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Recursive loops in informal algorithms are difficult to formulate, even for na ̈ıve adults (Khemlani et al., 2013).Children can formulate algorithms that do not require loops (Bucciarelli et al., 2016), and anecdotal evidence suggests thatthey can understand loops. As there were no previous studies, we examined how they made deductions of the consequencesof loops, and how they abduced loops in creating informal algorithms in everyday language. We therefore tested fifth-gradechildren’s ability carry out both these tasks in algorithms that rearrange the order of cars on a toy railway track with onesiding. Experiment 1 showed that they could deduce rearrangements from algorithms containing loops, and Experiment 2showed that they could formulate at least some algorithms that contained loops. These abilities are the likely precursors to thecomprehension of recursion and to computer programming.

The mental model theory postulates that reasoners build models of the situations described in premises, and that each model represents a possibility. The present paper proposes that causal relations, such as A causes B and A allows B. have meanings thatconcern only possibilities and a temporal constraint that B cannot precede A. This theory predicts that causes and enabling conditions differ in meanings, contrary to a long tradition in philosophy and psychology that they are logically indistinguishable. It also predicts that individuals should reason about causation on the basis of mental models rather than on fully explicit models. Three experiments corroborated these predictions.

The mental model theory of reasoning postulates that reasoners build models of the situations described in premises, and that these models normally make explicit only what is true. The theory has an unexpected consequence: it predicts the occurrence of inferences that are systematically invalid. These inferences should arise from reasoners failing to take into account what is false. We report an experiment that corroborated the occurrence of these illusory inferences, and that eliminated a number of altemative explanations for them. Results illuminate the controversy among various current theories of reasoning.

This paper presents a new theory of modal reasoning, i.e. reasoning about what may or may not be the case, and what must or must not be the case. A conclusion is possible if it holds in at least one mental model, whereas it is necessary if it holds in all the models. The theory makes a crucial prediction, which we corroborated experimentally. There is a key interaction: it is easier to infer that a situation is possible as opposed to impossible, whereas it is easier to infer that a situation is not necessary as opposed to necessary.

The mental model theory postulates that reasoners build models of the situations described in premises. A conclusion is possible if it occurs in at least one model; and it is impossible if it occurs in no models. According to the theory, reasoners can cope with what is true, but not with what is false. A computer implementation predicted that certain inferences should yield cognitive illusions, i.e. they have conclusions that should seem highly plausible but that are in reality gross errors. Experiment 1 showed that, as predicted, participants erroneously inferred that impossible situations were possible, and that possible situations were impossible, but they performed well with control problems. Experiment 2 replicated these results, using the same premises for both the illusory and the control inferences: the participants were susceptible both to illusions of possibility and to illusions of impossibility, but they coped with the control problems.

The mental model theory postulates that reasoners build models of the situations described in premises. A conclusion is possible if it occurs in at least one model; it is probable if occurs in most models; and it is necessary if it occurs in all models. The theory also postulates that reasoners represent as much information as possible in implicit models. Experiment 1 showed that, as predicted, conclusions about possible situations tend to correspond to explicit models rather than to implicit models. Experiment 2 yielded a discovery: there are illusory inferences with conclusions that seem plausible but that are in reality gross errors. In such cases, as the model theory predicts, subjects judge as the more probable of two events one that is impossible. For example, given that only one of the following two assertions is true: There is a king or an ace in the hand, or both. There is a queen or an ace in the hand, or both. subjects judge that the ace is more likely to be in the hand than the king. In fact, it is impossible for an ace to be in the hand.

The paper describes a theory of temporal reasoning and its implementation in a computer program. The theory postulates that individuals construct mental models, and it predicts that inferences that call for only one model to be constructed, such as: a happens before b. b happens before c. d happens while b. e happens while c. What is the temporal relation between d and e? will be easier than those that call for multiple models, such as a problem identical to the previous one except for its first premise: a happens before c. Experiment 1 showed that subjects were faster and more accurate with one-model problems than with multiple-model problems. They look more time to read a premise leading to multiple models than the corresponding premise in a one-model problem. Experiment 2 showed that if the question came first and was presented with all the premises, then subjects can ignore an irrelevant premise. As predicted, the difference between one-model and multiple-model problems with valid conclusions then disappeared. Experiment 3 showed that the size of a model, i.e., the number of events in it, and the distance apart of the critical events, also affected performance.

A cognitive account of propositional reasoning must consider both the representation of the propositions (premises and states of affairs) and the context in which the propositions are used. This paper is concerned with reasoning processes involving three different connectives (conjunctive, conditional and disjunctive connectives) in three different tasks (accomplishing a request for action expressed by a premise, judging a state of affairs as true or false with respect to a premise, drawing an inference from two premises). Our claim is that the ability to reason with connectives is explained in terms of construction and manipulation of mental models. We present a computer model that takes as input the modelistic representations of the premises and the speciHc state of affairs, compares such models and gives rise to a series of model manipulations in order to produce a result, i.e. an action, a judgement or an inference. A computer program reproduces the performances of subjects of different age groups, predicting both correct and erroneous inferences.

We describe an algorithm that constructs mental models of assertions containing sentential connectives, such as and. if, and or. It performs at three levels of expertise depending on the completeness of the models it constructs. At a rudimentary level of performance, it constructs models that make explicit as little as possible. One unexpected consequence is that it produces the same explicit models for assertions of the form: if p then q, and if r then s if p then q, 21 if r then s p and q, 01 r and s. W e initially suspected that there was a bug in the algorithm (or theory), but there was not. W e therefore carried out two experiments with logically-untrained subjects. Their results confirmed the phenomena: for many individuals, a conjunction of conditionals is equivalent to their disjunction, which in turn is equivalent to a disjunction of conjunctions.