Getting possibilities from the impossible

C. Elsenbroich, D. M. Gabbay, O. Rodrigues

Research output: Chapter in Book/Report/Conference proceedingConference paper


Abduction is often constructed as a consistent expansion of a database, i.e. abduction demands that a database Δ expanded by an explanation ε is not inconsistent ; Δ∪ε|≠⊥. The constraint is sensible if we stay within classical logic. Without it we end up with every formula inconsistent with Δ being an explanation for any other formula. But what if Δ is inconsistent itself? Then consistent abduction battles like Don Quixote against windmills. All we want from abduction is that it does not introduce inconsistency into a set Δ.
This article proposes a proof theory for abduction that can be applied to inconsistent databases by demanding that an abductively derived formula must be from the intersection of all maximal consistent subsets of the database. 

Original languageEnglish
Title of host publicationProceedings of the 11th Workshop on Nonmonotic Reasoning
Subtitle of host publicationNMR'06
EditorsJurgen Dix, Anthony Hunter
PublisherInstitut fur Informatik
Number of pages9
Publication statusPublished - 2006

Publication series

NameIFI Technical Report Series
PublisherInstitut fur Informatik
ISSN (Print)1860-8477


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