Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

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

  • 37 Accesses


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.

This is a preview of subscription content, log in to check access.


  1. 1

    Friedberg R M. Two recursively enumerable sets of incomparable degrees of unsolvability. Proc Natl Acad Sci, 1957, 43: 236–238

  2. 2

    Muchnik A A. On the separability of recursively enumerable sets (in Russian). Dokl Akad Nauk SSSR, 1956, 109: 29–32

  3. 3

    Rogers H. Theory of Recursive Functions and Effective Computability. Cambridge: The MIT Press, 1967

  4. 4

    Soare R I. Recursively Enumerable Sets and Degrees, a Study of Computable Functions and Computably Generated Sets. Berlin: Springer-Verlag, 1987

  5. 5

    Marek W, Truszczynski M. Nonmonotonic Logics: Context-Dependent Reasoning. Berlin: Springer. 1993

  6. 6

    Nicolas P, Saubion F, Stéphan I. Heuristics for a default logic reasoning system. Int J Artif Intell Tools, 2001, 10: 503–523

  7. 7

    Antoniou G. A tutorial on default logics. ACM Comput Surv, 1999, 31: 337–359

  8. 8

    Delgrande J P, Schaub T, Jackson W K. Alternative approaches to default logic. Artif Intell, 1994, 70: 167–237

  9. 9

    Lukaszewicz W. Considerations on default logic: an alternative approach. Comput Intell, 1988, 4: 1–16

  10. 10

    Reiter R. A logic for default reasoning. Artif Intell, 1980, 13: 81–132

  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. 529–544

  12. 12

    Li W. Mathematical Logic, Foundations for Information Science. Basel: Birkhäuser. 2010

  13. 13

    Li W, Sui Y, Sun M. The sound and complete R-calculus for revising propositional theories. Sci China Inf Sci, 2015, 58: 092101

  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, 2015

Download references


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).

Author information

Correspondence to Yuhui Wang.

Additional information

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, W., Sui, Y. & Wang, Y. The propositional normal default logic and the finite/infinite injury priority method. Sci. China Inf. Sci. 60, 092107 (2017). https://doi.org/10.1007/s11432-016-0551-5

Download citation


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