How People Reason about Temporal Relations

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

How to Make the Impossible Seem Probable

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

When 'Or' Means 'And': A Study in Mental models

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

Problem representations and illusions in reasoning

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

The evaluation of diagnostic explanations for inconsistencies

When individuals detect an inconsistency between a fact and their beliefs, they revise their beliefs. They also use their causal knowledge to create explanations of what led to the inconsistency. According to the theory in the present paper, an ideal explanation is a chain of a cause and an effect, where the effect explains the inconsistency. Two experiments corroborated this account. When participants evaluated explanations for inconsistencies, they rated a conjunction of a cause and its effect as more probable than the cause alone, which they rated as more probable than the effect alone. This trend violates the laws of probability – it is an instance of the "conjunction fallacy". It also violates the common assumption that individuals make minimal changes to their beliefs

Mental Models in Propositional Reasoning

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

The modulation of disjunctive assertions

The theory of mental models postulates that disjunctions of the sort, A or B, where A and B are sensible everyday clauses, have a core meaning that allows an inclusive interpretation, referring to three possibilities: A and not-B, not-A and B, and A and B. The meaning of the clauses and knowledge can modulate this meaning by blocking the construction of at least one model of a possibility, e.g., "Rui is playing tennis or he is surfing" blocks the model of Rui doing both activities. This theory is implemented in a computer program. Three experiments investigated the core interpretation and interpretations in which the contents of the clauses should block the model of A and B (as in the preceding example), the model of A and not-B, or the model of not-A and B. In Experiment 1, the participants listed the possibilities for each of the four sorts of disjunction. The results corroborated the predicted modulations. In Experiment 2, these predicted interpretations governed the conclusions that participants accepted from disjunctions and categorical premises. In Experiment 3, the predicted interpretations yielded reliable effects on the conclusions that the participants drew for themselves. We relate these results to theories of reasoning. PQJE_1154079_supplemental_material.docx.Fundação para a Ciência e a Tecnologi

Conhecimentos, modelos, e raciocínio condicional

A interpretação de frases, e em particular a interpretação de frases condicionais, pode ser modulada quer pelo significado das mesmas, pelos referentes, ou pelos conhecimentos gerais. O presente estudo examina o efeito pragmático dos conhecimentos no raciocínio a partir de pares de premissas condicionais. De acordo com a teoria dos modelos, inferências com a mesma forma, mas com conteúdos diferentes, deverão gerar um padrão de inferências diferente. Consideremos as seguintes premissas: Se a Maria não está em Paris, então ela está em França. Se a Maria está em França, então ele é estudante. A primeira premissa explora a inclusão espacial (Paris é em França), pelo que numa possibilidade Maria não está em Paris mas está em França, e noutra possibilidade Maria está em Paris e portanto está também em França. Assim, é impossível a Maria não estar em França, pelo que os indivíduos tenderão a inferir a partir da segunda premissa que ela é estudante. Em contraste, se considerarmos as seguintes premissas, que tem a mesma forma que as do exemplo anterior, mas um conteúdo diferente: Se o João não está em Roma, então ele está em França. Se o João está em França, então ele é estudante. A primeira premissa explora a exclusão espacial (Roma não é em França), pelo que numa possibilidade João não está em Roma e está em França, e noutra possibilidade ele está em Roma e não está em França. Assim, os indivíduos não têm nenhuma base para a inferência categórica de que ele é estudante, e deverão tender para a conclusão condicional de que Se o João não está em Roma então ele é estudante. Os problemas de inclusão geram menos possibilidades do que os problemas de exclusão, pelo que a teoria dos modelos prediz que os problemas de inclusão deverão ser mais fáceis do que os problemas de exclusão. O artigo relata duas experiências que corroboram as previsões da teoria dos modelos. Na Experiência 1, os participantes dão mais conclusões categóricas nas premissas de inclusão, mas apenas algumas conclusões condicionais nas premissas de exclusão. De facto, com as premissas de exclusão, obtém-se muitas conclusões outras. Para evitar isso fizemos uma segunda experiência, onde os participantes escolhem a conclusão a partir de quatro que são fornecidas: conclusão categórica; conclusão condicional; ambas; nenhuma (ao contrário da Experiência 1, onde os participantes escreviam a conclusão). A Experiência 2 replica a superioridade de conclusões categóricas com as premissas de inclusão, e encontra a superioridade de conclusões condicionais com as premissas de exclusão. ***** ABSTRACT ***** Meaning, reference, and general knowledge can all modulate the interpretation of assertions, and in particular the interpretation of conditionals. The present study examines the pragmatic effects of knowledge on reasoning from pairs of conditional premises. According to the theory of mental models, inferences of the same form but different content should yield different patterns of inference. Consider the following premises, e.g.: If Maria is not in Paris, then she’s in France. If Maria is in France, then she’s a student. The first premise exploits a spatial inclusion (Paris is in France), and so in one possibility Maria is not in Paris but is in France, and in another possibility Maria is in Paris and so she is also in France. Hence, it is impossible for Maria not to be in France, and so individuals should tend to infer from the second premise that she is a student. In contrast, consider the following premises that have the same form as those in the previous example, but a different content: If João is not in Roma, then he’s in France. If João is in France, then he’s a student. The first premise exploits a spatial exclusion (Roma is not in France), and so in one possibility João is not in Roma and is in France, and in another possibility he is Roma and so not in France. Hence, individuals have no grounds for the categorical inference that he is a student, and they should tend to infer the conditional conclusion, i.e., that If João is not in Roma, then he’s a student. The inclusion problems yield fewer possibilities than the exclusion problems, and so the model theory predicts that the inclusion problems should be easier than the exclusion problems. The paper reports two experiments that corroborated the predictions of the model theory. In Experiment 1, participants drew more categorical conclusion in the inclusion premises, but only a few drew the conditional conclusion from the exclusion premises. In fact, with de exclusion premises, we obtain many “other conclusions”. To avoid this we have made a second experiment, were participants chose a conclusion from four possibilities: the categorical conclusion, a conditional conclusion, both conclusions, or neither, instead of what happens in Experiment 1, were participants drew the conclusions for themselves from the premises. Experiment 2 replicated the superiority of categorical conclusion in the inclusion premises, and found the superiority of conditional conclusion in the exclusion premises

Mental Models in Deductive Reasoning.

Sin resumenSin resume

Temporal and spatial relations in sentential reasoning

The mental model theory postulates that the meanings of assertions, and knowledge about their context can modulate the logical meaning of sentential connectives, such as ‘‘if’’ and ‘‘or’’. One known effect of modulation is to block the representation of possibilities to which a proposition refers. But, modulation should also add relational information, such as temporal order, to models of possibilities. Three experiments tested this prediction. Experiment 1 showed that individuals spontaneously matched the tense of their conclusions (in Portuguese) to embody implied, but unexpressed, temporal relations in conditional premises. Experiment 2 demonstrated the same phenomenon in inferences from disjunctions. Experiment 3 showed that the number of such implicit relations in inferences from conditionals affects both accuracy and the speed of reasoning. These results support the modulation hypothesis