Philip Johnson

Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. The structure of mental models is iconic as far as possible. The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. Individuals tend to construct only a single, typical model. They spontaneously develop their own strategies for relational reasoning. Regardless of strategy, the difficulty of an inference depends on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principle

The mental model theory postulates that reasoners build models of the situations described in premises, and that these models normally represent only what is true. The theory has an unexpected consequence. It predicts the existence ofillusions in inferences. Certain inferences should have compelling but erroneous conclusions. Two experiments corroborated the occurrence of such illusions in inferences about what is possible from disjunctions of quantified assertions, such as, “at least some of the plastic beads are not red.” Experiment 1 showed that participants erroneously inferred that impossible situations were possible, and that possible situations were impossible, but that they performed well with control problems based on the same premises. Experiment 2 corroborated these findings in inferences from assertions based on dyadic relations, such as, “all the boys played with the girls.”

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

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

The mental model theory predicts that reasoners normally represent what is true, but not what is false. One consequence is that reasoners should make "illusory" inferences, which are compelling but invalid. Three experiments confirmed the existence of such illusions based on disjunctions of disjunctions. They also established a successful antidote to them: Reasoners are much less likely to succumb to illusions if the inferences concern disjunctions of physical objects (alternative newspaper advertisements) rather disjunctions of the truth values of assertions. The results shed light both on the cause of the illusions and on the current controversy among different theories of reasoning.

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

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

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.

The mental model theory postulates that reasoners build models of the situations described in premises. A conclusion is possible if it holds in at least one model of the premises; it is probable if it holds in most of the models; and it is necessary if it holds in all of the models. The theory also postulates that reasoners represent as little information as possible in explicit models and, in particular, that they represent only information about what is true. One unexpected consequence of this assumption is that there should be a category of illusory inferences: they will have conclusions that seem obvious, but that are wholly erroneous. Experiment 1 established the existence of such illusory inferences about probabilities. Overall, 88% of the intelligent adult subjects chose as more probable an outcome that was impossible for at least one of the illusory problems. Experiment 2 corroborated the phenomenon and showed that illusory inferences include a wide variety of problems. Finally, the paper argues that current theories based on formal rules of inference are unlikely to be able to explain the illusions

This chapter describes the main accounts of deductive competence, which explain what is computed in carrying out deductions. It argues that people have a modicum of competence, which is useful in daily life and a prerequisite for acquiring logical expertise. It outlines the three main sorts of theory of deductive performance, which explain how people make deductions: They rely on factual knowledge, formal rules, or mental models. It reviews recent experimental studies of deductive reasoning in order to help readers to assess these theories of performance

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