Title: Advancing Non-Monotonic Entailment within Propositional Defeasible Standpoint Logic

Abstract

Recent developments in defeasible reasoning have adapted preferential semantics and entailment frameworks, inspired by Kraus et al., to various modal logics. However, existing research in this area has predominantly concentrated on satisfiability verification and monotonic entailment strategies, which can suffer from inferential limitations. This trend is evident in propositional standpoint logics, a modal system where modalities are utilized to represent distinct viewpoints, leading to the formalization of Propositional Defeasible Standpoint Logic (PDSL).

This study introduces a methodology for extending the class of non-monotonic rational entailment relations—originally rooted in traditional KLM-style reasoning—to a specific fragment of PDSL. To achieve this, we enhance PDSL’s expressive power by introducing situated standpoint conditionals. These conditionals enable the expression of defeasible implications that hold within the context of a particular standpoint. Consequently, we reformulate the syntax of PDSL using situated conditionals, demonstrating that a significant portion of PDSL can be represented as a collection of such conditionals.

We then concentrate on defining non-monotonic entailment for this fragment. We present a technique for mapping ranking-based entailment relations from the propositional domain into the PDSL framework. This approach is initially outlined in its general form before being applied to the specific contexts of rational and lexicographic closures, ensuring a faithful translation of every inference into PDSL. Furthermore, we demonstrate that entailment checking within this PDSL fragment can be largely performed using algorithms derived from the propositional case, thereby maintaining established complexity bounds.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC