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”.     

Deductive schemas with uncertain premises using qualitative probability expressions

The new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that contained non-numerical expressions (e.g., “the chances are high”) and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that (1) except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, (2) the rate of conjunction fallacy was consistently low (not exceeding 20%, even with sure premises), and (3) participants' interpretation of the conditional agreed with de Finetti's “conditional event” but not with the material conditional.     

Content and strategy in syllogistic reasoning.

Syllogistic reasoning has been investigated as a general deductive process (Johnson-Laird & Byrne, 1991; Revlis, 1975; Rips, 1994). However, several studies have demonstrated the role of cognitive strategies in this type of reasoning. These strategies focus on the method used by the participants (Ford, 1995; Gilhooly, Logie, Wetherick, & Wynn, 1993) and strategies related to different interpretations of the quantified premises (Roberts, Newstead, & Griggs, 2001). In this paper, we propose that content (as well as individual cognitive differences) is an important factor in inducing a certain strategy or method for syllogistic resolution. Specifically, we suggest that syllogisms with a causal conditional premise that can be extended by an agency premise induce the use of a conditional method. To demonstrate this, we carried out two experiments. Experiment 1 provided evidence that this type of syllogism leads participants to draw the predicted conditional conclusions, in contrast with control content syllogisms. In Experiment 2, we demonstrated that the drawing of conditional conclusions is based on a causal conditional to an agent representation of the syllogism premises. These results support the role of content as inducing a particular strategy for syllogistic resolution. The implications of these results are discussed.     

Components of syllogistic reasoning

The present research sought to understand the components of syllogistic reasoning used in a syllogistic evaluation task. In this task, subjects must indicate whether a conclusion such as “Some Yale professors are humbugs” is definitely true, or never true of a set of premises such as “Some humbugs study syllogistic reasoning; some Yale professors study syllogistic reasoning”. A modified form of componential analysis (Sternberg 1977, 1978) was used to decompose the syllogistic evaluation task with abstract content into encoding and encoding plus combination subtasks. The response-choice data from these subtasks were used to provide (a) direct tests of a proposed theory of syllogistic reasoning, and in particular, of its assumptions about sources of error in syllogistic reasoning; and (b) direct inferences regarding the representation of relations between the subject and predicate of the premises as encoded and combined. The results supported a proposed transitive-chain model of syllogistic reasoning.     

Supposition and representation in human reasoning

We report the results of three experiments designed to assess the role of suppositions in human reasoning. Theories of reasoning based on formal rules propose that the ability to make suppositions is central to deductive reasoning. Our first experiment compared two types of problem that could be solved by a suppositional strategy. Our results showed no difference in difficulty between problems requiring affirmative or negative suppositions and very low logical solution rates throughout. Further analysis of the error data showed a pattern of responses, which suggested that participants reason from a superficial representation of the premises in these arguments and this drives their choice of conclusion. Our second experiment employed a different set of suppositional problems but with extremely similar proofs in terms of the rules applied and number of inferential steps required. As predicted by our interpretation of reasoning strategies employed in Experiment 1, logical performance was very much higher on these problems. Our third experiment showed that problems that could be solved by constructing an initial representation of the premises were easier than problems in which this representation was not sufficient. This effect was independent of the suppositional structure of the problems. We discuss the implications of this research for theories of reasoning based on mental models and inference rules.     

“At least one” problem with “some” formal reasoning paradigms

In formal reasoning, the quantifier "some" means "at least one and possibly all." In contrast, reasoners often pragmatically interpret "some" to mean "some, but not all" on both immediate-inference and Euler circle tasks. It is still unclear whether pragmatic interpretations can explain the high rates of errors normally observed on syllogistic reasoning tasks. To address this issue, we presented participants (reasoners) in the present experiments either standard quantifiers or clarified quantifiers designed to precisely articulate the quantifiers' logical interpretations. In Experiment 1, reasoners made significantly more logical responses and significantly fewer pragmatic responses on an immediate-inference task when presented with logically clarified as opposed to standard quantifiers. In Experiment 2, this finding was extended to a variant of the immediate-inference task in which reasoners were asked to deduce what followed from premises they were to assume to be false. In Experiment 3, we used a syllogistic reasoning task and observed that logically clarified premises reduced pragmatic and increased logical responses relative to standard ones, providing strong evidence that pragmatic responses can explain some aspects of the errors made in the syllogistic reasoning task. These findings suggest that standard quantifiers should be replaced with logically clarified quantifiers in teaching and in future research.     

条件推理中否定前件下信念偏差发生阶段的ERP研究

以日常生活中的条件推理语句为实验材料,采用大、小前提和结论依次呈现的“推断-判断”范式,利用事件相关电位(event-related brain potential, ERP)技术探讨了条件推理中否定前件下信念偏差效应的脑内时程动态变化。结果发现：在行为反应上,较信念促进,信念阻碍下的正确率更低反应时更长;在脑电上,两条件(信念阻碍和信念促进)诱发的ERP波形仅在大前提加工阶段出现明显的分离。这表明该推理下的信念偏差效应可能早在对大前提的语义表征阶段就已发生。     

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.     

