合情推理与一阶合情逻辑 / Plausible Reasoning and First-Order Plausible Logic
1️⃣ 一句话总结
本文提出了一套用于进行合情推理(即基于大概率成立但偶尔会错的陈述进行推理,不涉及概率计算)的逻辑原则,并定义了一种一阶逻辑系统——合情逻辑(PL),它能够满足大部分原则并正确处理所有经典案例,是目前已知唯一具备此能力的逻辑系统。
Defeasible statements are statements that are likely, or probable, or usually true, but may occasionally be false. Plausible reasoning makes conclusions from statements that are either facts or defeasible statements without using numbers. So there are no probabilities or suchlike involved. Seventeen principles of logics that do plausible reasoning are suggested and several important plausible reasoning examples are considered. There are 14 necessary principles and 3 desirable principles, one of which is not formally stated. A first-order logic, called Plausible Logic (PL), is defined that satisfies all but two of the desirable principles and reasons correctly with all the examples. As far as we are aware, this is the only such logic. PL has 8 reasoning algorithms because, from a given plausible reasoning situation, there are different sensible conclusions. This article is a condensation of my book `Plausible Reasoning and Plausible Logic' (PRPL), which is to be submitted. Each section of this article corresponds to a chapter in PRPL, and vice versa. The proofs of all the results are in PRPL, so they are omitted in this article.
合情推理与一阶合情逻辑 / Plausible Reasoning and First-Order Plausible Logic
本文提出了一套用于进行合情推理(即基于大概率成立但偶尔会错的陈述进行推理,不涉及概率计算)的逻辑原则,并定义了一种一阶逻辑系统——合情逻辑(PL),它能够满足大部分原则并正确处理所有经典案例,是目前已知唯一具备此能力的逻辑系统。
源自 arXiv: 2604.19036