The paper presents the conjunctive bias in memory-a novel phenomenon that helps to clarify representations of logical connectives. The conjunctive bias is a tendency toward more accurate recall and recognition of conjunctive forms than of forms based on other logical connectives and a tendency to recall and recognize other logical forms as if they were conjunctions. Three experiments, in which participants' memory representations associated with different logical connectives were examined, were conducted to test the conjunctive bias hypothesis. In Experiment 1, participants learned picture-proposition pairs involving either conjunctions or disjunctions and then had to recall each proposition when cued with its picture. In Experiments 2 and 3, recognition memory for conjunctions, disjunctions, and conditionals was examined with an old/new recognition procedure. The findings of these experiments provide evidence for the conjunctive bias. Furthermore, the results of Experiment 3 suggest that corjunctive bias is not simply a pragmatically caused preference for conjunctions. The discussion focuses on the implications of these findings for current theories of deductive 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”.     

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.     

Verbal learning: Incremental vs. all-or-none theory

The incremental and all-or-none theories of verbal learning are compared by means of a little-used but methodologically superior variation of the “drop-out” paradigm with paired associates. Earlier experiments purporting to be relevant to the controversy are rejected as failing to offer a conclusive distinction between the two theories. The results presented here are taken to support the incremental theory. It is suggested that irregularities in the results of this and other experiments are caused by several intrusive factors, and a “dual-factor” hypothesis which was put forward to account for these irregularities is questioned on logical and methodological grounds.     

Divided attention, order of report and responses to immediately successive signals

Two effects, “divided-attention” and “order of report”, are operationally denned. Their relative contributions to the reduction in efficiency which accompanies the recognition of difficult nonverbal signals, presented simultaneously, is considered. Experiment I evaluated the two effects in the absence of a fixed order of report and emphasis instructions, confounding features of previous studies. The results showed: an overall impairment of performance with simultaneous signals; a contribution of both effects to the decrement, with a suggestion of the primacy of the “order of report” effect; and a significant interaction between the latter effect and modality, such that visual signals showed the greater effect. Experiment II using similar signals tested the assumption that simultaneity of presentation is a necessary condition for obtaining reduced efficiency with multiple signals. The assumption was only partially confirmed, a significant decrement in performance occurring only for the second of two successively presented signals. Similarities between the two sets of results are noted, as well as between these and modality differences obtained with verbal materials. Two possible accounts of the data are proposed, one based on “input”, the other on “storage” models of divided-attention. The hypothesis that subjects report the most clearly perceived signal first is rejected as an independent explanation.     

Temporal and spatial relations in sentential reasoning

The mental model theory postulates that the meanings of assertions, and knowledge about their context can modulate the logical meaning of sentential connectives, such as "if" and "or". One known effect of modulation is to block the representation of possibilities to which a proposition refers. But, modulation should also add relational information, such as temporal order, to models of possibilities. Three experiments tested this prediction. Experiment 1 showed that individuals spontaneously matched the tense of their conclusions (in Portuguese) to embody implied, but unexpressed, temporal relations in conditional premises. Experiment 2 demonstrated the same phenomenon in inferences from disjunctions. Experiment 3 showed that the number of such implicit relations in inferences from conditionals affects both accuracy and the speed of reasoning. These results support the modulation hypothesis.     

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.     

Naming and equivalence: Response latencies for emergent relations

In an attempt to distinguish between associative network and verbal mediation accounts of equivalence formation, three experiments were carried out in which conditional stimulus relations were established and response latencies assessed during tests for emergent relations. In Experiment 1, three groups of adults were trained with six three-member classes of visual stimuli, using different kinds of stimuli for each group: readily nameable pictograms, which were “preassociated” (Group 1); equally nameable but “non-associated” pictograms (Group 2); or non-associated “abstract” stimuli, designed to discourage the use of verbal mediators (Group 3). For those trained with pictograms, equal response latencies were observed on all tested relations, viz. trained associations, symmetry, transitivity, and transitivity with symmetry, but for subjects given abstract stimuli response latencies were greater on tests requiring transitivity. In Experiment 2 this result was replicated with methodological refinements, using only groups trained with preassociated pictograms or abstract stimuli. In Experiment 3 subjects were pretrained to label abstract stimuli with either individual names or class names. Latencies were longer for tests involving transitivity in the case of those subjects using individual names, but equal response latencies were observed on all four types of test for those using class names. The results suggest that equivalence classesMaybe supported by either an associative network or by verbal mediation, depending on stimulus conditions and the subsequent strategies employed by subjects.     

