A parens form can be extruded upward and capped to construct stacks of boxes similar to parens trees, but with contact replacing connectivity.
These boxes can then be extruded again into a third dimension, constructing a three-dimensional block representation that is physically manipulable.
Containment becomes concrete contact. Block forms are not anthropomorphized, they are simply concrete structures in a physical environment.
Like Cuisenaire Rods used to teach elementary numerical concepts to preschoolers through physical manipulation, logic blocks could be used to teach elementary logical concepts. The difficulty is that the concepts taught by logic blocks are those of diagrammatic boundary logic rather than the more familiar string-based logic embedded in language.