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Toward probabilistic natural logic for syllogistic reasoning

Natural language contains an abundance of reasoning patterns. Historically, there have been many attempts to capture their rational usage in normative systems of logical rules. However, empirical studies have repeatedly shown that human inference differs from what is characterized by logical validity. In order to better characterize the patterns of human reasoning, psychologists have proposed a number of theories of reasoning. In this paper, we combine logical and psychological perspectives on human reasoning. We develop a framework integrating Natural Logic and Mental Logic traditions. We model inference as a stochastic process where the reasoner arrives at a conclusion following a sequence of applications of inference steps (both logical rules and heuristic guesses). We estimate our model (i.e. assign weights to all possible inference rules) on a dataset of human syllogistic inference while treating the derivations as latent variables in our model. The computational model is accurate in predicting human conclusions on unseen test data (95% correct predictions) and outperforms other previous theories. We further discuss the psychological plausibility of the model and the possibilities of extending the model to cover larger fragments of natural language.