A logical expression of reasoning

A non-monotonic logic, the Logic of Plausible Reasoning (LPR), capable of coping with the demands of what we call complex reasoning, is introduced. It is argued that creative complex reasoning is the way of reasoning required in many instances of scientific thought, professional practice and common life decision taking. For managing the simultaneous consideration of multiple scenarios inherent in these activities, two new modalities, weak and strong plausibility, are introduced as part of the Logic of Plausible Deduction (LPD), a deductive logic specially designed to serve as the monotonic support for LPR. Axiomatics and semantics for LPD, together with a completeness proof, are provided. Once LPD has been given, LPR may be defined via a concept of extension over LPD. Although the construction of LPR extensions is first presented in standard style, for the sake of comparison with existing non-monotonic formalisms, alternative more elegant and intuitive ways for constructing non-monotonic LPR extensions are also given and proofs of their equivalence are presented.     

Conditional reasoning and causation

An experiment was conducted to investigate the relative contributions of syntactic form and content to conditional reasoning. The content domain chosen was that of causation. Conditional statements that described causal relationships (if mean value of cause, then mean value of effect) were embedded in simple arguments whose entailments are governed by the rules of truth-functional logic (i.e., modus ponens, modus tollens, denying the antecedent, and affirming the consequent). The causal statements differed in terms of the number of alternative causes and disabling conditions that characterized the causal relationship. (A disabling condition is an event that prevents an effect from occurring even though a relevant cause is present). Subjects were required to judge whether or not each argument's conclusion could be accepted. Judgements were found to vary systematically with the number of alternative causes and disabling conditions. Conclusions of arguments based on conditionals with few alternative causes or disabling conditions were found to be more acceptable than conclusions based on those with many.     

Conditional reasoning and conditionalization

In solving conditional reasoning problems, reasoners are assumed to compute the probability of the conclusion, conditionalizing first on the categorical premise, giving the knowledge-based component, and conditionalizing then on the conditional-statement premise, from which the assumption-based component is derived. Because reasoners find it difficult to compute the second-step conditionalization except when the conditional-statement premise is found to be related to the result of the first-step conditionalization as for modus ponens or, possibly, for modus tollens, the knowledge-based component generally dominates reasoning performance. After representing all the possible cases in which conditional-argument forms may appear, this approach was found to be consistent with the results from the 3 experiments reported in this study, whereas 2 alternative hypotheses account for only some of the results.     

Metacognitive experience and transfer of logical reasoning

The experiments examine the influence of metacognitive experience on the transfer of logical processes in a problem solving setting. Subjects were presented with two versions of Wason's (1966) selection task. Although they were able to perform successfully on the concrete tasks (following a minimal explanation of the correct solution on an initial trial), the majority were not able to transfer a successful method to the abstract tasks. Verbalization during, or following, the concrete tasks produced substantial transfer effects however. It is suggested that verbalization may lead to an increased awareness of past behaviour, particularly of those aspects necessary for successful solution.     

Mental models and logical reasoning problems in the GRE

The Graduate Record Examination (GRE) contains a class of complex reasoning tests known as logical reasoning problems. These problems are demanding for human reasoners and beyond the competence of any existing computer program. This article applies the mental model theory of reasoning to the analysis of these problems. It predicts 3 main causes of difficulty, which were corroborated by the results of 4 experiments: the nature of the logical task (Experiment 1), the set of foils (Experiment 2), and the nature of the conclusions (Experiments 3 and 4). This article shows how these factors can be applied to the design of new problems.     

