Parameterised Complexity for Abduction
Abductive reasoning is a non-monotonic formalism stemming from the work of Peirce. It describes the process of deriving the most plausible explanations of known facts. Considering the positive version asking for sets of variables as explanations, we study, besides asking for existence of the set of explanations, two explanation size limited variants of this reasoning problem (less than or equal to, and equal to). In this paper, we present a thorough classification regarding the parameterised complexity of these problems under a wealth of different parameterisations. Furthermore, we analyse all possible Boolean fragments of these problems in the constraint satisfaction approach with co-clones. Thereby, we complete the parameterised picture started by Fellows et al. (AAAI 2012), partially building on results of Nordh and Zanuttini (Artif. Intell. 2008). In this process, we outline a fine-grained analysis of the inherent intractability of these problems and pinpoint their tractable parts.