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.

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三段论推理中的逻辑、​​概率和语用学

三段论推理位于语言和逻辑的自然推理和形式推理的有趣交汇处。三段论包含一个正式的推理系统，但使用自然语言量词（例如，所有、一些) 并邀请自然语言得出结论。然而，人们倾向于从三段论中得出的结论与纯粹的逻辑系统有很大的不同。自然语言理解的原则是罪魁祸首吗？我们介绍了三段论推理的概率语用观点：我们将自然语言论证的推理分解为两个子问题：语言理解和语言产生。我们在 Rational Speech Act 框架内将这些过程的模型形式化，并探索实用推理对结论产生的压力。我们在最近的大型三段论推理数据集上测试我们的模型，发现从三段论中选择结论的过程最好建模为务实的说话者，其目标是将天真的听众的信念与他们自己的信念保持一致。我们将我们的模型与之前发布的模型进行了比较，这些模型实现了两种替代理论——心理模型和概率启发式——发现我们的模型定量地预测了响应的完整分布，与以前的账户一样或更好，但参数要少得多。我们的研究结果表明，最好不要将人类三段论推理理解为对理想逻辑推理的不良近似，而是将其理解为支持自然交流的理性概率推理。