将非单调推理引入立场逻辑,实现观点间的合理推断。
Towards Non-Monotonic Entailment in Propositional Defeasible Standpoint Logic
- 用情境化条件句扩展立场逻辑,表达特定观点下的默认推理
- 提出方法将命题逻辑中的理性蕴含迁移至立场逻辑片段
- 保持原有复杂度,适合形式化推理与多视角决策研究者
近期缺陷推理研究将Kraus等人风格的优先语义和单调蕴含引入模态逻辑,但主要聚焦于可满足性判断与单调蕴含,可能推导能力较弱。在命题立场逻辑中,模态词可表示不同观点,已形成命题缺陷立场逻辑(PDSL)。本文提出将经典KLM风格的非单调理性蕴含关系推广至PDSL的一个片段。通过引入情境化立场条件句,使条件句可在特定观点背景下成立,重构了PDSL的语法表达。研究表明,该片段可由一系列情境化条件句表征。进一步定义了从命题情形到PDSL情形的排名型蕴含关系转移方法,涵盖理性闭包与词典序闭包两种具体情形,并实现忠实翻译。同时证明,该片段的蕴含判定可主要沿用命题情形的算法,且保持相同的复杂度界。
原文摘要 · Abstract (English)
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics. However, work in this field has focussed primarily on satisfiability checking, and monotonic notions of entailment, which may be inferentially weak. One particular modal logic where this has been introduced is propositional standpoint logics, where modalities can express the views of different viewpoints. This has resulted in the formalisation of propositional defeasible standpoint logic (PDSL). In this paper, we propose a means of lifting the class of (non-monotonic) rational entailment relations from traditional KLM-style reasoning to a fragment of PDSL. In order to do so, we extend the expressivity of PDSL via situated standpoint conditionals, allowing us to talk about a defeasible conditional holding in the context of a given standpoint. This allows us to re-characterise the syntax of PDSL in terms of situated conditionals, and shows that a large fragment of PDSL is expressible as a set of situated conditionals. We then focus on characterising non-monotonic entailment in this fragment, defining a method to transport any ranking-based entailment relation from the propositional case into the PDSL case. This is first described in the general case and then considered in the specific cases of rational and lexicographic closures, providing a faithful translation of each inference into PDSL. We also show that entailment-checking in this fragment of PDSL can be done largely using algorithms from the propositional case, while preserving complexity bounds.
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