Standpoint Logics with Defeasible Beliefs

2026-06-07

AI Summary

This work addresses the formal representation and reasoning of defeasible beliefs under multiple perspectives by integrating Kraus–Lehmann–Magidor (KLM) defeasible logic with standpoint logic, yielding Defeasible Restricted Standpoint Logics (DRSL). By introducing preference models, ranking functions, and a KLM-style axiomatic system, the paper establishes the first foundational representation theorem for DRSL. It systematically extends classical entailment relations—such as rational closure and lexicographic closure—from propositional settings to standpoint-enriched scenarios. The resulting framework achieves a unified semantic and algorithmic treatment of multi-perspective defeasible reasoning while preserving the original computational complexity of the underlying logics.

Abstract

In this paper, we integrate the defeasible logic of Kraus, Lehmann and Magidor (KLM) with the standpoint logic framework of Gómez Álvarez and Rudolph. This is done with the goal of formally expressing knowledge taking into account multiple (possibly contradicting) viewpoints, which in turn may hold defeasible beliefs. In doing so, we utilise Defeasible Restricted Standpoint Logics (DRSL), introduced by Leisegang et al. Our work expands on previous work by providing a foundational representation result for DRSL semantics and systematically lifting several well-known entailment relations from the propositional case to the standpoint-enhanced setting. In particular, we characterise the semantics for DRSL through a set of KLM-style postulates adapted for the standpoints case. We furthermore provide a means to lift preferential entailment, and the class of entailment relations based on single ranking functions from the purely propositional to the standpoint-enhanced context, including rational and lexicographic closure. We show this can be done equivalently through semantic and algorithmic means. Furthermore, we show that, for each considered form of entailment, the complexity class of entailment checking does not change when moving from propositional KLM to DRSL.

Problem

• standpoint logic
• defeasible beliefs
• multiple viewpoints
• knowledge representation
• non-monotonic reasoning

Innovation

• Defeasible Logic
• Standpoint Logic
• Preferential Entailment
• Rational Closure
• Computational Complexity