Win-stay behaviour in the rat

The Law of Effect dictates that animals will repeat the just-reinforced response “win-stay”, and yet there have been apparent violations of this by rats running for food in mazes, in the form of “win-shift” behaviour. Four experiments analysed the conditions determining win-stay and win-shift behaviour. All the experiments employed a schedule in which reinforcement was distributed across two choices, and in which the probability of reinforcement for the first response after previous reinforcement was equivalent for the two options. Despite this lack of programmed differential reinforcement, rats showed a significant win-stay tendency in Experiment 1, with no spatial bias. Experiments 2 and 3 used respectively a Y-maze and an operant chamber in which responding required a return to a central choice point. In both situations, significant win-shift behaviour resulted initially, at relatively high frequencies of reinforcement, but this win-shift changed to significant win-stay over many sessions, and with intermittent reinforcement. Experiment 4 introduced explicitly non-reinforced trials and demonstrated a “lose-shift” tendency, parallel to win-stay. Possible artefacts underlying win-stay and win-shift behaviour are rejected, and various mechanisms for these effects, including theories of optimal choice and associative learning, are discussed.     

Towards a pattern-based logic of probability judgements and logical inclusion “fallacies”

Probability judgements entail a conjunction fallacy (CF) if a conjunction is estimated to be more probable than one of its conjuncts. In the context of predication of alternative logical hypothesis, Bayesian logic (BL) provides a formalisation of pattern probabilities that renders a class of pattern-based CFs rational. BL predicts a complete system of other logical inclusion fallacies (IFs). A first test of this prediction is investigated here, using transparent tasks with clear set inclusions, varying in observed frequencies only. Experiment 1 uses data where BL makes dominant predictions; Experiment 2's predictions were less clear, and we additionally investigated judgements about the second-most probable hypotheses. The results corroborated a pattern-probability account and cannot be easily explained by other theories of CFs (e.g. inverse probability, confirmation). IFs were not limited to conjunctions, but rather occurred systematically for several logical connectives. Thus, pattern-based probability judgements about logical relations may constitute a basic class of intuitive but potentially rational probability judgements.     

A study of the effect of structural information and familiarity in form perception

Two experiments were carried out to investigate the influence of structural information and familiarity on the processing of visual forms. Pairs of “well” structured and nameable and “poorly” structured and non-nameable fragmented forms were employed as stimuli. The effects of structure and familiarity were assessed by manipulating the visual hemifield of presentation and the task. In Experiment 1 stimuli were judged as being either in the same orientation or mirror-reversed, a task that does not require high-level semantic information to be processed. Experiment 2 required physically identical forms to be matched, which may use either physical or name information. In Experiment 1 “same” judgements were equivalent for both types of stimuli, and “different' judgements were longer for the “poorly” structured (non-nameable) forms. In Experiment 2 there was little overall difference between “well” and “poorly” structured forms, though response times to “well” structured (nameable) forms were slowed for right-visual-field presentations. It is suggested that familiarity may not be sufficient to provide a perceptual advantage for nameable forms, as the advantage for nameable stimuli was confined to “same” judgements in Experiment 1 and response times were shorter for non-nameable stimuli in Experiment 2. Rather, performance depends upon factors such as the computation of global shape (due to structural properties of collinearity and closure) and on the use of different kinds or representations (physical versus name) in matching.     

Facilitation and inhibition caused by the orienting of attention in propositional reasoning tasks

In an attempt to study the orienting of attention in reasoning, we developed a set of propositional reasoning tasks structurally similar to Posner's (1980) spatial cueing paradigm, widely used to study the orienting of attention in perceptual tasks. We cued the representation in working memory of a reasoning premise, observing whether inferences drawn using that premise or a different, uncued one were facilitated, hindered, or unaffected. The results of Experiments 1a, 1b, 1c, and 1d, using semantically (1a-1c) or statistically (1d) informative cues, showed a robust, long-lasting facilitation for drawing inferences from the cued rule. In Experiment 2, using uninformative cues, inferences from the cued rule were facilitated with a short stimulus onset asynchrony (SOA), whereas they were delayed when the SOA was longer, an effect that is similar to the “inhibition of return” (IOR) in perceptual tasks. Experiment 3 used uninformative cues, three different SOAs, and inferential rules with disjunctive antecedents, replicating the IOR-like effect with the long SOAs and, at the short SOA, finding evidence of a gradient-like behaviour of the facilitation effect. Our findings show qualitative similarities to some effects typically observed in the orienting of visual attention, although the tasks did not involve spatial orienting.     

Human reasoning: Deduction rules or mental models, or both?

A good deal of energy is currently being expended into discovering the fundamental machinery underlying deductive reasoning. Is it based upon mental models (arrays) or deduction rules (propositions)? The appeal of finding a “grand unified theory” of reasoning is obvious, but the likelihood of achieving this must also be considered.

This paper discusses the use of experimental psychology in attempts to discover the processes associated with the fundamental reasoning mechanism. One particular problem is that individuals can use different strategies to solve reasoning problems. The consequences of this are assessed in relation to: (1) the assumptions underlying the experiments, (2) the choice of tasks and task presentations intended to enable the fundamental reasoning processes to be viewed directly, and (3) the power status of the theories and the nature of the evidence required to show that either theory is superior. Under close scrutiny the debate appears to be unresolvable by using empirical techniques. However, although the main conclusions are negative, it is suggested that approaches that directly investigate individual differences are likely to be useful alternatives.     

