How do people make deductions? The orthodox view in psychology is that they use formal rules of inference like those of a “natural deduction” system.Deductionargues that their logical competence depends, not on formal rules, but on mental models. They construct models of the situation described by the premises, using their linguistic knowledge and their general knowledge. They try to formulate a conclusion based on these models that maintains semantic information, that expresses it parsimoniously, and that makes explicit something not directly (...) stated by any premise. They then test the validity of the conclusion by searching for alternative models that might refute the conclusion. The theory also resolves long-standing puzzles about reasoning, including how nonmonotonic reasoning occurs in daily life. The book reports experiments on all the main domains of deduction, including inferences based on prepositional connectives such as “if” and “or,” inferences based on relations such as “in the same place as,” inferences based on quantifiers such as “none,” “any,” and “only,” and metalogical inferences based on assertions about the true and the false. Where the two theories make opposite predictions, the results confirm the model theory and run counter to the formal rule theories. Without exception, all of the experiments corroborate the two main predictions of the model theory: inferences requiring only one model are easier than those requiring multiple models, and erroneous conclusions are usually the result of constructing only one of the possible models of the premises. (shrink)

This paper reports three studies of temporal reasoning. A problem of the following sort, where the letters denote common everyday events: A happens before B. C happens before B. D happens while B. E happens while C. What is the relation between D and EEfficacylls for at least two alternative models to be constructed in order to give the right answer for the right reason. However, the first premise is irrelevant to this answer, and so if reasoners were to ignore (...) it, then they would need to construct only one model. Experiment 1 showed that one-model problems were answered faster and more accurately than multiple-model problems. When the question preceded the premises in the statement of the multiple-model problems there was a slight tendency for the latencies of response to speed up in the predicted way. Experiment 2 modified the procedure, in part by using practice problems with many irrelevant premises, so that reasoners might grasp the advantage of ignoring them. Its results showed that when the premises preceded the question, the multiple-model problems were significantly harder than one-model problems. But when the question was presented first, the difference was significantly reduced in line with the theory's prediction. Experiment 3 used only problems with valid conclusions, and so the construction of multiple models was never necessary. However, there was still a significant difference between one-model problems and multiple-model problems. (shrink)

The communicative theory of emotions postulates that emotions are communications both within the brain and between individuals. Basic emotions owe their evolutionary origins to social mammals, and they enable human beings to use repertoires of mental resources appropriate to recurring and distinctive kinds of events. These emotions also enable them to cooperate with other individuals, to compete with them, and to disengage from them. The human system of emotions has also grafted onto basic emotions propositional contents about the cause of (...) the emotion, the self, and other matters. Complex emotions always contain such contents, whereas basic emotions can be experienced without them. This article explains the role of basic emotions in social relationships, their effects on reasoning, and their pathology in psychological illness, such as depression and obsessive-compulsive disorder. (shrink)

This paper explores the ways in which Wilbur and Orville Wright thought as they tackled the problem of designing and constructing a heavier-than-air craft that would fly under its own power and under their control. It argues that their use of analogy and their use of knowledge in diagnostic reasoning lies outside the scope of current psychological theories and their computer implementations. They used analogies based on mental models of one system, such as the wings, to help them to develop (...) theories of another system, such as the propellers. They were also skilled reasoners, who were adept at finding counterexamples to arguments. (shrink)

Abstract Theories of induction in psychology and artificial intelligence assume that the process leads from observation and knowledge to the formulation of linguistic conjectures. This paper proposes instead that the process yields mental models of phenomena. It uses this hypothesis to distinguish between deduction, induction, and creative forms of thought. It shows how models could underlie inductions about specific matters. In the domain of linguistic conjectures, there are many possible inductive generalizations of a conjecture. In the domain of models, however, (...) generalization calls for only a single operation: the addition of information to a model. If the information to be added is inconsistent with the model, then it eliminates the model as false: this operation suffices for all generalizations in a Boolean domain. Otherwise, the information that is added may have effects equivalent (a) to the replacement of an existential quantifier by a universal quantifier, or (b) to the promotion of an existential quantifier from inside to outside the scope of a universal quantifier. The latter operation is novel, and does not seem to have been used in any linguistic theory of induction. Finally, the paper describes a set of constraints on human induction, and outlines the evidence in favor of a model theory of induction. (shrink)

This paper replies to Politzer’s (2007) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.

The theory of mental models postulates that meaning and knowledge can modulate the interpretation of conditionals. The theory's computer implementation implied that certain conditionals should be true or false without the need for evidence. Three experiments corroborated this prediction. In Experiment 1, nearly 500 participants evaluated 24 conditionals as true or false, and they justified their judgments by completing sentences of the form, It is impossible that A and ___ appropriately. In Experiment 2, participants evaluated 16 conditionals and provided their (...) own justifications, which tended to be explanations rather than logical justifications. In Experiment 3, the participants also evaluated as possible or impossible each of the four cases in the partitions of 16 conditionals: A and C, A and not-C, not-A and C, not-A and not-C. These evaluations corroborated the model theory. We consider the implications of these results for theories of reasoning based on logic, probabilistic logic, and suppositions. (shrink)

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. (shrink)

We describe a dual-process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non-numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, (...) for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non-numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P, P, P, disjunctions: P, P, P, and conditional probabilities P, P, P. They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning. (shrink)

