Generality and Equivalence Relations in Default Logic
Katsumi Inoue and Chiaki Sakama
Proceedings of the 22nd Conference on Artificial Intelligence (AAAI-07),
pages 434-439, 2007.
Generality or refinement relations between different theories have
important applications to generalization in inductive logic programming,
refinement of ontologies, and coordination in multi-agent systems.
We study generality relations in disjunctive default logic by
comparing the amounts of information brought by default theories.
Intuitively, a default theory is considered more general than
another default theory if the former brings more information than the latter.
Using techniques in domain theory, we introduce different types of
generality relations over default theories.
We show that generality relations based on the Smyth and Hoare orderings
reflect orderings on skeptical and credulous consequences, respectively,
and that two default theories are equivalent if and only if they are
equally general under these orderings.
These results naturally extend both generality relations over
first-order theories and those for answer set programming.
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