Facts and Possibilities: A Model‐Based Theory of Sentential Reasoning

This article presents a fundamental advance in the theory of mental models as an explanation of reasoning about facts, possibilities, and probabilities. It postulates that the meanings of compound assertions, such as conditionals (if) and disjunctions (or), unlike those in logic, refer to conjunctions of epistemic possibilities that hold in default of information to the contrary. Various factors such as general knowledge can modulate these interpretations. New information can always override sentential inferences; that is, reasoning in daily life is defeasible (or nonmonotonic). The theory is a dual process one: It distinguishes between intuitive inferences (based on system 1) and deliberative inferences (based on system 2). The article describes a computer implementation of the theory, including its two systems of reasoning, and it shows how the program simulates crucial predictions that evidence corroborates. It concludes with a discussion of how the theory contrasts with those based on logic or on probabilities.     

Logic and belief across the lifespan: the rise and fall of belief inhibition during syllogistic reasoning

Popular reasoning theories postulate that the ability to inhibit inappropriate beliefs lies at the heart of the human reasoning engine. Given that people's inhibitory capacities are known to rise and fall across the lifespan, we predicted that people's deductive reasoning performance would show similar curvilinear age trends. A group of children (12‐year‐olds), young adults (20‐year‐olds), and older adults (65+‐year‐olds) were presented with a classic syllogistic reasoning task and a decision‐making questionnaire. Results indicated that on syllogisms where beliefs and logic conflicted, reasoning performance showed the expected curvilinear age trend: Reasoning performance initially increased from childhood to early adulthood but declined again in later life. On syllogisms where beliefs and logic were consistent and sound reasoning did not require belief inhibition, however, age did not affect performance. Furthermore, across the lifespan we observed that the better people were at resisting intuitive temptations in the decision‐making task, the less they were biased by their beliefs on the conflict syllogisms. As with the effect of age, one's ability to override intuitions in the decision‐making task did not mediate reasoning performance on the no‐conflict syllogisms. Results lend credence to the postulated central role of inhibitory processing in those situations where beliefs and logic conflict.     

Theories of categorical reasoning and extended syllogisms

The aim of this study was to examine the predictions of three theories of human logical reasoning, (a) mental model theory, (b) formal rules theory (e.g., PSYCOP), and (c) the probability heuristics model, regarding the inferences people make for extended categorical syllogisms. Most research with extended syllogisms has been restricted to the quantifier “All” and to an asymmetrical presentation. This study used three-premise syllogisms with the additional quantifiers that are used for traditional categorical syllogisms as well as additional syllogistic figures. The predictions of the theories were examined using overall accuracy as well as a multinomial tree modelling technique. The results demonstrated that all three theories were able to predict response selections at high levels. However, the modelling analyses showed that the probability heuristics model did the best in both Experiments 1 and 2.     

Statistical inference and Aristotle's Rhetoric

Formal logic operates in a closed system where all the information relevant to any conclusion is present, whereas this is not the case when one reasons about events and states of the world. Pollard and Richardson drew attention to the fact that the reasoning behind statistical tests does not lead to logically justifiable conclusions. In this paper statistical inferences are defended not by logic but by the standards of everyday reasoning. Aristotle invented formal logic, but argued that people mostly get at the truth with the aid of enthymemes—incomplete syllogisms which include arguing from examples, analogies and signs. It is proposed that statistical tests work in the same way—in that they are based on examples, invoke the analogy of a model and use the size of the effect under test as a sign that the chance hypothesis is unlikely. Of existing theories of statistical inference only a weak version of Fisher's takes this into account. Aristotle anticipated Fisher by producing an argument of the form that there were too many cases in which an outcome went in a particular direction for that direction to be plausibly attributed to chance. We can therefore conclude that Aristotle would have approved of statistical inference and there is a good reason for calling this form of statistical inference classical.     

Illusory inferences with quantifiers

The psychological study of reasoning with quantifiers has predominantly focused on inference patterns studied by Aristotle about two millennia ago. Modern logic has shown a wealth of inference patterns involving quantifiers that are far beyond the expressive power of Aristotelian syllogisms, and whose psychology should be explored. We bring to light a novel class of fallacious inference patterns, some of which are so attractive that they are tantamount to cognitive illusions. In tandem with recent insights from linguistics that quantifiers like “some” are treated as wh-questions, these illusory inferences are predicted by the erotetic theory of reasoning, which postulates that a process akin to question asking and answering is behind human inference making.     

