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On the parameterized complexity of non-monotonic logics

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Abstract

We investigate the application of Courcelle’s theorem and the logspace version of Elberfeld et al. in the context of non-monotonic reasoning. Here we formalize the implication problem for propositional sets of formulas, the extension existence problem for default logic, the expansion existence problem for autoepistemic logic, the circumscriptive inference problem, as well as the abduction problem in monadic second order logic and thereby obtain fixed-parameter time and space efficient algorithms for these problems. On the other hand, we exhibit, for each of the above problems, families of instances of a very simple structure that, for a wide range of different parameterizations, do not have efficient fixed-parameter algorithms (even in the sense of the large class XPnu, resp., XLnu) under standard complexity assumptions.

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Authors and Affiliations

  1. Institut für Theoretische Informatik, Gottfried Wilhelm Leibniz Universität Hannover, Appelstrasse 4, 30167, Hannover, Germany

    Arne Meier, Irina Schindler, Michael Thomas & Heribert Vollmer

  2. Department of Computer and Information Science, Linköpings Universitet, 581 83, LinköPing, Sweden

    Johannes Schmidt

Authors
  1. Arne Meier
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  2. Irina Schindler
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  3. Johannes Schmidt
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  4. Michael Thomas
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  5. Heribert Vollmer
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Correspondence to Arne Meier.

Additional information

This work is supported in part by DFG Grant VO 630/6-2 and ME 4279/1-1. Part of this work has been published in a preliminary form in: A. Meier and J. Schmidt and M. Thomas and H. Vollmer, On the Parameterized Complexity of Default Logic and Autoepistemic Logic, Proc. LATA 2012, pp. 389–400, vol. 7183 LNCS.

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Meier, A., Schindler, I., Schmidt, J. et al. On the parameterized complexity of non-monotonic logics. Arch. Math. Logic 54, 685–710 (2015). https://doi.org/10.1007/s00153-015-0435-x

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