This chapter explores a semantics-oriented approach to the origins of syntactic structure. It reports on preliminary experiments whereby speakers introduce hierarchical constructions and grammatical markers to express which conceptualization strategy hearers are supposed to invoke. This grammatical information helps hearers to avoid semantic ambiguity or errors in interpretation. A simulation study is performed for spatial grammar using robotic agents that play language games about objects in their shared world. The chapter uses a reconstruction of a fragment of German spatial language to identify the niche of spatial grammar, and then reports on acquisition and formation experiments in which agents seeded with a `pidgin German' without grammar are made to interact until rudiments of hierarchical structure and grammatical marking emerge.