Appears in collection : Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

A complementation proves useful to separate divergent terms from convergent terms. Hence the relevance of complementation in the context of renormalisation. The very notion of separation is furthermore related to that of locality. We extend the correspondence between Euclidean structures on vector spaces and orthogonal complementation to a one to one correspondence between a class of locality structures and orthocomplementations on bounded lattices. This is joint work with P. Clavier, Li Guo and Bin Zhang