Toward Probabilistic Natural Logic for Syllogistic Reasoning
Fangzhou Zhai

Abstract:
Logic emerged as the discipline of reasoning and its syllogistic fragment investigates one of the most fundamental aspect of human reasoning. However, empirical studies have shown that human inference differs from what is characterized by traditional logical validity. In order to better characterize the patterns of human reasoning, psychologists and philosophers have proposed a number of theories of syllogistic reasoning. We contribute to this endeavor by proposing a model based on natural logic with empirically weighted inference rules. Following the mental logic tradition, our basic assumptions are, firstly, natural language sentences are the mental representation of reasoning; secondly, inference rules are among the basic mental operations of reasoning; thirdly, subjects make guesses that depend on a few heuristics. We implemented the model and trained it with the experimental data. The model was able to make around 95% correct predictions and, as far as we can see from the data we have access to, it outperformed all other syllogistic theories. We further discuss the psychological plausibility of the model and the possibilities of extending the model to cover larger fragments of natural language.