1 research outputs found
Parameterised Complexity of Abduction in Schaefer's Framework
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
two-dimensional classification of these problems. The first dimension is
regarding the parameterised complexity under a wealth of different
parameterisations. The second dimension spans through all possible Boolean
fragments of these problems in Schaefer's constraint satisfaction framework
with co-clones (STOC 1978). Thereby, we almost 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 parameterised intractability of these
problems and pinpoint their FPT parts. As the standard algebraic approach is
not applicable to our problems, we develop an alternative method that makes the
algebraic tools partially available again.Comment: gave a more precise title and corrected proof