Modeling Human Syllogistic Reasoning: The Role of "No Valid Conclusion"

Model-Based Explanation of Feedback Effects in Syllogistic Reasoning

For decades, a significant number of models explaining human syllogistic inference processes were developed. There is profound work fitting the models' parameters and analyzing each model's ability to account for the data in order to support or reject the underlying theories. However, the model parameters are rarely used to extract explanations and hypotheses for phenomena that go beyond the original scope of the models. In this work, we apply three state-of-the-art models,  the probability heuristics model (PHM), mReasoner, and TransSet, to data from reasoning experiments where participants received feedback for their conclusions. We derived hypotheses based on the models' explanations for the feedback effect and put these to the test by conducting an experiment targeting the hypotheses. The work contributes to the field in three ways: (a) the feedback effect could be replicated and was shown to be a robust effect; (b) we demonstrate the use of the model parameters in order to derive new hypotheses; (c) we present possible explanations for the feedback effect based on existing theories.

Logic, Probability, and Pragmatics in Syllogistic Reasoning

Syllogistic reasoning lies at the intriguing intersection of natural and formal reasoning of language and logic. Syllogisms comprise a formal system of reasoning yet make use of natural language quantifiers (e.g., all, some) and invite natural language conclusions. The conclusions people tend to draw from syllogisms, however, deviate substantially from the purely logical system. Are principles of natural language understanding to blame? We introduce a probabilistic pragmatic perspective on syllogistic reasoning: We decompose reasoning with natural language arguments into two subproblems: language comprehension and language production. We formalize models of these processes within the Rational Speech Act framework and explore the pressures that pragmatic reasoning places on the production of conclusions. We test our models on a recent, large data set of syllogistic reasoning and find that the selection process of conclusions from syllogisms are best modeled as a pragmatic speaker who has the goal of aligning the beliefs of a naive listener with those of their own. We compare our model to previously published models that implement two alternative theories-Mental Models and Probability Heuristics-finding that our model quantitatively predicts the full distributions of responses as well as or better than previous accounts, but with far fewer parameters. Our results suggest that human syllogistic reasoning may be best understood not as a poor approximation to ideal logical reasoning, but rather as rational probabilistic inference in support of natural communication.