Hierarchical default logic
We present a formal framework for ordered default reasoning which has desirable mathematical properties yet is relatively simple and can be implemented using standard theorem provers. By expressing default logic as a relation from theories to extensions we are able to formalise Brewka's prioritized default logic as a composite relation. We also decompose the extension relation by factoring out deductive closure. The resulting augmentations can be computed for decidable cases, and provide an extension membership test for composite extensions. Finally we define the equivalent formalism in autoepistemic logic.
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