The complexity of logic-based abduction

  • Thomas Eiter
  • Georg Gottlob
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)

Abstract

Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logic- based abduction. Candidates for abductive explanations are usually subjected to minimality criteria such as subset-minimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant problems related to abduction on propositional theories. They show that the different variations of abduction provide a rich collection of natural problems populating all major complexity classes between P and Σ3P, Π3P in the refined polynomial hierarchy. More precisely, besides polynomial, NP-complete and co-NP-complete abduction problems, abduction tasks that are complete for the classes ΔiP, ΔiP[O(logn), ΣiP, and ΠiP, for i=2,3, are identified.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Thomas Eiter
    • 1
  • Georg Gottlob
    • 1
  1. 1.Christian Doppler Laboratory for Expert Systems Institut für InformationssystemeTechnische Universität WienWienAustria

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