Efficient reasoning for inconsistent Horn formulae

Joao Marques-Silva, Alexey Ignatiev, Carlos Mencía, Rafael Peñaloza

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

10 Citations (Scopus)


Horn formulae are widely used in different settings that include logic programming, answer set programming, description logics, deductive databases, and system verification, among many others. One concrete example is concept subsumption in lightweight description logics, which can be reduced to inference in propositional Horn formulae. Some problems require one to reason with inconsistent Horn formulae. This is the case when providing minimal explanations of inconsistency. This paper proposes efficient algorithms for a number of decision, function and enumeration problems related with inconsistent Horn formulae. Concretely, the paper develops efficient algorithms for finding and enumerating minimal unsatisfiable subsets (MUSes), minimal correction subsets (MCSes), but also for computing the lean kernel. The paper also shows the practical importance of some of the proposed algorithms.

Original languageEnglish
Title of host publicationLogics in Artificial Intelligence
Subtitle of host publication15th European Conference, JELIA 2016 Larnaca, Cyprus, November 9–11, 2016 Proceedings
EditorsLoizos Michael, Antonis Kakas
Place of PublicationCham Switzerland
Number of pages17
ISBN (Electronic)9783319487588
ISBN (Print)9783319487571
Publication statusPublished - 2016
Externally publishedYes
EventLogics in Artificial Intelligence, European Conference 2016 - Larnaca, Cyprus
Duration: 9 Nov 201611 Nov 2016
Conference number: 15th

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceLogics in Artificial Intelligence, European Conference 2016
Abbreviated titleJELIA 2016
Internet address

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