A Variable Occurrence-Centric Framework for Inconsistency Handling (Extended Version)

TL;DR

This paper presents a novel syntactic framework focusing on variable occurrences to analyze and resolve inconsistencies in propositional bases, introducing new concepts like MIR and MCR for improved conflict handling.

Contribution

It introduces a variable occurrence-centric framework with MIR and MCR concepts, enabling more precise inconsistency analysis and non-explosive inference methods.

Findings

MIR captures conflicts missed by minimal inconsistent subsets

MCR-based methods restore consistency effectively

New semantics assign truth to variable occurrences

Abstract

In this paper, we introduce a syntactic framework for analyzing and handling inconsistencies in propositional bases. Our approach focuses on examining the relationships between variable occurrences within conflicts. We propose two dual concepts: Minimal Inconsistency Relation (MIR) and Maximal Consistency Relation (MCR). Each MIR is a minimal equivalence relation on variable occurrences that results in inconsistency, while each MCR is a maximal equivalence relation designed to prevent inconsistency. Notably, MIRs capture conflicts overlooked by minimal inconsistent subsets. Using MCRs, we develop a series of non-explosive inference relations. The main strategy involves restoring consistency by modifying the propositional base according to each MCR, followed by employing the classical inference relation to derive conclusions. Additionally, we propose an unusual semantics that assigns truth values to variable occurrences instead of the variables themselves. The associated inference relations are established through Boolean interpretations compatible with the occurrence-based models.