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 Σ P3 , Π P3 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 Δ Pi , Δ Pi [O(logn), Σ Pi , and Π Pi , for i=2,3, are identified.
This paper is an overview of [10], which contains detailed proofs of all results.
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Eiter, T., Gottlob, G. (1993). The complexity of logic-based abduction. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_10
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