用信息论量化概念间的内涵继承关系，揭示其与外延继承的本质联系。
Intensional Inheritance Between Concepts: An Information-Theoretic Interpretation
- 基于信息论定义概念间内涵继承的量化公式，融合属性交互信息。
- 在属性互斥情形下推导出两种理论框架下的继承值，具可计算性。
- 揭示外延继承是内涵继承的特例，为概念推理提供统一数学基础。
本文旨在形式化并量化两个概念之间的‘内涵继承’概念。我们将概念F对概念W的内涵继承定义为命题‘x是F’对命题‘x是W’所提供的信息量。为此，考虑由属性集{F₁, F₂, …, Fₙ}和{W₁, W₂, …, Wₘ}及其对应度量{d₁, d₂, …, dₙ}和{e₁, e₂, …, eₘ}定义的概念，属性间可能存在重叠。通过香农信息论与算法信息论推导出包含属性间交互信息的内涵继承公式。研究了所有属性互斥的特殊情况，并在两种框架下计算了该情形下的继承值。同时基于互信息公式推导出P(W|F)的表达式。最后探讨了内涵继承与传统集合论‘外延继承’的关系，结论表明在本信息论框架下，外延继承是内涵继承的一个特例。
原文摘要 · Abstract (English)
This paper addresses the problem of formalizing and quantifying the concept of "intensional inheritance" between two concepts. We begin by conceiving the intensional inheritance of $W$ from $F$ as the amount of information the proposition "x is $F$ " provides about the proposition "x is $W$. To flesh this out, we consider concepts $F$ and $W$ defined by sets of properties $\left\{F_{1}, F_{2}, \ldots, F_{n}\right\}$ and $\left\{W_{1}, W_{2}, \ldots, W_{m}\right\}$ with associated degrees $\left\{d_{1}, d_{2}, \ldots, d_{n}\right\}$ and $\left\{e_{1}, e_{2}, \ldots, e_{m}\right\}$, respectively, where the properties may overlap. We then derive formulas for the intensional inheritance using both Shannon information theory and algorithmic information theory, incorporating interaction information among properties. We examine a special case where all properties are mutually exclusive and calculate the intensional inheritance in this case in both frameworks. We also derive expressions for $P(W \mid F)$ based on the mutual information formula. Finally we consider the relationship between intensional inheritance and conventional set-theoretic "extensional" inheritance, concluding that in our information-theoretic framework, extensional inheritance emerges as a special case of intensional inheritance.
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