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Regular disjunction-free default theories

  • Formal Methods
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Abstract

In this paper, the class of regular disjunction-free default theories is introduced and investigated. A transformation from regular default theories to normal default theories is established. The initial theory and the transformed theory have the same extensions when restricted to old variables. Hence, regular default theories enjoy some similar properties (e.g., existence of extensions, semi-monotonicity) as normal default theories. Then, a new algorithm for credulous reasoning of regular theories is developed. This algorithm runs in a time not more thanO(1. 45n), wheren is the number of defaults. In case of regular prerequisite-free or semi-2CNF default theories, the credulous reasoning can be solved in polynomial time. However, credulous reasoning for semi-Horn default theories is shown to be NP-complete although it is tractable for Horn default theories. Moreover, skeptical reasoning for regular unary default theories is co-NP-complete.

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Authors and Affiliations

  1. Institute of Logic and Cognition, Sun Yat-Sen University, 510275, Guangzhou, P.R. China

    Xi-Shun Zhao

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  1. Xi-Shun Zhao
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Correspondence to Xi-Shun Zhao.

Additional information

This research was supported by the MOE Project (Grant No. 01JB72040001), the National Social Science Foundation of China under Grant No. 02BZX046, and the National Natural Science Foundation of China under Grant No. 10161005.

Xi-Shun Zhao received his Ph.D. degree in 1999 from Nanjing University, and M.S. degree in 1988 from Institute of Software, the Chinese Academy of Science. During 2000.4–2001.3 he worked as a visiting professor in Department of Mathematics and Computer Science at Paderborn University in Germany. He is currently a professor and Ph.D. supervisor in Institute of Logic and Cognition, Sun Yat-Sen University. His main research interests are mathematical logic and theoretical research in artificial intelligence.

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Zhao, XS. Regular disjunction-free default theories. J. Comput. Sci. & Technol. 19, 329–340 (2004). https://doi.org/10.1007/BF02944903

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  • DOI: https://doi.org/10.1007/BF02944903

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