Top-Down Decomposability

One half of Full Decomposability: every labelling of the framework can be obtained by combining local labellings of the parts of any partition. The local labellings come from the semantics' own (canonical) local function, so the property is only defined for semantics compatible with complete semantics.

Reference

Baroni, P., Boella, G., Cerutti, F., Giacomin, M., van der Torre, L. & Villata, S. (2014). On the Input/Output Behavior of Argumentation Frameworks. Artificial Intelligence, 217, pp. 144–197.