Science China Information Sciences

, 60:092107 | Cite as

The propositional normal default logic and the finite/infinite injury priority method

Research Paper
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Abstract

In propositional normal default logic, given a default theory (Δ,D) and a well-defined ordering of D, there is a method to construct an extension of (Δ,D) without any injury. To construct a strong extension of (Δ,D) given a well-defined ordering of D, there may be finite injuries for a default δD. With approximation deduction ⊢s in propositional logic, we will show that to construct an extension of (Δ,D) under a given welldefined ordering of D, there may be infinite injuries for some default δD.

Keywords

default extension strong extension finite/infinite injury priority method recursively enumerablesets 

Notes

Acknowledgements

This work was supported by Open Fund of the State Key Laboratory of Software Development Environment (Grant No. SKLSDE-2010KF-06), Beihang University, and National Basic Research Program of China (973 Program) (Grant No. 2005CB321901).

References

  1. 1.
    Friedberg R M. Two recursively enumerable sets of incomparable degrees of unsolvability. Proc Natl Acad Sci, 1957, 43: 236–238CrossRefMATHGoogle Scholar
  2. 2.
    Muchnik A A. On the separability of recursively enumerable sets (in Russian). Dokl Akad Nauk SSSR, 1956, 109: 29–32MathSciNetMATHGoogle Scholar
  3. 3.
    Rogers H. Theory of Recursive Functions and Effective Computability. Cambridge: The MIT Press, 1967MATHGoogle Scholar
  4. 4.
    Soare R I. Recursively Enumerable Sets and Degrees, a Study of Computable Functions and Computably Generated Sets. Berlin: Springer-Verlag, 1987CrossRefMATHGoogle Scholar
  5. 5.
    Marek W, Truszczynski M. Nonmonotonic Logics: Context-Dependent Reasoning. Berlin: Springer. 1993CrossRefMATHGoogle Scholar
  6. 6.
    Nicolas P, Saubion F, Stéphan I. Heuristics for a default logic reasoning system. Int J Artif Intell Tools, 2001, 10: 503–523CrossRefGoogle Scholar
  7. 7.
    Antoniou G. A tutorial on default logics. ACM Comput Surv, 1999, 31: 337–359CrossRefGoogle Scholar
  8. 8.
    Delgrande J P, Schaub T, Jackson W K. Alternative approaches to default logic. Artif Intell, 1994, 70: 167–237MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Lukaszewicz W. Considerations on default logic: an alternative approach. Comput Intell, 1988, 4: 1–16CrossRefGoogle Scholar
  10. 10.
    Reiter R. A logic for default reasoning. Artif Intell, 1980, 13: 81–132MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Avron A, Lev I. Canonical propositional Gentzen-type systems. In: Proceedings of the 1st International Joint Conference on Automated Reasoning. London: Springer, 2001. 529–544MATHGoogle Scholar
  12. 12.
    Li W. Mathematical Logic, Foundations for Information Science. Basel: Birkhäuser. 2010MATHGoogle Scholar
  13. 13.
    Li W, Sui Y, Sun M. The sound and complete R-calculus for revising propositional theories. Sci China Inf Sci, 2015, 58: 092101MathSciNetGoogle Scholar
  14. 14.
    Li W, Sui Y. The R-calculus and the finite injury priority method. In: Proceedings of the 2nd International Conference on Artificial Intelligence, Vancouver, 2015Google Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Software Development EnvironmentBeihang UniversityBeijingChina
  2. 2.Key Laboratory of Intelligent Information Processing, Institute of Computing TechnologyChinese Academy of SciencesBeijingChina
  3. 3.School of Computer and Control EngineeringUniversity of Chinese Academy of SciencesBeijingChina

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