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).
Friedberg R M. Two recursively enumerable sets of incomparable degrees of unsolvability. Proc Natl Acad Sci, 1957, 43: 236–238CrossRefMATHGoogle Scholar
Muchnik A A. On the separability of recursively enumerable sets (in Russian). Dokl Akad Nauk SSSR, 1956, 109: 29–32MathSciNetMATHGoogle Scholar
Rogers H. Theory of Recursive Functions and Effective Computability. Cambridge: The MIT Press, 1967MATHGoogle Scholar
Soare R I. Recursively Enumerable Sets and Degrees, a Study of Computable Functions and Computably Generated Sets. Berlin: Springer-Verlag, 1987CrossRefMATHGoogle Scholar