From Orthocomplementations to Locality

Abstract

After some background on lattices, the locality framework introduced in earlier work by the authors is extended to cover posets and lattices. We then extend the correspondence between Euclidean structures on vector spaces and orthogonal complementations to a one-to-one correspondence between a class of locality structures and orthocomplementations on bounded lattices. This recasts in the context of renormalisation classical results in lattice theory.