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.
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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).
Conflict of interest
The authors declare that they have no conflict of interest.
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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
- strong extension
- finite/infinite injury priority method
- recursively enumerablesets