Multi-valued dependencies (MVDs) are an important class of constraints that is fundamental for relational database design. Although modern applications increasingly require the support of complex data types such as lists, sets, multisets, unions and references, the challenge of providing well-founded data models that can handle such objects has not been met yet. Those data models will greatly benefit from automated database design techniques that generalise methods from relational databases. Lists represent an inevitable data structure whenever order matters and data is allowed to occur repeatedly. Lists are therefore supported by many advanced data models such as genomic sequence, deductive and object-oriented data models including XML. In this paper, we continue to study the impact of lists on MVDs. The definition of MVDs is based on a Brouwerian algebra of nested attributes which allows to specify actual constraints among complex objects, and to reason independently from any specif...