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Parameterised Complexity of Abduction in Schaefer’s Framework

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Logical Foundations of Computer Science (LFCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11972))

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Abstract

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.

Funded by German Research Foundation (DFG), project ME 4279/1-2.

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Author information

Authors and Affiliations

  1. Institut für Theoretische Informatik, Leibniz Universität Hannover, Hanover, Germany

    Yasir Mahmood & Arne Meier

  2. Department of Computer Science and Informatics, School of Engineering, Jönköping University, Jönköping, Sweden

    Johannes Schmidt

Authors
  1. Yasir Mahmood
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  2. Arne Meier
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Correspondence to Yasir Mahmood .

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Editors and Affiliations

  1. The Graduate Center, CUNY, New York, NY, USA

    Sergei Artemov

  2. Cornell University, Ithaca, NY, USA

    Anil Nerode

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Mahmood, Y., Meier, A., Schmidt, J. (2020). Parameterised Complexity of Abduction in Schaefer’s Framework. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2020. Lecture Notes in Computer Science(), vol 11972. Springer, Cham. https://doi.org/10.1007/978-3-030-36755-8_13

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