Semantic mappings between data sources play a key role in several data sharing architectures. Mappings provide the relationships between data stored in different sources, and therefore enable answering queries that require data from other nodes in a data sharing network. Composing mappings is one of the core problems that lies at the heart of several optimization methods in data sharing networks, such as caching frequently traversed paths and redundancy analysis. This paper investigates the theoretical underpinnings of mapping composition. We study the problem for a rich mapping language, GLAV, that combines the advantages of the known mapping formalisms global-as-view and local-as-view. We first show that even when composing two simple GLAV mappings, the full composition may be an infinite set of GLAV formulas. Second, we show that if we restrict the set of queries to be in CQ_k (a common restriction in practice), then we can always encode the infinite set of GLAV formulas using a finite representation. Furthermore, we describe an algorithm that given a query and a finite encoding of an infinite set of GLAV formulas, finds all the certain answers to the query. Consequently, we show that for a commonly occuring class of queries it is possible to pre-compose mappings, thereby potentially offering significant savings in query processing.
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