Formal typological analysis provides an otherwise unobtainable level of insight into both theories and the linguistic facts they analyze. This dissertation develops Property Theory (Alber & Prince 2016, 2017, in prep., Alber, DelBusso & Prince 2016), a theory of typological structure in Optimality Theory (OT; Prince & Smolensky 1993/2004). The list of languages generated in an OT factorial typology shows what the theory predicts, but not why it does so nor how it organizes the languages in the typological space. Property analysis answers these questions, finding the core structure that emerges directly from the logic of OT.

As a theory of formal OT typologies, Property Theory has a complex internal structure. The dissertation develops algorithms to translate between the formal objects of Property Theory (properties) and those of OT (ranking conditions). It examines cross-property dependencies and sufficient conditions on a set of properties for it to generate OT grammars, and thus an OT typology.

In taking typologies themselves as objects of study, property analysis leads to a re-conception of core constraint relationships and identification of classes of intensionally equivalent systems that share an internal formal structure while differing in the empirical areas analyzed. The dissertation develops a typological definition of stringently-related constraints and shows that systems with such constraints have a common structure, explaining diverse data in the same way. It shows that this organization characterizes analyses deriving the Final-Over-Final Condition, a typology of possible cross-linguistic syntactic structures.