Dialectic in the eleventh and twelfth centuries: garlandus compotista

Dialectic is a standard and important part of the logica vetus (or old logic) in medieval philosophy. It has its ultimate origins in Aristotle's Topics,its fundamental source in Boethius's De topicis differentiis,and its flowering in its absorption into fourteenth-century theories of consequences or conditional inferences. The chapter on Topics in Garlandus Compotista's logic book is the oldest scholastic work on dialectic still extant. In this paper I show the differences between Boethius's Theory of Topics and Garlandus's in order to illustrate the role of Topics in early scholastic logic. I argue that for Garlandus Topics are warrants for the inference from the antecedent to the consequent in a conditional proposition and that he is interested in Topics because of his overriding interest in hypothetical syllogisms. I conclude by discussing briefly the relationship between Garlandus's use of Topics and twelfth-century accounts.     

Effects of belief and logic on syllogistic reasoning: Eye-movement evidence for selective processing models

Studies of syllogistic reasoning have demonstrated a nonlogical tendency for people to endorse more believable conclusions than unbelievable ones. This belief bias effect is more dominant on invalid syllogisms than valid ones, giving rise to a logic by belief interaction. We report an experiment in which participants' eye movements were recorded in order to provide insights into the nature and time course of the reasoning processes associated with manipulations of conclusion validity and believability. Our main dependent measure was people's inspection times for syllogistic premises, and we tested predictions deriving from three contemporary mental-models accounts of the logic by belief interaction. Results supported recent "selective processing" theories of belief bias (e.g., Evans, 2000; Klauer, Musch, & Naumer, 2000), which assume that the believability of a conclusion biases model construction processes, rather than biasing the search for falsifying models (e.g., Oakhill & Johnson-Laird, 1985) or a response stage of reasoning arising from subjective uncertainty (e.g., Quayle & Ball, 2000). We conclude by suggesting that the eye-movement analyses in reasoning research may provide a useful adjunct to other process-tracing techniques such as verbal protocol analysis.     

Inductive reasoning about causally transmitted properties

Different intuitive theories constrain and guide inferences in different contexts. Formalizing simple intuitive theories as probabilistic processes operating over structured representations, we present a new computational model of category-based induction about causally transmitted properties. A first experiment demonstrates undergraduates’ context-sensitive use of taxonomic and food web knowledge to guide reasoning about causal transmission and shows good qualitative agreement between model predictions and human inferences. A second experiment demonstrates strong quantitative and qualitative fits to inferences about a more complex artificial food web. A third experiment investigates human reasoning about complex novel food webs where species have known taxonomic relations. Results demonstrate a double-dissociation between the predictions of our causal model and a related taxonomic model [Kemp, C., & Tenenbaum, J. B. (2003). Learning domain structures. In Proceedings of the 25th annual conference of the cognitive science society]: the causal model predicts human inferences about diseases but not genes, while the taxonomic model predicts human inferences about genes but not diseases. We contrast our framework with previous models of category-based induction and previous formal instantiations of intuitive theories, and outline challenges in developing a complete model of context-sensitive reasoning.     

Syllogistic reasoning and belief-bias inhibition in school children: evidence from a negative priming paradigm

Research on deductive reasoning in adolescents and adults has shown that errors in deductive logic are not necessarily due to a lack of logical ability but can stem from an executive failure to inhibit biases. Few studies have examined this dissociation in children. Here, we used a negative priming paradigm with 64 children (8-10 years old) to test the role of cognitive inhibition in syllogisms with belief-bias effects. On trials where negative priming was predicted, results were as follows: For the first syllogism (A), the strategy 'unbelievable-equals-invalid' had to be inhibited. The logic of the syllogism led to affirming a conclusion inconsistent with one's knowledge of the world, such as 'All elephants are light.' For the second syllogism (B), one's real-world knowledge and the syllogism's logic were congruent but the latter required affirming exactly what had been inhibited for A (i.e. that elephants are heavy). A negative priming effect on the A-B sequence was reflected in a significant drop in reasoning performance on B. This supports the idea that during cognitive development, inhibitory control is required for success on syllogisms where beliefs and logic interfere.     