Evidence that logical reasoning depends on conscious processing

Humans, unlike other animals, are equipped with a powerful brain that permits conscious awareness and reflection. A growing trend in psychological science has questioned the benefits of consciousness, however. Testing a hypothesis advanced by [Lieberman, M. D., Gaunt, R., Gilbert, D. T., & Trope, Y. (2002). Reflection and reflexion: A social cognitive neuroscience approach to attributional inference. Advances in Experimental Social Psychology, 34, 199-249], four studies suggested that the conscious, reflective processing system is vital for logical reasoning. Substantial decrements in logical reasoning were found when a cognitive load manipulation preoccupied conscious processing, while hampering the nonconscious system with consciously suppressed thoughts failed to impair reasoning (Experiment 1). Nonconscious activation (priming) of the idea of logical reasoning increased the activation of logic-relevant concepts, but failed to improve logical reasoning performance (Experiments 2a-2c) unless the logical conclusions were largely intuitive and thus not reliant on logical reasoning (Experiment 3). Meanwhile, stimulating the conscious goal of reasoning well led to improvements in reasoning performance (Experiment 4). These findings offer evidence that logical reasoning is aided by the conscious, reflective processing system.     

Conditional reasoning with a spatial content requires visuo-spatial working memory

In previous research, Toms, Morris, and Ward (1993) have shown that conditional reasoning is impaired by a concurrent task calling on executive functions but not by concurrent tasks that load on the slave systems of the working memory system as conceptualised by Baddeley and Hitch (1974). The present article replicates and extends this previous work by studying problems based on spatial as well as nonspatial relations. In the study 42 participants solved 16 types of spatial or nonspatial problems, both in a single-task condition and under concurrent matrix tapping, a task loading the visuo-spatial sketch pad. The findings were consistent with those of Toms et al. (1993) for problems with a nonspatial content. However, when the content was spatial, and only then, a dual-task impairment was observed: processing time of the first premise was lengthened, especially for problems with negations in the antecedent term, the consequent term, or both; moreover, the number of correctly solved problems with negations in both terms was smaller. The implications of these findings for the mental models theory and the mental logic theory are discussed.     

Error processes in syllogistic reasoning

In recent years, a number of proposals have been advanced to account for the errors that subjects make in deductive inferences from invalid syllogisms. Principles such as erroneous conversion of premises, probabilistic inference, feature selection, and various other interpretation and combination processes have been suggested. The present paper focuses on the 32 invalid categorical syllogisms for which conversion of premises does not provide an explanation of subject error. An explanation is presented in terms of three error processes: the erroneous conversion of conclusions resulting from backward processing, the erroneous integration of information from the two premises, and the failure to consider hypothetical possibilities. Empirical predictions regarding the differential difficulty of the various premise combinations as well as the pattern of correlations between premise combinations are derived from this formulation, and data are presented that support these predictions.     

Conditional reasoning with causal premises: Evidence for a retrieval model

This study examined the hypothesis that a key process in conditional reasoning with concrete premises involves on-line retrieval of information about potential alternate antecedents. Participants were asked to solve reasoning problems with causal conditional premises (If cause P then effect Q). These premises were inserted into short contexts. The availability of potential alternatives was varied from one context to another by adding statements that explicitly invalidated one or more of these alternatives (i.e., other causes that lead to the effect (Q). The invalidated alternatives differed in the degree of their semantic association to the consequent term (Q). The results show that the effect of invalidating one or more potential alternatives on the two uncertain logical forms, AC and DA, was largely determined by their relative associative strength. These results strongly support a model for conditional reasoning with causal premises that supposes that a key element in responding to the uncertain logical forms is on-line retrieval of at least one potential alternative antecedent.     

Logic and human reasoning: an assessment of the deduction paradigm

The study of deductive reasoning has been a major paradigm in psychology for approximately the past 40 years. Research has shown that people make many logical errors on such tasks and are strongly influenced by problem content and context. It is argued that this paradigm was developed in a context of logicist thinking that is now outmoded. Few reasoning researchers still believe that logic is an appropriate normative system for most human reasoning, let alone a model for describing the process of human reasoning, and many use the paradigm principally to study pragmatic and probabilistic processes. It is suggested that the methods used for studying reasoning be reviewed, especially the instructional context, which necessarily defines pragmatic influences as biases.     

