知识系统中不一致性的度量理论和方法及其应用研究

Inconsistency in knowledge systems is one of most pervasive and important issues in artificial intelligence and its application domains. Recently, measuring inconsistency has been increasingly recognized as a necessary starting point for understanding the nature of inconsistency and for subsequent proper handling of the inconsistency in real-world applications. This project focuses on the following issues on theories and methods for measuring inconsistency in knowledge systems including (1) to propose a family of inconsistency measures for propositional knowledge bases based on minimal inconsistent subsets and to discuss logical properties and computational complexity issues of these measures; (2) to propose a family of inconsistency measures for nonmonotonic multi-context systems and to discuss logical properties and computational complexity systems issues of these measures; (3) to propose approaches to measuring inconsistency with constraints on resolving inconsistency; (4) to establish collections of postulates appropriate for characterizing variable-based inconsistency measures, inconsistency measures based on minimal inconsistent subsets, and inconsistency measures for nonmonotonic multi-context systems, respectively; (5) to verify the applicability of these theories and methods by an application of some inconsistency measures to requirements engineering.

知识系统中的不一致性一直是人工智能及其应用领域的重要研究问题之一。 最近， 在很多应用领域，对不一致性的度量环节被逐渐视为理解和刻画不一致性的本质特性以及进一步有效处理不一致性的重要起点。 本项目针对度量不一致性的理论和方法，主要研究：（1）构建命题知识库中基于极小不一致子集的不一致性度量， 并讨论其逻辑性质和相关计算复杂性；（2）构建非单调多上下文系统中不一致性度量， 并讨论其逻辑性质和相关计算复杂性；（3）建立带有关于消解不一致性约束的不一致性度量方法；（4） 分别建立面向基于变量的不一致性度量方法、基于极小不一致子集的不一致性度量方法、非单调多上下文系统中不一致性的度量方法的公设集；（5）不一致性度量理论和方法在需求工程中的示范应用。

本项目对知识系统中不一致性的度量理论和方法进行了系统研究，所取得的重要研究进展包括:.a)针对命题知识库的情形提出了带约束的不一致性度量理论和方法，并基于Halpern-Pearl因果模型对相关不一致性度量给予直观解释，这种直观可解释性和对约束的考虑有力地提升了不一致性相关度量理论和方法在不一致性消解决策中的适应性和可用性；.b)基于Priest的极小不一致悖论逻辑(Minimally Inconsistent Logic of Paradox)框架讨论了公式与不一致性的无关或独立性，得到了在语法层面和超协调语义层面都和不一致性无关的公式集的刻画定理，并基于这种更具一般性的刻画提出双自由公式独立性公设(Bi-free Formula Independence Postulate)来替代自由公式独立性公设(Free Formula Independence Postulate)， 改进了在刻画不一致性度量方面具有重要影响的Hunter-Konieczny公设集；.c)构建了择优多上下文系统(Preferential multi-context system )，将知识（库）优先级信息在知识系统中不一致性分析和处理方面的角色引入多上下文系统，利用与极大协调子系统相容的不一致性诊断(Diagnosis)来刻画择优多上下文系统中的不一致性；.d)基于诊断，我们引入因果分析模型定义了多上下文系统中桥规则层次(bridge-level)的不一致性度量和系统层次 (system-level)的不一致性度量；.e)我们以软件需求方面的案例作为应用案例，演示了所提出的带约束的不一致性度量理论和方法在实际应用中的可用性和有效性。

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