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SCIENCE CHINA Information Sciences, Volume 60, Issue 9: 092107(2017) https://doi.org/10.1007/s11432-016-0551-5

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

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  • ReceivedAug 17, 2016
  • AcceptedNov 19, 2016
  • PublishedApr 27, 2017

Abstract

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


Acknowledgment

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).

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