Persisting Effects of Instruction on Young Children's Syllogistic Reasoning with Incongruent and Abstract Premises

Studies of reasoning have often invoked a distinction between a natural or ordinary consideration of the premises, in which they are interpreted, and even distorted, in the light of empirical knowledge, and an analytic or logical consideration of the premises, in which they are analysed in a literal fashion for their logical implications. Two or three years of schooling have been seen as critical for the spontaneous use of analytic reasoning. In two experiments, however, 4-year-olds who were given brief instructions that prompted use of an analytic approach continued to adopt this approach one week later. Thus, when given syllogistic problems in which the major premise was incongruent with their empirical knowledge (e.g. “All snow is black”), instructed children reasoned more accurately from that premise both immediately and a week later as compared to children given only a basic introduction. A third experiment showed that instructions also improved 4-year-olds' performance on hard-to-imagine, abstract material (e.g. “All mib is white”). Similarities between the effects of brief instruction and of schooling are discussed.     

Syllogistic reasoning time: Disconfirmation disconfirmed

University of Saskatchewan, Saskatoon, Saskatchewan, Canada Models of deductive reasoning typically assume that reasoners dedicate more logical analysis to unbelievable conclusions than to believable ones (e.g., Evans, Newstead, Allen, & Pollard, 1994; Newstead, Pollard, Evans, & Allen, 1992). When the conclusion is believable, reasoners are assumed to accept it without much further thought, but when it is unbelievable, they are assumed to analyze the conclusion, presumably in an attempt to disconfirm it. This disconfirmation hypothesis leads to two predictions, which were tested in the present experiment: Reasoners should take longer to reason about problems leading to unbelievable conclusions, and reasoners should consider more models or representations of premise information for unbelievable conclusions than for believable ones. Neither prediction was supported by our data. Indeed, we observed that reasoners took significantly longer to reason about believable conclusions than about unbelievable ones and generated the same number of representations regardless of the believability of the premises. We propose a model, based on a modified version of verbal reasoning theory (Polk & Newell, 1995), that does not depend on the disconfirmation assumption.     

Ampliative abduction

In Peirce's and Hanson's characterization of abductive inference, the abducted hypothesis (but not others) is present in the premises, so that the inference can hardly be taken as ampliative. Abduction has consequently been treated as part of the process whereby already generated hypotheses are judged in terms of their plausibility, simplicity, etc. I propose an interpretation of abduction which supports an ampliative view. It relies on a distinction between two logical stages in the generation of hypotheses, one “factual” and one “explanatory”. I also indicate how we may reconstruct Peirce's and Hanson's original inference in an ampliative form.     

“如果P,那么Q,……?”─—儿童充分条件假言演绎推理能力发展初探

以日常生活事件为内容的三套测验题探查了9－15岁儿童充分条件假言推理能力的发展。研究发现被试有关能力的发展可以区分出三种不同水平；儿童对充分条件假言推理规则的掌握没有固定的难易顺序，这取决于课题任务的性质和主体思维发展水平。研究还探查了发展的个体内部差异和个体之间的差异以及影响差异的各种内外因素。     

The probabilistic approach to human reasoning

A recent development in the cognitive science of reasoning has been the emergence of a probabilistic approach to the behaviour observed on ostensibly logical tasks. According to this approach the errors and biases documented on these tasks occur because people import their everyday uncertain reasoning strategies into the laboratory. Consequently participants' apparently irrational behaviour is the result of comparing it with an inappropriate logical standard. In this article, we contrast the probabilistic approach with other approaches to explaining rationality, and then show how it has been applied to three main areas of logical reasoning: conditional inference, Wason's selection task and syllogistic reasoning.     

Getting one step closer to deduction: Introducing an alternative paradigm for transitive inference

Transitive inference is claimed to be “deductive”. Yet every group/species ever reported apparently uses it. We asked 58 adults to solve five-term transitive tasks, requiring neither training nor premise learning. A computer-based procedure ensured all premises were continually visible. Response accuracy and RT (non-discriminative nRT) were measured as is typically done. We also measured RT confined to correct responses (cRT). Overall, very few typical transitive phenomena emerged. The symbolic distance effect never extended to premise recall and was not at all evident for nRT; suggesting the use of non-deductive end-anchor strategies. For overall performance, and particularly the critical B?D inference, our findings indicate that deductive transitive inference is far more intellectually challenging than previously thought. Contrasts of our present findings against previous findings suggest at least two distinct transitive inference modes, with most research and most computational models to date targeting an associative mode rather than their desired deductive mode. This conclusion fits well with the growing number of theories embracing a “dual process” conception of reasoning. Finally, our differing findings for nRT versus cRT suggest that researchers should give closer consideration to matching the RT measure they use to the particular conception of transitive inference they pre-held.     

