Consistency of XML schema mappings, which means that some document conforming to the source schema can be mapped into a document conforming to the target schema, is an essentially necessary property. It is also important for XML schema mappings to be absolutely consistent, that is, every document conforming to the source schema can be mapped into a document conforming to the target schema. As a known result, consistency of a mapping between general DTDs is EXPTIME-complete even if the class of document patterns for defining mappings is restricted to downward axes and qualifiers. In addition, the known tractability result is only on a restricted class of document patterns under restricted DTDs called nested-relational DTDs. Moreover, there are few known results on the tractability of absolute consistency. In this paper, we discuss the consistency and absolute consistency problems under restricted DTDs called disjunction-capsuled DTDs, which were proposed by Ishihara et al, and their extended classes. We first show that for many document pattern classes, both problems are solvable in polynomial time under disjunction-capsuled DTDs. Then, we show that our results are extended to some superclasses of disjunction-capsuled DTDs, which are also proper superclasses of nested-relational DTDs.
