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 δ ∈ D. 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 δ ∈ D.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Friedberg R M. Two recursively enumerable sets of incomparable degrees of unsolvability. Proc Natl Acad Sci, 1957, 43: 236–238
Muchnik A A. On the separability of recursively enumerable sets (in Russian). Dokl Akad Nauk SSSR, 1956, 109: 29–32
Rogers H. Theory of Recursive Functions and Effective Computability. Cambridge: The MIT Press, 1967
Soare R I. Recursively Enumerable Sets and Degrees, a Study of Computable Functions and Computably Generated Sets. Berlin: Springer-Verlag, 1987
Marek W, Truszczynski M. Nonmonotonic Logics: Context-Dependent Reasoning. Berlin: Springer. 1993
Nicolas P, Saubion F, Stéphan I. Heuristics for a default logic reasoning system. Int J Artif Intell Tools, 2001, 10: 503–523
Antoniou G. A tutorial on default logics. ACM Comput Surv, 1999, 31: 337–359
Delgrande J P, Schaub T, Jackson W K. Alternative approaches to default logic. Artif Intell, 1994, 70: 167–237
Lukaszewicz W. Considerations on default logic: an alternative approach. Comput Intell, 1988, 4: 1–16
Reiter R. A logic for default reasoning. Artif Intell, 1980, 13: 81–132
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
Li W. Mathematical Logic, Foundations for Information Science. Basel: Birkhäuser. 2010
Li W, Sui Y, Sun M. The sound and complete R-calculus for revising propositional theories. Sci China Inf Sci, 2015, 58: 092101
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
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11432-016-0551-5