Towards Non-Monotonic Entailment in Propositional Defeasible Standpoint Logic

2026-06-02

AI Summary

Traditional propositional defeasible stance logic (PDSL) supports only monotonic entailment, limiting its capacity to model nonmonotonic reasoning effectively. This work addresses this limitation by incorporating KLM-style rational nonmonotonic consequence relations into a fragment of PDSL, introducing contextualized stance conditionals to enrich its syntactic expressiveness and thereby enabling nonmonotonic entailment within PDSL for the first time. By adapting techniques such as preferential semantics, ranked models, and rational closure into a modal stance logic framework, the paper establishes a faithful translation mechanism from propositional nonmonotonic logics into multi-stance contexts. The proposed approach achieves efficient nonmonotonic entailment checking while preserving the original computational complexity bounds of PDSL.

Abstract

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.

Problem

• non-monotonic entailment
• defeasible reasoning
• standpoint logic
• rational closure
• modal logic

Innovation

• non-monotonic entailment
• defeasible reasoning
• standpoint logic
• situated conditionals
• rational closure