## A complete classification of the complexity of propositional abduction (2006)

Venue: | SIAM Journal on Computing |

Citations: | 16 - 3 self |

### BibTeX

@ARTICLE{Creignou06acomplete,

author = {Nadia Creignou and Bruno Zanuttini},

title = {A complete classification of the complexity of propositional abduction},

journal = {SIAM Journal on Computing},

year = {2006},

volume = {36},

pages = {207--229}

}

### OpenURL

### Abstract

Abstract. Abduction is the process of explaining a given query with respect to some background knowledge. For instance, p is an explanation for the query q given the knowledge p → q. This problem is well-known to have many applications, in particular in Artificial Intelligence, and has been widely studied from both an AI and a complexity-theoretic point of view. In this paper we completely classify the complexity of propositional abduction in Schaefer’s famous framework. We consider the case where knowledge bases are taken from a class of formulas in generalized conjunctive normal form. This means that the propositional formulas considered are conjunctions of constraints taken from a fixed finite language. We show that according to the properties of this language, deciding whether at least one explanation exists is either polynomial, NP-complete or ΣP 2-complete. Our results are stated for a query consisting of a single, positive literal and for assumption-based solutions, i.e., the solutions must be formed upon a distinguished subset of the variables that is part of the input. We however show that our results can be interpreted “dually ” for negative queries, and thus also for unrestricted (positive or negative) queries.