The modulation of disjunctive assertions

Reasoning about possibilities: Modal logics, possible worlds, and mental models

Everyone reasons about possibilities. This article explains how they could do so using mental models. The theory makes four major claims: 1. Correct inferences are necessary, referring only to facts or possibilities to which the premises refer and not ruling any of them out, for example: She left or hid; Therefore, it's possible that she left and possible that she hid. 2. A possibility such as that she hid, which is represented in an intuitive model, presupposes the possibility that it did not occur, she did not hide, which, if reasoners deliberate, is represented in the resulting model. 3. Reasoners condense consistent possibilities, such as the earlier pair, into one possibility: it is possible that she left and she hid. 4. Inconsistencies, such as she left or hid, and she neither left nor hid, refer to no possibilities whatsoever - they have an empty model - and so their only effects are local. Hence, any inference can be withdrawn with impunity if there is knowledge to the contrary. Experiments have corroborated each of these principles. They are incompatible with four essentials of standard modal logics, which concern deductions based on "possible" or "necessary". Their formal deductions correspond to valid inferences, which have no counterexamples in which the premises are true but the conclusion is false. And so the article examines the differences between the two approaches, and explores the adaptation of a modal logic to account for correct human reasoning. Its feasibility is an open question.

The Analytic Truth and Falsity of Disjunctions

Disjunctive inferences are difficult. According to the theory of mental models, it is because of the alternative possibilities to which disjunctions refer. Three experiments corroborated further predictions of the mental model theory. Participants judged that disjunctions, such as Either this year is a leap year or it is a common year are true. Given a disjunction such as Either A or B, they tended to evaluate the four cases in its 'partition': A and B, A and not-B, not-A and B, not-A and not-B, as 'possible' or 'impossible' in ways that bore out the difference between inclusive disjunctions ('or both') and exclusive disjunctions ('but not both'). Knowledge usually concerns what is true, and so when participants judge that a disjunction is false, or contingent, and evaluate the cases in its partition, they depend on inferences that yield predictable errors. They tended to judge that disjunctions, such as follows: Either the food is cold or else it is tepid, but not both, are true, though in fact they could be false. They tended to infer 'mirror-image' evaluations that yield the same possibilities for false disjunctions as those for true disjunctions. The article considers the implications of these results for alternative theories based on classical logic or on the probability calculus.

The Relation Between Factual and Counterfactual Conditionals

What is the relation between factual conditionals: If A happened then B happened, and counterfactual conditionals: If A had happened then B would have happened? Some theorists propose quite different semantics for the two. In contrast, the theory of mental models and its computer implementation interrelates them. It postulates that both can have a priori truth values, and that the semantic bases of both are possibilities: states that are possible for factual conditionals, and that were once possible but that did not happen for counterfactual conditionals. Two experiments supported these relations. Experiment 1 showed that, like factual conditionals, certain counterfactuals are true a priori, and others are false a priori. Experiment 2 replicated this result and showed that participants selected appropriate paraphrases, referring, respectively, to real and to counterfactual possibilities, for the two sorts of conditional. These results are contrary to alternative accounts of conditionals.

Facts and Possibilities: A Model-Based Theory of Sentential Reasoning

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.

Reasoning from an incompatibility: False dilemma fallacies and content effects

In the present studies, we investigated inferences from an incompatibility statement. Starting with two propositions that cannot be true at the same time, these inferences consist of deducing the falsity of one from the truth of the other or deducing the truth of one from the falsity of the other. Inferences of this latter form are relevant to human reasoning since they are the formal equivalent of a discourse manipulation called the false dilemma fallacy, often used in politics and advertising in order to force a choice between two selected options. Based on research on content-related variability in conditional reasoning, we predicted that content would have an impact on how reasoners treat incompatibility inferences. Like conditional inferences, they present two invalid forms for which the logical response is one of uncertainty. We predicted that participants would endorse a smaller proportion of the invalid incompatibility inferences when more counterexamples are available. In Study 1, we found the predicted pattern using causal premises translated into incompatibility statements with many and few counterexamples. In Study 2A, we replicated the content effects found in Study 1, but with premises for which the incompatibility statement is a non-causal relation between classes. These results suggest that the tendency to fall into the false dilemma fallacy is modulated by the background knowledge of the reasoner. They also provide additional evidence on the link between semantic information retrieval and deduction.