---
title: "Splitting Meanings: A Unified View on Paraconsistency and Inconsistency Measurement"
authors:
  - "Yakoub Salhi"
doi: "10.24963/ijcai.2026/449"
url: "https://ijcai.org/proceedings/2026/449"
pdf: "https://ijcai.org/proceedings/2026/0449.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "4035-4043"
track: "Main Track"
keywords:
  - "Knowledge Representation and Reasoning: Non-monotonic reasoning"
  - "Knowledge Representation and Reasoning: Other"
  - "Knowledge Representation and Reasoning: Reasoning about knowledge and belief"
---

# Splitting Meanings: A Unified View on Paraconsistency and Inconsistency Measurement

Yakoub Salhi

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 4035-4043. DOI: [10.24963/ijcai.2026/449](https://doi.org/10.24963/ijcai.2026/449)

## Abstract

We propose a modular logical framework for both reasoning with and measuring  inconsistency in propositional knowledge bases. The framework extends propositional logic with markers attached to occurrences of atoms and interpreted as pointers to worlds. This allows different occurrences of the same atom to be evaluated in different contexts unless they share a marker. We define paraconsistent entailment relations via abnormality functions that associate  each model with a set of deviations from a preferred behavior. Each entailment relation is then defined with respect to  models that are minimal under set inclusion. We show that suitable markings and abnormality functions capture several existing forms of inconsistency-tolerant reasoning, including entailment  based on maximal satisfiable subsets and the minimally inconsistent Logic of Paradox. We also show how a range of inconsistency measures can be expressed in the same setting. Thus our framework provides a uniform  basis for diverse approaches to inconsistency handling and  measurement.