Bias in Conditional Inference: Implications for Mental Models and Mental Logic

Three experiments are reported in which subjects are given the opportunity to make any of the four inferences associated with conditional statements: modus ponens (MP), denial of the antecedent (DA), affirmation of the consequent (AC), and modus tollens (MT). The primary purpose of the research was to establish the generality and robustness of polarity biases that may be occasioned by systematic rotation of negative components in the conditional rules. In Experiments 1 & 2, three forms of conditionals were used: “if (not) p then (not) q”, “(not) p only if (not) q” and “(not) q if (not) p”. Experiment 1 used a conclusion evaluation task, whereas Experiment 2 used a conclusion production task. In Experiment 3, thematic conditionals were presented with and without a preceding scenario.

The biases investigated were (a) affirmative premise bias—the tendency to draw more inferences from affirmative premises and (b) negative conclusion bias—the tendency to draw more inferences with negative conclusions. The suggestive evidence for affirmative premise bias in the literature was not supported: very little evidence was found for it in the current experiments. Robust findings of negative conclusion bias were, however, found across the three experiments, although the bias was mostly restricted to DA and MT inferences. This suggests that the bias is best regarded as a difficulty with double negation.

The results are discussed with respect to both the mental logic and mental model accounts of propositional reasoning. Neither theory as currently formulated can explain all of our findings, although a plausible revision of each is considered.     

The negations of conjunctions,conditionals, and disjunctions

How do reasoners understand and formulate denials of compound assertions, such as conjunctions and disjunctions? A theory based on mental models postulates that individuals enumerate models of the various possibilities consistent with the assertions. It therefore predicts a novel interaction: in affirmations, conjunctions, A and B, which refer to one possibility, should be easier to understand than disjunctions, A or B, which refer to more than one possibility; in denials, conjunctions, not(A and B), which refer to more than one possibility, should be harder to understand than disjunctions, not(A or B), which do not. Conditionals are ambiguous and they should be of intermediate difficulty. Experiment 1 corroborated this trend with a task in which the participants selected which possibilities were consistent with assertions, such as: Bob denied that he wore a yellow shirt and he wore blue pants on Tuesday. Experiment 2 likewise showed that participants' own formulations of verbal denials yielded the same trend in which denials of conjunctions were harder than denials of conditionals, which in turn were harder than denials of disjunctions.     

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.     

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.     

Inducing a Rule in Wason's 2-4-6 Task: A Test of the Information-Quantity and Goal-Complementarity Hypotheses

In the standard 2-4-6 induction task, subjects are instructed to discover the rule generating sequences of three numbers by inventing number triples for which they receive immediate feedback. The rule is “ascending numbers”. Performance is greatly aided with Dual Goal (DG) instructions that ask subjects to discover two rules, one that generates “Dax” triples (equivalent to “yes” instances with Single Goal [SG] instructions) and another that generates “Med” triples (equivalent to “no” instances). The present study eliminates two explanations for this effect suggested by Wharton, Cheng, and Wickens (1993). Experiment 1 tested their Information-Quantity hypothesis that the effect results simply from the DG subjects testing more triples prior to proposing a rule. Our DG subjects were more likely to solve the problem and produced more “negative” triples than SG subjects when both groups generated exactly 15 triples. Two further groups received feedback only after generating all 15 triples, and again DG subjects were more likely to solve the problem and to generate more “negative” triples. Experiment 2 tested Wharton et al.'s Goal-Complementarity hypothesis that success under DG instructions hinges on preserving the complementary representation of the two rules. We compared SG instructions with three types of DG instructions that suggested different types of triples (Dax, Med, both Dax and Med, neither Dax nor Med). DG instructions were more effective in promoting successful rule discovery regardless of differences in rule complementarity. Our analysis of the heterogeneity of the examplars generated with DG instructions in both experiments suggest that success on the 2-4-6 task is as much a consequence of the breadth of hypotheses that subjects entertain as it is a consequence of the testing strategy.     

Verbal reasoning and working memory

A series of experiments was carried out to explore the hypothesis that a central working memory (WM) system is utilized during verbal reasoning. WM was provisionally defined in terms of two major features of short-term memory (STM): its limited storage capacity and its use of speech-coded information. The reasoning task required subjects to match (verify) as rapidly as possible a sentence of varying grammatical form with a symbolic referent. Experiments I and II studied the effect of storing an additional STM load on sentence verification latencies. As many as six items could be correctly recalled with no slowing of verification speed. Experiment III used a different procedure in which the STM items had to be articulated aloud during verification. In this case six-item STM loads slowed verification speed considerably, and did so more for the more difficult sentences. Only a small non-significant slowing of verification speed was obtained when redundant messages were articulated. Experiment IV showed that latencies were also increased by introducing phonemic similarity into the verification task. Generally the results were not fully consistent with the hypothesis of WM as a limited capacity store called upon by the verification task. Instead they supported the view that the WM is a general executive system with a limited capacity for information processing. It was proposed that the articulatory system, used in rehearsal and concerned with speech-coding, is a “peripheral” of the more central WM executive and plays a relatively minor role in verbal reasoning.