多视角推理是AI处理冲突信息的核心挑战,做知识表示与推理的研究者可以关注这个复杂度不变的理论突破,直接用于多智能体或争议性知识库场景。
本文提出将KLM可废止逻辑与立场逻辑相结合,形式化表达多个可能矛盾视角下的可废止信念。作者利用可废止受限立场逻辑(DRSL),为DRSL语义提供了基础表示结果,并系统地将多种命题蕴涵关系提升到立场增强场景。研究还展示了如何通过语义和算法手段提升优先蕴涵及基于单排序函数的蕴涵关系(包括理性和词典序闭包)。关键发现是,从命题KLM到DRSL,每种蕴涵检查的复杂度类保持不变。
Standpoint Logics with Defeasible Beliefs
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.