Is inferential reasoning just probabilistic reasoning in disguise?

Oaksford, Chater, and Larkin (2000) have suggested that people actually use everyday probabilistic reasoning when making deductive inferences. In two studies, we explicitly compared probabilistic and deductive reasoning with identical if-then conditional premises with concrete content. In the first, adults were given causal premises with one strongly associated antecedent and were asked to make standard deductive inferences or to judge the probabilities of conclusions. In the second, reasoners were given scenarios presenting a causal relation with zero to three potential alternative antecedents. The participants responded to each set of problems under both deductive and probabilistic instructions. The results show that deductive and probabilistic inferences are not isomorphic. Probabilistic inferences can model deductive responses only using a limited, very high threshold model, which is equivalent to a simple retrieval model. These results provide a clearer understanding of the relations between probabilistic and deductive inferences and the limitations of trying to consider these two forms of inference as having a single underlying process.     

Debiasing by instruction: The case of belief bias

Abstract

The study is concerned with the question of whether robust biases in reasoning can be reduced or eliminated by verbal instruction in principles of reasoning. Three experiments are reported in which the effect of instructions upon the belief bias effect in syllogistic reasoning is investigated. Belief bias is most clearly marked by a tendency for subjects to accept invalid conclusions which are a priori believable. Experiment 1 attempted to replicate and extend an experiment reported by Newstead, Pollard, Evans and Allen (1992). In contrast with their experiment, it was found that belief bias was maintained despite the use of augmented instructions which emphasised the principle of logical necessity. Experiment 2 provided an exact replication of the augmented instructions condition of Newstead et al., including the presence of problems with belief-neutral conclusions. Once again, significant effects of conclusion believability were found. A third experiment examined the use of elaborated instructions which lacked specific reference to the notion of logical necessity. The use of these instructions significantly reduced the effects of belief on the reasoning observed.

Taking the current findings together with the experiment of Newstead et al., the overall conclusion is that elaborated instructions can reduce the belief bias effect in syllogistic reasoning, but not eliminate it. This conclusion is discussed with reference to (1) the practical implications for improving thinking and reasoning via verbal instruction and (2) the nature of the belief bias phenomenon.     

A three-factor model of syllogistic reasoning: The study of isolable stages

Computer models of the syllogistic reasoning process are constructed. The models are used to determine the influence of three factors—the misinterpretation of the premises, the limited capacity of working memory, and the operation of the deductive strategy—on subjects’ behavior. Evidence from Experiments 1, 2, and 3 suggests that all three factors play important roles in the production of errors when “possibly true” and “necessarily false” are the two response categories. This conclusion does not agree with earlier analyses that had singled out one particular factor as crucial. Evidence from Experiment 4 suggests that the influence of the first two factors remains strong when “necessarily true” is used as an additional response category. However, the third factor appears to interact with task demands. Some concluding analyses suggest that the models offer alternative explanations for certain well established results.     

Strategies in Syllogistic Reasoning

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies revealed by the participants' use of paper and pencil as aids to reasoning. Experiment 3 used a new technique to externalize thinking. The participants had to refute, if possible, putative conclusions by constructing external models that were examples of the premises but counterexamples of the conclusions. Experiment 4 used the same techniques to examine the participants' strategies as they drew their own conclusions from syllogistic premises. The results of the experiments showed that individuals not trained in logic can construct counterexamples, that they use similar operations to those implemented in the computer model, but that they rely on a much greater variety of interpretations of premises and of search strategies than the computer model does. We re-evaluates current theories of syllogistic reasoning in the light of these results.     

Tremor Frequencies

In an attempt to improve logical reasoning performances, 64 introductory psychology students were randomly assigned to experimental and control groups. The experimental condition involved solving logic syllogisms when the obvious “logical error” was not included as a possible answer. Control subjects solved the same problems with the “logical error” included as a choice. An analysis of variance procedure applied to the subjects' logic pretest-posttest gain scores indicated that the experimental group did significantly better than the control group on invalid principles. The results were discussed in terms of Piaget's theory of logical thinking and the possibility of performance rather than competence problems in adult reasoning. The need to develop more effective instructional techniques to enhance transfer of learning was underscored.     

Laws of language use and formal logic

After a review of recent work connected with Grice's maxims of conversation, special attention is paid to the principles related to the concept of informativeness. The operation of those principles constrains logic by limiting the meaning of logical particles and, more importantly, by contradicting axioms and many theorems of the propositional calculus. It is argued that, as the development of the individual's formal operations proceeds, a conflict with laws of language use arises. The notion of a conflict between two subsystems, logical and linguistic, is used in a developmental perspective to account, in a unified manner, for the observed discrepancy between subjects' behavior in deductive and inductive reasoning tasks and predictions based on formal logic.