Two experiments investigated inferences based on suppositions. In Experiment 1, the subjects decided whether suppositions about individuals' veracity were consistent with their assertions—for example, whether the supposition “Ann is telling the truth and Beth is telling a lie”, is consistent with the premises: “Ann asserts: I am telling the truth and Beth is telling the truth. Beth asserts: Ann is telling the truth”. It showed that these inferences are more difficult than ones based on factual premises: “Ann asserts: I live (...) in Dublin and Beth lives in Dublin”. There was no difference between problems about truthtellers and liars, who always told the truth or always lied, and normals, who sometimes told the truth and sometimes lied. In Experiment 2, the subjects made inferences about factual matters set in three contexts: a truth-inducing context in which friends confided their personality characteristics, a lie-inducing context in which business rivals advertised their products, and a neutral context in which computers printed their program characteristics. Given the supposition that the individuals were lying, it was more difficult to make inferences in a truth-inducing context than in the other two contexts. We discuss the implications of our results for everyday reasoning from suppositions, and for theories of reasoning based on models or inference rules. (shrink)

Four experiments examined the strategies that individuals develop in sentential reasoning. They led to the discovery of five different strategies. According to the theory proposed in the paper, each of the strategies depends on component tactics, which all normal adults possess, and which are based on mental models. Reasoners vary their use of tactics in ways that are not deterministic. This variation leads different individuals to assemble different strategies, which include the construction of incremental diagram corresponding to mental models, and (...) the pursuit of the consequences of a single model step by step. Moreover, the difficulty of a problem (i.e. the number of mental models required by the premises) predisposes reasoners towards certain strategies. Likewise, the sentential connectives in the premises also bias reasoners towards certain strategies, e.g., conditional premises tend to elicit reasoning step by step whereas disjunctive premises tend to elicit incremental diagrams. (shrink)

This second volume in the Counterpoints Series focuses on alternative models of visual-spatial processing in human cognition. The editors provide a historical and theoretical introduction and offer ideas about directions and new research designs.

We report three experimental studies of reasoning with double conditionals, i.e. problems based on premises of the form: If A then B. If B then C. where A, B, and C, describe everyday events. We manipulated both the logical structure of the problems, using all four possible arrangements (or “figures” of their constituents, A, B, and C, and the believability of the two salient conditional conclusions that might follow from them, i.e. If A then C, or If C then A. (...) The experiments showed that with figures for which there was a valid conclusion, the participants more often, and more rapidly, drew the valid conclusion when it was believable than when it was unbelievable. With figures for which there were no valid conclusions, the participants tended to draw whichever of the two conclusions was believable. These results were predicted by the theory that reasoning depends on constructing mental models of the premises. (shrink)

We report three experimental studies of reasoning with double conditionals, i.e. problems based on premises of the form: If A then B. If B then C. where A, B, and C, describe everyday events. We manipulated both the logical structure of the problems, using all four possible arrangements (or ''figures" of their constituents, A, B, and C, and the believability of the two salient conditional conclusions that might follow from them, i.e. If A then C , or If C then (...) A . The experiments showed that with figures for which there was a valid conclusion, the participants more often, and more rapidly, drew the valid conclusion when it was believable than when it was unbelievable. With figures for which there were no valid conclusions, the participants tended to draw whichever of the two conclusions was believable. These results were predicted by the theory that reasoning depends on constructing mental models of the premises. (shrink)

Good reasoning can lead to success; bad reasoning can lead to catastrophe. Yet it's not obvious how we reason, and why we make mistakes. This book by one of the pioneers of the field, Philip Johnson-Laird, looks at the mental processes that underlie our reasoning. It provides the most accessible account yet of the science of reasoning.

People reject ‘paradoxical’ inferences, such as: Luisa didn't play music; therefore, if Luisa played soccer, then she didn't play music. For some theorists, they are invalid for everyday conditionals, but valid in logic. The theory of mental models implies that they are valid, but unacceptable because the conclusion refers to a possibility inconsistent with the premise. Hence, individuals should accept them if the conclusions refer only to possibilities consistent with the premises: Luisa didn't play soccer; therefore, if Luisa played a (...) game then she didn't play soccer. Two experiments corroborated this prediction for three sorts of ‘paradox’, including a disjunctive paradox. (shrink)

(2013). The processes of inference. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 4-20. doi: 10.1080/19462166.2012.674060.

In this study on deduction, the authors argue that people reason by imagining the relevant state of affairs, ie building an internal model of it, formulating a tentative conclusion based on this model and then searching for alternative models.

Some philosophers argue that the principles of human reasoning are impeccable, and that mistakes are no more than momentary lapses in “information processing”. This article makes a case to the contrary. It shows that human reasoners commit systematic fallacies. The theory of mental models predicts these errors. It postulates that individuals construct mental models of the possibilities to which the premises of an inference refer. But, their models usually represent what is true in a possibility, not what is false. This (...) procedure reduces the load on working memory, and for the most part it yields valid inferences. However, as a computer program implementing the theory revealed, it leads to fallacious conclusions for certain inferences—those for which it is crucial to represent what is false in a possibility. Experiments demonstrate the variety of these fallacies and contrast them with control problems, which reasoners tend to get right. The fallacies can be compelling illusions, and they occur in reasoning based on sentential connectives such as “if” and “or”, quantifiers such as “all the artists” and “some of the artists”, on deontic relations such as “permitted” and “obligated”, and causal relations such as “causes” and “allows”. After we have reviewed the principal results, we consider the potential for alternative accounts to explain these illusory inferences. And we show how the illusions illuminate the nature of human rationality. (shrink)

Good reasoning can lead to success; bad reasoning can lead to catastrophe. Yet, it's not obvious how we reason, and why we make mistakes. This new book by one of the pioneers of the field, Philip Johnson-Laird, looks at the mental processes that underlie our reasoning. It provides the most accessible account yet of the science of reasoning.

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (shrink)

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it occurs. (...) The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning. (shrink)