区分知识中三类否定，构建数学基础支持智能推理
Three Kinds of Negation in Knowledge and Their Mathematical Foundations
- 从概念上划分矛盾、对立、中介三类否定
- 提出SCOI与LCOI框架，证明其核心运算性质
- 为知识推理提供统一数学工具，适合逻辑与认知研究者
在人工智能领域，理解、区分、表达和计算知识中的否定是知识处理与研究的基础问题。本文分析哲学、逻辑学、语言学等领域中否定的理解与特征，基于矛盾与对立的区分，提出知识中存在三类不同类型的否定：矛盾否定、对立否定和中介否定。为建立充分反映这些否定形式内在联系、属性与规律的数学基础，本文引入包含矛盾否定、对立否定和中介否定的集合结构SCOI，以及相应的逻辑系统LCOI，并证明了SCOI的主要运算性质及LCOI中的形式推理关系。
原文摘要 · Abstract (English)
In the field of artificial intelligence, understanding, distinguishing, expressing, and computing the negation in knowledge is a fundamental issue in knowledge processing and research. In this paper, we examine and analyze the understanding and characteristics of negation in various fields such as philosophy, logic, and linguistics etc. Based on the distinction between the concepts of contradiction and opposition, we propose that there are three different types of negation in knowledge from a conceptual perspective: contradictory negation, opposite negation, and intermediary negation. To establish a mathematical foundation that fully reflects the intrinsic connections, properties, and laws of these different forms of negation, we introduce SCOI: sets with contradictory negation, opposite negation and intermediary negation, and LCOI: logic with contradictory negation, opposite negation and intermediary negation, and we proved the main operational properties of SCOI as well as the formal inference relations in LCOI.
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