Default Reasoning with Preference within Only Knowing Logic

The main construction in this paper is an encoding of default logic into an ``only knowing'' logic with degrees of confidence. By imposing simple and natural constraints on the encoding we show that the ``only knowing'' logic can accommodate ordered default theories and that the constrained encoding implements a prescriptive interpretation of preference between defaults. An advantage of the encoding is that it provides a transparent formal rendition of such a semantics. A feature of the construction is that the generation of extensions can be carried out within the ``only knowing'' logic, using object level concepts alone.