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

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.

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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

Reasoning from connectives and relations between entities

This article reports investigations of inferences that depend both on connectives between clauses, such as or else, and on relations between entities, such as in the same place as. Participants made more valid inferences from biconditionals—for instance, Ann is taller than Beth if and only if Beth is taller than Cath—than from exclusive disjunctions (Exp. 1). They made more valid transitive inferences from a biconditional when a categorical premise affirmed rather than denied one of its clauses, but they made more valid transitive inferences from an exclusive disjunction when a categorical premise denied rather than affirmed one of its clauses (Exp. 2). From exclusive disjunctions, such as Either Ann is not in the same place as Beth or else Beth is not in the same place as Cath, individuals tended to infer that all three individuals could be in different places, whereas in fact this was impossible (Exps. 3a and 3b). The theory of mental models predicts all of these results

Naive Probability: Model-Based Estimates of Unique Events

Abstract 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(A), P(B), P(A and B), disjunctions: P(A), P(B), P(A or B or both), and conditional probabilities P(A), P(B), P(B|A). 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

Razonamiento con condicionales múltiples. La perspectiva de los modelos mentales

Multi-conditional problems can be used to corripare the mental model theory and mental rule theories of deductive reasoriing. The two theories make coiitrasting predictions about performance. The mental model theory relates the difficulty of a problem with the number of models the reasoner has to construct, whereas inentul rule theories explain this difficultyin terms of the number and complexity of the rues of inference to be applied. Experiment 1 tested the fivo theories using multiconditional problems and measured both accuracy and latency. The results supported the mental model theory, but there was a ceiling effect for accuracy and some unexpected time measurements. In experiment 2 the ceiling effect disappeared, and the mental rnodel theory was again corroborated. The paper discusses when reasoners are likely to construct mental models, the limitations of the human cognitive system and its strategic nature.Los problemas multi-condicionales permiten contrastar las principales teorías sobre el razonamiento deductivo, la de los "modelos mentales" y la de la "lógica mental", dado que sus predicciones sobre la ejecucidn son prácticamente opuestas. La primera relaciona la dificultad de un probleina con el número de modelos que es necesario construir, mientras que la segunda explica esta dificultad en función del número y complejidad de las reglas de inferencia que deben aplicarse. En un primer experimento comparamos ambas teorías utilizando medidas de precisión y temporales. Los resultados apoyaron la teoría de los modelos mentales, si bien encontramos un efecto techo en las medidas de precisión y algún resultadoimprevisto en las medidas ternporales. En un segundo experimento se replicaron los resultados desapareció el efecto techo, confirinándose así la teoría de los modelos mentales. Se discute cuándo es probable que los sujetos construyan los modelos en relación con las limitaciones de procesamiento del sistema cognitivo y su naturaleza estratégica

The real foundation of fictional worlds

I argue that judgements of what is ‘true in a fiction’ presuppose the Reality Assumption: the assumption that everything that is (really) true is fictionally the case, unless excluded by the work. By contrast with the more familiar Reality Principle, the Reality Assumption is not a rule for inferring implied content from what is explicit. Instead it provides an array of real-world truths that can be used in such inferences. I claim that the Reality Assumption is essential to our ability to understand stories, drawing on a range of empirical evidence that demonstrates our reliance on it in narrative comprehension. However, the Reality Assumption has several unintuitive consequences, not least that what is fictionally the case includes countless facts that neither authors nor readers could (or should) ever consider. I argue that such consequences provide no reason to reject the Reality Assumption. I conclude that we should take fictions, like non-fictions, to be about the real world