We develop the definition and results about the sympathetically solitary class in terms of circumscription; however, they also apply straightforwardly to Default Logic, Autoepistemic Logic, and several other non-monotonic formalisms as well.
The sympathetically solitary class generalizes Lifschitz' solitary
class. It also includes, as a special case, the simple application of
the Closed World Assumption to unit-clausal databases, when there is
domain closure and a complete theory of equality, e.g., uniqueness of
names. However, sympathetically solitary overlaps with, and neither
includes nor is included by, the following classes: logic programs
with negation by failure; Horn; default inheritance cf. Touretzky;
predicate completion; and the general Closed World Assumption.
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