Signs are either simple or compositional; in the general case, signs have two compositionality dimensions: the dimension of components (daughters) and the dimension of contexts (mothers). Compositionality is an abstraction from space-time structure (deictic semantic, and phonological structure).
Compositionality is defined primarily as an Immediate Dominance (ID) relation. This relation is tree-structured. The Cognitive Machine is able to cope with arbitrary tree-hierarchies (perhaps also with arbitrary general hierarchies, i.e. heterarchies, though this is not at issue here).
ID Compositionality is primarily a function of one, main item in a given structure, the head. In formalisations, the head may either be represented explicitly as one constituent of the structure, the Immediate Constituent Structure, ICS, method), in which case the structure inherits the proprties of the head, or with the head as the dominating category (the Dependency Structure, DS, method), in which the properties of the structure are identical with those of the head.