# 归纳逻辑

> 【EN】An inductive logic is a system of reasoning that articulates how evidence claims bear on the truth of hypotheses. As with any logic, it does this via the evaluation of arguments. Each argument consists of premise statements and a conclusion statement. A logic employs principles and rules to evaluate the extent to which the truth of an argument’s premise statements support the truth of its conclusion statement. In a deductive logic the truth of the premises of a good argument guarantees the truth of its conclusion. Good deductive arguments are called deductively valid ; their premises are said to logically entail their conclusions, where logical entailment means that every logically possible state of affairs that makes the premises true also makes the conclusion true. … 【中】该词条把归纳逻辑界定为一种通过评估论证来刻画证据如何影响假设为真的推理系统。论证由前提与结论构成，逻辑用原则与规则衡量支持度。与演绎逻辑中前提保证结论不同，归纳只给予一定程度的支持。词条讨论支持函数的逻辑公理、贝叶斯定理的比率形式与几率形式、贝叶斯区间估计、辅助假设的认识论地位与似然不精确的情形。

- ID: m13248
- 分类: structure
- 领域: 逻辑学

## 定义

归纳逻辑是一套通过评估论证来刻画证据陈述如何影响假设为真的推理系统。与演绎逻辑不同，好归纳论证的前提之真并不保证结论为真，只给予某种程度的支持。 脚手架作用：- 证据评估：用似然比衡量一条证据对竞争假设的支持强弱 - 信念更新：按贝叶斯定理把新证据折算为置信度的移动 - 预测外推：据已有样本估计未观察个例落入某类的概率

## 机制

归纳支持被形式化为概率式的支持函数：给定背景假设与证据，假设的确信度按贝叶斯定理更新，证据的区分力体现在似然比上——同一证据对竞争假设的支持强弱之比，决定了置信度往哪边移动。因此支持度不是二值的，而是随证据积累连续变化。

## 练习

1) 列出待检验的假设与若干竞争假设；2) 明确证据，并估计各假设下该证据出现的似然；3) 用贝叶斯定理的比率或几率形式更新置信度；4) 检验结论对先验设定与辅助假设是否敏感。

## 脚手架用法

- 证据评估：用似然比衡量一条证据对竞争假设的支持强弱 - 信念更新：按贝叶斯定理把新证据折算为置信度的移动 - 预测外推：据已有样本估计未观察个例落入某类的概率

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