A Variable Occurrence-Centric Framework for Inconsistency Handling (Extended Version)
This work addresses inconsistency management in logical reasoning, which is incremental as it builds on existing methods for propositional bases.
The paper tackles inconsistency handling in propositional bases by introducing a syntactic framework that focuses on variable occurrences, proposing Minimal Inconsistency Relations (MIRs) and Maximal Consistency Relations (MCRs) to analyze conflicts and develop non-explosive inference relations, with MIRs capturing conflicts missed by minimal inconsistent subsets.
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.