OT grammars, beyond partial orders: ERC sets and antimatroids

Grammars in Optimality Theory can be characterized by sets of Elementary Ranking Conditions (ERCs). Antimatroids are structures that arose initially in the study of lattices. In this paper we prove that antimatroids and consistent ERC sets have the same formal structures. We do so by defining two functions Antimat and RCErc, Antimat being a function from consistent sets of ERCs to antimatroids and RCErc a function from antimatroids to ERC sets. We then show that these functions are inverses of each other and that both maintain the structural properties of ERC sets and antimatroids. This establishes that antimatroids and consistent ERC sets have the same formal structure, allowing linguists to import from the sizable work done on antimatroids any and all results.