Conditional reasoning, representation, and empirical evidence on a concrete task

This study examined interactions between empirical data, internal representations, and reasoning performance on a conditional reasoning task using a concrete apparatus. Subjects were asked an initial series of questions in order to determine the pattern of inferences they made after simple exposure to the apparatus. They were subsequently shown two different experimental manipulations designed to provide data about the internal structure of the apparatus without giving information about specific inferences. Some subjects did change their reasoning in response to the new data, although most remained stable throughout the experiment. These results are consistent with the idea that reasoning may require generation of an internal representation of a problem space. It was also concluded that the relation between reasoning and empirical evidence cannot be understood without supposing that evidence is often interpreted by subjects according to their reasoning patterns.     

Conditional reasoning following contradictory evidence: A developmental analysis

Recent evidence suggests that young adults do not correctly understand the logical relationship of the conditional (if p the q) as it applies to hypothesis testing, and most training procedures have not been productive. However, the introduction of contradictory evidence following faulty inferences has led to accurate inferences with conditional statements. Third and seventh grade and college studients (9, 13, and 21 years of age, respectively) were tested to assess developmental differences in improvement following contradiction training and to test whether improved performance transfers to other conditional reasoning tasks. Significant improvement in conditional reasoning was found for the young adult group following the introduction of contradictory evidence, and the positive effect of the treatment transferred across tasks. The third grade students showed no effects from the introduction of the contradiction, but the seventh graders were often confused by the introduction of the contradiction. Seventh grade and college student performances were generally worse than that of the third graders for the positive instances (p · q), but while the contradiction training improved college studients' performance it did not affect the seventh graders. The results are discussed in terms of changes in cognitive structures.     

Individual differences in logical intuitions on reasoning problems presented under two-response paradigm

ABSTRACT

Studies on individual differences in susceptibility to cognitive biases have identified several cognitive dispositions which were thought to predict reasoning by contributing to the efficiency of analytic thought. However, hybrid models suggest that differences between reasoners may arise already in the intuitive stages of the reasoning process. To address this possibility, we examined standard individual difference measures, mindware instantiation, and conflict detection efficiency as predictors of the accuracy on conflict problems presented under a two-response paradigm. We found that almost half of conflict reasoning problems were solved correctly already at the initial response stage and that the individual differences in initial reasoning performance were predicted by participants’ cognitive reflection, mindware instantiation, and detection efficiency. The findings advance the specification of hybrid dual-process models and provide corroborating evidence that a part of the link between bias susceptibility and cognitive dispositions is due to differences in intuitive processing.     

Negative emotions can attenuate the influence of beliefs on logical reasoning

Although the influence of beliefs on logical reasoning is well documented, how emotions modulate the effect of beliefs during reasoning remains unexamined. We instructed participants to reason about syllogisms involving neutral or emotionally charged content. We also manipulated the consistency of beliefs with logical validity. When content was neutral, participants exhibited the belief-bias effect observed in previous studies of reasoning. In contrast, when confronted with emotionally charged content participants were less likely to be influenced by their beliefs. Our results suggest that under certain conditions negative emotions can attenuate the influence of beliefs during logical reasoning. Drawing on the affect infusion model, we attribute this effect to a more vigilant, systematic scrutiny of beliefs in the presence of negative emotions.     

A new experimental method to identify the process of logical reasoning

Abstract: A new method to identify the process of logical reasoning is presented. In spite of its indispensability and importance, we have had few methods to identify a subject's reasoning process, except that of using verbal protocol data. In this paper, for the purpose of objective identification of the reasoning process, we propose a new method to obtain the subject's reasoning process, in terms of a resolution tree for a task of which the logical structure can be written by first-order predicate logic. The results of an experiment using this method are presented. They revealed some interesting features of human reasoning such as, large differences between subjects, remarkable parallel processes, and the existence of subgoals for each subject.