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Mappings between disparate models are fundamental to any
application that requires interoperability between heterogeneous
data and applications. Generating mappings is a laborintensive
and error prone task. To build a system that helps
users generate mappings, we need an explicit representation
of mappings. This representation needs to have well-defined
semantics to enable reasoning and comparison between mappings.
This paper first presents a powerful framework for
defining languages for specifying mappings and their associated
semantics. We examine the use of mappings and identify
the key inference problems associated with mappings. These
properties can be used to determine whether a mapping is adequate
in a particular context. Finally, we consider an instance
of our framework for a language representing mappings
between relational data. We present sound and complete
algorithms for the corresponding inference problems.