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.

翻译：近期可废止推理领域的研究将Kraus等人提出的偏好语义与蕴涵概念应用于模态逻辑。然而，该领域的研究主要聚焦于可满足性检验及单调蕴涵概念，后者在推理强度上可能较弱。作为引入此类逻辑的典型案例，命题立场逻辑中的模态词可表达不同视角的观点，由此催生了命题可废止立场逻辑（PDSL）的形式化。本文提出一种方法，将经典KLM风格推理中的（非单调）理性蕴涵关系提升至PDSL片段。为此，我们通过情境化立场条件句扩展PDSL的表达能力，使得在给定立场语境中讨论可废止条件句成为可能。据此，我们基于情境条件句重新刻画PDSL语法，证明PDSL的大部分片段可表示为情境条件句集合。接着聚焦该片段中非单调蕴涵的刻画，定义一种将命题层面的基于排序的蕴涵关系迁移至PDSL的方法。该方法首先在一般情况下进行描述，随后在理性闭包与词典闭包两类具体情况下展开讨论，为每种推理提供忠实翻译至PDSL的映射。我们还证明，该PDSL片段中的蕴涵检验可主要借助命题层面的算法完成，且保持复杂度界限不变。