Reasoning about Extensions

Conclusions can be drawn from incomplete or inconsistent specifications by separating the corresponding information in two sorts: the facts known for sure and others, that being not certain, are plausible and will be used to extend the former. This approach is formalized in Default Logic. Among the conclusions of such an specification there may be properties that are derived from facts know for sure, other derived from plausible facts and even other derived using inconsistent information. To these different sorts of conclusions correspond different degrees of credibility. It is possible to accept or reject some more doubtful conclusions by choosing the type of consequences (credulous or skeptical, for example) that are of interest in each case. There is however no consequence relation that, in a uniform way, allows to express the different strength of those conclusions. In order to achieve such a goal we need to enlarge the language where the consequences of a specification are written..