The situation of the multimodal and symmetric extensions is more intricate. Expressivity here is directly related to the kind of restrictions one imposes on structural resource management. At one end of the spectrum, multimodality without structural rules does not lead us beyond context-free recognition: Jäger (2003) shows that the pure residuation logic for n-ary families of type-forming operations stays strictly context-free. If one requires structural rules to be resource-sensitive (no copying or deletion) and, for the unary modalities, non-expanding, one obtains the full expressivity of context-sensitive grammars, and the PSPACE complexity that goes with it (Moot 2002). (PSPACE consists of those problems  solvable using some polynomial amount of memory space.  See the entry on   computability and complexity.  If one imposes no restrictions on structural rules (specifically, if one allows copying and deletion operations), unsurprisingly, one obtains the expressivity of unrestricted rewriting systems (Carpenter 1999). A controlled use of copying is used in the analysis of anaphora resolution in Jäger 2005.