将可驳回信念与多视角逻辑结合,形式化表达冲突观点下的知识推理。
Standpoint Logics with Defeasible Beliefs
- 融合KLM可驳回逻辑与立场逻辑,构建支持冲突观点的推理框架。
- 证明各类蕴含关系在立场增强下复杂度不变,保持计算可行性。
- 适用于需要处理多方意见且信念可被推翻的智能系统设计。
本文将Kraus、Lehmann和Magidor的可驳回逻辑(KLM)与Gómez Álvarez和Rudolph的立场逻辑框架相结合,旨在形式化表达包含多个(可能矛盾)视角的知识,这些视角本身可持有可驳回信念。为此,我们采用Leisegang等人提出的可驳回受限立场逻辑(DRSL)。本工作在先前基础上提供DRSL语义的奠基性表示结果,并系统地将若干经典命题蕴含关系从命题情形推广至立场增强设置。特别地,我们通过一组适配立场场景的KLM式公理刻画了DRSL的语义。此外,我们提出方法将偏好蕴含及基于单一排序函数的蕴含关系类(包括理性闭包与词典序闭包)从纯命题域提升至立场增强语境,并证明其语义与算法两种方式等价。同时,我们表明:对每种考虑的蕴含形式,从命题KLM到DRSL,蕴含判定的复杂度类保持不变。
原文摘要 · Abstract (English)
In this paper, we integrate the defeasible logic of Kraus, Lehmann and Magidor (KLM) with the standpoint logic framework of Gómez Álvarez and Rudolph. This is done with the goal of formally expressing knowledge taking into account multiple (possibly contradicting) viewpoints, which in turn may hold defeasible beliefs. In doing so, we utilise Defeasible Restricted Standpoint Logics (DRSL), introduced by Leisegang et al. Our work expands on previous work by providing a foundational representation result for DRSL semantics and systematically lifting several well-known entailment relations from the propositional case to the standpoint-enhanced setting. In particular, we characterise the semantics for DRSL through a set of KLM-style postulates adapted for the standpoints case. We furthermore provide a means to lift preferential entailment, and the class of entailment relations based on single ranking functions from the purely propositional to the standpoint-enhanced context, including rational and lexicographic closure. We show this can be done equivalently through semantic and algorithmic means. Furthermore, we show that, for each considered form of entailment, the complexity class of entailment checking does not change when moving from propositional KLM to DRSL.
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