Towards Propositional KLM-Style Defeasible Standpoint Logics

TL;DR

This paper introduces Defeasible Restricted Standpoint Logic (DRSL), integrating standpoint reasoning into propositional KLM logic, providing a formal framework for multiple viewpoints with exceptions, and characterizing rational closure both algorithmically and semantically.

Contribution

It presents the first formal system combining standpoint logic with KLM defeasible reasoning, defining semantics and algorithms for rational closure in this integrated framework.

Findings

Rational closure for DRSL is characterized by a single ranked standpoint structure.

Semantic and algorithmic characterizations of rational closure are equivalent.

Entailment-checking complexity for DRSL matches that of propositional KLM.

Abstract

The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning new contradictory information. Standpoint logics are a group of logics, introduced to the field of Knowledge Representation in the last 5 years, which allow for multiple viewpoints to be integrated into the same ontology, even when certain viewpoints may hold contradicting beliefs. In this paper, we aim to integrate standpoints into KLM propositional logic in a restricted setting. We introduce the logical system of Defeasible Restricted Standpoint Logic (DRSL) and define its syntax and semantics. Specifically, we integrate ranked interpretations and standpoint structures, which provide the semantics for propositional KLM and propositional standpoint logic respectively, in order to introduce ranked standpoint structures for DRSL. Moreover, we extend the non-monotonic entailment relation of rational closure from the propositional KLM case to the DRSL case. The main contribution of this paper is to characterize rational closure for DRSL both algorithmically and semantically, showing that rational closure can be characterized through a single representative ranked standpoint structure. Finally, we conclude that the semantic and algorithmic characterizations of rational closure are equivalent, and that entailment-checking for DRSL under rational closure is in the same complexity class as entailment-checking for propositional KLM.