Modality, probability, and mental models.

Abstract

We report 3 experiments investigating novel sorts of inference, such as: A or B or both. Therefore, possibly (A and B). Where the contents were sensible assertions, for example, . Most participants accepted the inferences as valid, though they are invalid in modal logic and in probabilistic logic too. But, the theory of mental models predicts that individuals should accept them. In contrast, inferences of this sort—A or B but not both. Therefore, A or B or both—are both logically valid and probabilistically valid. Yet, as the model theory also predicts, most reasoners rejected them. The participants’ estimates of probabilities showed that their inferences tended not to be based on probabilistic validity, but that they did rate acceptable conclusions as more probable than unacceptable conclusions. We discuss the implications of the results for current theories of reasoning.

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

“…But it is not valid in the model theory, because its premise does not support the possibility of both A and B . As the model theory predicts, almost no participants (3%) accepted such inferences from an exclusive to an inclusive disjunction (Hinterecker et al., , Experiment 1). Skeptics might argue that the participants based their decision on the clash between “but not both” and “or both.” But this argument fails to explain why more participants (24%) accepted the inference from an inclusive to an exclusive disjunction: A or B or both. Therefore, A or B but not both. …”

“…The program makes the same predictions regardless of the values of its two parameters for the data from Hinterecker et al. (; Experiment 3). Fig.…”

“…Top right panel: Data from Hinterecker et al. (), which tests the theory's second prediction. Bottom panel : Data from Khemlani and Johnson‐Laird (, Experiment 2), which tests the theory's third prediction.…”

“…Top left panel: Data from Hinterecker et al. (), which tests the theory's first prediction (see Table ). Top right panel: Data from Hinterecker et al.…”

Mental Models are Compatible with Logical Forms

“…Its main theses are to be found in many works (e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). However, the most important aspects of it for this paper are related to language.…”