Problems with Default Logic
There are several ways to look at the fact that the account of default logic which can be provided for theories with non normal defaults is rather poor from a semantical point of view. An aspect of this problem seems to be that extensions of a default theory with non normal defaults need not be incompatible. Indeed, the extensions of a default theory gather the sentences which are consequences of that default theory. Accordingly, conclusions deserving the most confidence should be found in models common to all extensions of the default theory. But it happens that the first order models which gather those “most reliable conclusions” contradict the justification of each default of the theory! Let us illustrate this with the aid of an example inspired from Lukaszewicz [1984b]. Assume that on Sundays I go fishing unless I do not wake up early and represent it by the following semi-normal default.
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