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The description logic handbook
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We consider semistructured data as multirooted edge-labelled directed graphs, and path inclusion constraints on these graphs. A path inclusion constraint p@?q is satisfied by a semistructured data if any node reached by the regular query p is also reached by the regular query q. In this paper, two problems are mainly studied: the implication problem and the problem of the existence of a finite exact model. -We give a new decision algorithm for the implication problem of a constraint p@?q by a set of bounded path constraints p"i@?u"i where p, q, and the p"i's are regular path expressions and the u"i's are words, improving in this particular case, the more general algorithms of S. Abiteboul and V. Vianu, and N. Alechina et al. In the case of a set of word equalities u"i=v"i, we provide a more efficient decision algorithm for the implication of a word equality u=v, improving the more general algorithm of P. Buneman et al. We prove that, in this case, implication for nondeterministic models is equivalent to implication for (complete) deterministic ones. -We introduce the notion of exact model: an exact model of a set of path constraints C satisfies the constraint p@?q if and only if this constraint is implied by C. We prove that any set of constraints has an exact model and we give a decidable characterization of data which are exact models of bounded path inclusion constraints sets.