The modulation of disjunctive assertions

Abstract

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 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. Keywords: deductive reasoning, disjunctions, logic, mental models, modulationWord count: In logic, sentential connectives corresponding to if, or, and and, have constant meanings, which map the truth values of their clauses onto a truth value for the compound as a whole, e.g., an inclusive disjunction A or B or both is true if at least one of its clauses is true (Jeffrey, 1981). In daily life, the meanings of connectives vary from one assertion to another (Evans, Newstead, & Byrne, 1993), and understanding does not concern truth values (Johnson-Laird & Byrne, 1991). Consider, for instance, the difference between these two disjunctions:Filomena is eating clams or Paulo is eating sardines. and:Luís is eating gazpacho or he is eating vegetable broth.Typically, individuals are biased towards an inclusive interpretation of the first example, which includes the possibility that both of its clauses are true, but a sizeable minority prefers an exclusive interpretation (Newstead & Griggs, 1983). In contrast, individuals tend to concur that the second example is an exclusive disjunction because it A c c e p t e d M a n u s c r i p t 3 excludes the possibility that Luis is eating both sorts of soup at the same time. The theory of mental models -the "model theory" for short -postulates that understanding depends on constructing mental representations of the possibilities to which assertions refer. These representations are models that insofar as possible have a structure isomorphic to the structure of the situations to which the assertions refer. And the theory distinguishes between mental models, which represent only clauses that hold in each possibility, and fully explicit models, which also represent clauses that do not hold (see, e.g., Johnson-Laird & Byrne, 2002;Johnson-Laird, 2006; Khemlani & JohnsonLaird, 2013). Because mental models do not represent clauses that do not hold in a possibility, they predict the occurrence of "illusory" inferences in certain cases, i.e., inferences from disjunctions that are systematically fallacious. Such errors are r...

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