  For data integration in information ecosystems, semantic heterogeneity is a
known difficulty. In this paper, we propose Shadow Theory as the philosophical
foundation to address this issue. It is based on the notion of shadows in
Plato's Allegory of the Cave. What we can observe are just shadows, and
meanings of shadows are mental entities that only exist in viewers' cognitive
structures. With enterprise customer data integration example, we proposed six
design principles and algebra to support required operations.
