In this paper we present a mechanism for approximately translating
Boolean query constraints across heterogeneous information sources.
Achieving the best translation is challenging because
sources support different constraints for formulating queries, and 
often these constraints cannot be precisely translated.
For instance, a query [score > 8] might be ``perfectly'' translated as
[rating][>][0.8] at some site, but can only be approximated
as [grade][=][A] at another.
Unlike other work, our general framework adopts a
customizable ``closeness'' metric for the translation
that combines both precision and recall.
Our results show that for query translation we need to handle
interdependencies among both query conjuncts as well as disjuncts.
As the basis, we identify the essential requirements of a rule system
for users to encode the mappings for atomic semantic units.
Our algorithm then translates complex queries by rewriting them in
terms of the semantic units.
We show that, under practical assumptions, our algorithm generates
the best approximate translations with respect
to the closeness metric of choice.
We also discuss how the precision and recall of the translated
queries can be estimated.