Most previous schema mapping works focus on creating mappings in specific data models for data transformation, failing to capture a richer set of possible relationships between schema elements. For example, most schema matching approaches might discover that `TA' in one schema equals `grad TA' in another one, even though the relationship can be modeled more accurately by saying that `grad TA' is a specialization of `TA'. Deepening the mapping semantics in turn allow richer application semantics. This paper presents and proves the effectiveness of SeMap, a system that constructs a complex, semantically richer mapping (including `Has-a', `Is-a', `Associates' and `Equivalent' relationship types) that can be used across data models. We achieve this goal by: (1) exploiting semantic evidence for possible matches; (2) finding a globally optimal match assignment; (3) identifying the relationship embedded in the selected matches. We implemented our seman...