Reasoning with maximal consistent signatures

TL;DR

This paper investigates reasoning with inconsistent information using maximal consistent subsignatures, analyzing their properties, dualities, and implications for non-monotonic reasoning, complexity, and paraconsistent logic.

Contribution

It introduces a detailed analysis of maximal consistent subsignatures and their duals, extending the understanding of reasoning with inconsistent data.

Findings

Hitting set duality applies to maximal consistent subsignatures.

Inference relations based on these subsignatures satisfy certain rationality postulates.

The approach relates to inconsistency measurement and paraconsistent reasoning.

Abstract

We analyse a specific instance of the general approach of reasoning based on forgetting by Lang and Marquis. More precisely, we discuss an approach for reasoning with inconsistent information using maximal consistent subsignatures, where a maximal consistent subsignature is a maximal set of propositions such that forgetting the remaining propositions restores consistency. We analyse maximal consistent subsignatures and the corresponding minimal inconsistent subsignatures in-depth and show, among others, that the hitting set duality applies for them as well. We further analyse inference relations based on maximal consistent subsignatures wrt. rationality postulates from non-monotonic reasoning and computational complexity. We also consider the relationship of our approach with inconsistency measurement and paraconsistent reasoning.