On minimal inconsistent signatures and their application to inconsistency measurement

Thimm, Matthias, Santos Ribeiro Santos, Jandson, Peuter, Dennis and Sofronie-Stokkermans, Viorica 2025. On minimal inconsistent signatures and their application to inconsistency measurement. Presented at: NMR’25, Melbourne, Australia, 11-13 November 2025. Published in: Rapberger, Anna and Rudolph, Sebastian eds. CEUR Workshop Proceedings. CEUR, pp. 267-280.

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Abstract

Minimal inconsistent sets have played an important role in the analysis and general handling of inconsistency in logical knowledge bases. We introduce a semantical counterpart of this notion we call minimal inconsistent signature, which is a minimal set of propositions such that projecting the knowledge base onto it still preserves the inconsistency. We analyse minimal inconsistent signatures and the corresponding dual notion of maximal consistent signatures in depth and show, among others, that the hitting set duality applies for them as well. We apply our new notions to the field of inconsistency measurement and derive a series of new inconsistency measures, which we analyse in terms of postulate satisfaction and general behaviour. Finally, we analyse the computational complexity of various problems within this new context.

Item Type:	Conference or Workshop Item - published (Paper)
Status:	Published
Schools:	Schools > Computer Science & Informatics
Publisher:	CEUR
ISSN:	1613-0073
Date of First Compliant Deposit:	6 February 2026
Last Modified:	06 Feb 2026 11:01
URI:	https://orca.cardiff.ac.uk/id/eprint/184378

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