I will be sharing some ongoing research about mathematical models of bare phrase structure, leading up to a proposal for an innovative spatial model.
In the first week, I will demonstrate that the category of BPS phrase markers, viewed solely as a subcategory of membership-ordered sets, is not rich enough to keep track of the syntactically significant “spatial” data in the category of phrase markers. I will show that the data needed to enrich this category are roughly all of the idiosyncratic properties of MERGE.
In week two, I will define a category of spaces which can model bare phrase structure derivations that is an abstraction of the order-relations in a tree. I will show how this category can be set up to naturally represent many “derivational” generalizations of the important spatial properties of phrase markers, such as equidistance, comp/spec/adjunct, projection, and dominance. This is made possible by the ability to represent feature configurations in the derivation itself. Taken together, this will naturally force an encoding of the properties missing from the category of membership-ordered sets needed to represent phrase markers.