Belief inhibition in children's reasoning: memory-based evidence

Adult reasoning has been shown as mediated by the inhibition of intuitive beliefs that are in conflict with logic. The current study introduces a classic procedure from the memory field to investigate belief inhibition in 12- to 17-year-old reasoners. A lexical decision task was used to probe the memory accessibility of beliefs that were cued during thinking on syllogistic reasoning problems. Results indicated an impaired memory access for words associated with misleading beliefs that were cued during reasoning if syllogisms had been solved correctly. This finding supports the claim that even for younger reasoners, correct reasoning is mediated by inhibitory processing as soon as intuitive beliefs conflict with logical considerations.     

How our brains reason logically

The aim of this article is to strengthen links between cognitive brain research and formal logic. The work covers three fundamental sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional “if...then”, reasoning in the predicate calculus, i.e. inferences based on quantifiers such as “all”, “some”, “none”, and reasoning with n-place relations. Studies with brain-damaged patients and neuroimaging experiments indicate that such logical inferences are implemented in overlapping but different bilateral cortical networks, including parts of the fronto-temporal cortex, the posterior parietal cortex, and the visual cortices. I argue that these findings show that we do not use a single deterministic strategy for solving logical reasoning problems. This account resolves many disputes about how humans reason logically and why we sometimes deviate from the norms of formal logic.

Premise Misinterpretation and Syllogistic Reasoning

A study by Ceraso and Provitera (1971) found that elaboration of the premises used in syllogistic reasoning led to substantially improved performance. This finding is of considerable importance because of the implications it has for mental logic and mental models theories of reasoning. Three experiments are reported, which replicated and extended the original findings. It was found that elaboration led to a significant improvement in performance, but that this was confined to multiple model syllogisms, where the elaboration has the effect of reducing the number of models involved. A fourth experiment indicated that elaboration can vary within the same syllogism depending on the direction of the conclusion drawn. These findings are best explained under the assumption that reasoners build mental models when solving problems and that elaboration can reduce the number of possible models.     

A mixed Rasch model of dual-process conditional reasoning

A fine-grained dual-process approach to conditional reasoning is advocated: Responses to conditional syllogisms are reached through the operation of either one of two systems, each of which can rely on two different mechanisms. System1 relies either on pragmatic implicatures or on the retrieval of information from semantic memory; System2 operates first through inhibition of System1, then (but not always) through activation of analytical processes. It follows that reasoners will fall into one of four groups of increasing reasoning ability, each group being uniquely characterized by (a) the modal pattern of individual answers to blocks of affirming the consequent (AC), denying the antecedent (DA), and modus tollens (MT) syllogisms featuring the same conditional; and (b) the average rate of determinate answers to AC, DA, and MT. This account receives indirect support from the extant literature and direct support from a mixed Rasch model of responses given to 18 syllogisms by 486 adult reasoners.     

My point is valid,yours is not: myside bias in reasoning about abortion

The study explores whether people are more inclined to accept a conclusion that confirms their prior beliefs and reject one they personally object to even when both follow the same logic. Most of the prior research in this area has relied on the informal reasoning paradigm; in this study, however, we applied a formal reasoning paradigm to distinguish between cognitive and motivational mechanisms leading to myside bias in reasoning on value-laden topics (in this case abortions). Slovak and Polish (N?=?387) participants indicated their attitudes toward abortion and then evaluated logical syllogisms with neutral, pro-choice, or pro-life content. We analysed whether participants’ prior attitudes influenced their ability to solve these logically identical reasoning tasks and found that prior attitudes were the strongest predictor of myside bias in evaluating both valid and invalid syllogisms, even after controlling for logical validity (the ability to solve neutral syllogisms) and previous experience of logic.     

The source of belief bias effects in syllogistic reasoning.

