Restricted Four-Valued Logic for Default Reasoning

In Reiter's default logic, it is possible that no useful information can be brought from inconsistent knowledge or no extension of incoherent default theories exists. In this paper, based on Belnap's four-valued logic, we propose a new variant of default logic called the restricted four-valued default logic to tolerate inconsistency and incoherency of knowledge in default reasoning. Our proposal can maintain both the expressive power of full default logic and the ability of default reasoning. Moreover, we present a transformation-based approach to compute the restricted four-valued extensions.

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