将可废止逻辑与多视角立场融合,构建可处理矛盾观点的推理系统。
Towards Propositional KLM-Style Defeasible Standpoint Logics
- 引入分级立场结构,统一处理默认规则与多视角矛盾。
- 证明理性封闭可通过单一代表性结构表征,计算复杂度与经典系统相当。
- 适合研究知识表示、非单调推理与多源信息整合的学者。
KLM可废止推理方法在经典逻辑中引入弱化蕴含,使规则例外和新信息导致旧结论撤销成为可能。立场逻辑是近五年提出的知识表示框架,支持在同一个本体中整合多个可能存在矛盾观点的视角。本文在受限条件下将立场逻辑融入命题KLM逻辑,提出可废止受限立场逻辑(DRSL),定义其语法与语义。具体地,结合等级解释与立场结构,构建了适用于DRSL的等级立场结构,并将理性封闭的非单调蕴含关系从命题KLM扩展至DRSL。主要贡献在于:算法与语义双重刻画理性封闭,证明其可由单一代表性等级立场结构实现。最后,证明两种刻画等价,且在理性封闭下DRSL的蕴含判定复杂度与命题KLM同属同一复杂度类。
原文摘要 · Abstract (English)
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning new contradictory information. Standpoint logics are a group of logics, introduced to the field of Knowledge Representation in the last 5 years, which allow for multiple viewpoints to be integrated into the same ontology, even when certain viewpoints may hold contradicting beliefs. In this paper, we aim to integrate standpoints into KLM propositional logic in a restricted setting. We introduce the logical system of Defeasible Restricted Standpoint Logic (DRSL) and define its syntax and semantics. Specifically, we integrate ranked interpretations and standpoint structures, which provide the semantics for propositional KLM and propositional standpoint logic respectively, in order to introduce ranked standpoint structures for DRSL. Moreover, we extend the non-monotonic entailment relation of rational closure from the propositional KLM case to the DRSL case. The main contribution of this paper is to characterize rational closure for DRSL both algorithmically and semantically, showing that rational closure can be characterized through a single representative ranked standpoint structure. Finally, we conclude that the semantic and algorithmic characterizations of rational closure are equivalent, and that entailment-checking for DRSL under rational closure is in the same complexity class as entailment-checking for propositional KLM.
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