In studies of the belief bias effect in syllogistic reasoning, an interaction between logical validity and the believability of the conclusion has been found; in essence, logic has a larger effect on unbelievable than on believable conclusions. Two main explanations have been proposed for this finding. The selective scrutiny account claims that people focus on the conclusion and only engage in logical processing if this is found to be unbelievable; while the misinterpreted necessity account claims that subjects misunderstand what is meant by logical necessity and respond on the basis of believability when indeterminate syllogisms are presented. Experiments 1 and 2 compared the predictions of these two theories by examining whether the interaction would disappear if only determinate syllogisms were used. It did, thus providing strong support for the misinterpreted necessity explanation. However, the results are also consistent with a version of the mental models theory, and so Experiment 3 was carried out to compare these two explanations. The mental models theory received strong support, as it did also in the follow-up Experiments 4 and 5. It is concluded that people try to construct a mental model of the premises but, if there is a believable conclusion consistent with the first model they produce, then they fail to construct alternative models.     

中外两种推理理论的实验比较研究

通过两个实验对中国学者提出的“推理题与推理者的推理知识双重结构模型”和Evans提出的“双重加工理论”进行了实验比较研究。实验一通过两种评定方法对相应性质命题进行评定后所得实验结果表明Evans等(1983)有关“信念效应”研究中的“结论可信性”变量可以视为与胡竹菁等(1996)实验中的“内容正确性”变量是同一性质的变量; 实验二根据“形式正确性”和“内容正确性”两个自变量设计的推理实验结果与Evans等(1983)的研究结果基本一致; 但增加“内容熟悉性”这一自变量设计的推理实验结果表明“推理题与推理者的推理知识双重结构模型”比Evans提出的“双重加工理论”能更好地解释推理者对性质三段论的推理结果。     

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.     

On the conflict between logic and belief in syllogistic reasoning

Three experiments are reported that investigate the weighting attached to logic and belief in syllogistic reasoning. Substantial belief biases were observed despite controls for possible conversions of the premises. Equally substantial effects of logic were observed despite controls for two possible response biases. A consistent interaction between belief and logic was also recorded; belief bias was more marked on invalid than on valid syllogisms. In all experiments, verbal protocols were recorded and analyzed. These protocols are interpreted in some cases as providing rationalizations for prejudiced decisions and, in other cases, as reflecting a genuine process of premise to conclusion reasoning. In the latter cases, belief bias was minimal but still present. Similarly, even subjects who focus primarily on the conclusion are influenced to an extent by the logic. Thus a conflict between logic and belief is observed throughout, but at several levels of extent.     

Logic feels so good-I like it! Evidence for intuitive detection of logicality in syllogistic reasoning

When people evaluate syllogisms, their judgments of validity are often biased by the believability of the conclusions of the problems. Thus, it has been suggested that syllogistic reasoning performance is based on an interplay between a conscious and effortful evaluation of logicality and an intuitive appreciation of the believability of the conclusions (e.g., Evans, Newstead, Allen, & Pollard, 1994). However, logic effects in syllogistic reasoning emerge even when participants are unlikely to carry out a full logical analysis of the problems (e.g., Shynkaruk & Thompson, 2006). There is also evidence that people can implicitly detect the conflict between their beliefs and the validity of the problems, even if they are unable to consciously produce a logical response (e.g., De Neys, Moyens, & Vansteenwegen, 2010). In 4 experiments we demonstrate that people intuitively detect the logicality of syllogisms, and this effect emerges independently of participants' conscious mindset and their cognitive capacity. This logic effect is also unrelated to the superficial structure of the problems. Additionally, we provide evidence that the logicality of the syllogisms is detected through slight changes in participants' affective states. In fact, subliminal affective priming had an effect on participants' subjective evaluations of the problems. Finally, when participants misattributed their emotional reactions to background music, this significantly reduced the logic effect.     

Logical reasoning,world knowledge,and mental imagery: Interconnections in cognitive processes

To better understand the role of problem content in verbal reasoning, the effect of two aspects of problem representation on conditional reasoning was examined. Specifically, this study focused on the effect of availability of knowledge schemata and mental imagery on recognition of indeterminacy. Four groups of 20 adults solved syllogisms that varied in imagery value and in tendency to access knowledge schemata (assessed by ratings of the relatedness of antecedent and consequent clauses of premises). When problems both were high in imagery value and had related clauses, performance was significantly better on indeterminate syllogisms. Access to schemata may permit elaborative processing and the generation of counterexamples to invalid inferences; imagery may support representation of problems and generation of elaborative information in memory.