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General default logic

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Abstract

In this paper, we propose a new nonmonotonic logic called general default logic. On the one hand, it generalizes Reiter’s default logic by adding to it rule-like operators used in logic programming. On the other hand, it extends logic programming by allowing arbitrary propositional formulas. We show that with this new logic, one can formalize naturally rule constraints, generalized closed world assumptions, and conditional defaults. We show that under a notion of strong equivalence, sentences of this new logic can be converted to a normal form. We also investigate the computational complexity of various reasoning tasks in the logic, and relate it to some other nonmonotonic formalisms such as Lin and Shoham’s logic of GK and Moore’s autoepistemic logic.

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Authors and Affiliations

  1. Intelligent Systems Lab, School of Computing and Mathematics, University of Western Sydney, Sydney, New South Wales, Australia

    Yi Zhou & Yan Zhang

  2. Department of Computer Science, Hong Kong University of Science and Technology, Hong Kong, People’s Republic of China

    Fangzhen Lin

Authors
  1. Yi Zhou
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  2. Fangzhen Lin
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  3. Yan Zhang
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Correspondence to Yi Zhou.

Additional information

This paper is an extended version of the authors’ LPNMR’07 [43] and NMR’08 [44] papers.

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Zhou, Y., Lin, F. & Zhang, Y. General default logic. Ann Math Artif Intell 57, 125–160 (2009). https://doi.org/10.1007/s10472-009-9161-6

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