A linking theory explains how verbs' semantic arguments are mapped to their syntactic arguments---the inverse of the Semantic Role Labeling task from the shallow semantic parsing literature. In this paper, we develop the Computational Linking Theory framework as a method for implementing and testing linking theories proposed in the theoretical literature. We deploy this framework to assess two cross-cutting types of linking theory: local v. global models and categorical v. featural models. To further investigate the behavior of these models, we develop a measurement model in the spirit of previous work in semantic role induction: the Semantic Proto-Role Linking Model. We use this model, which implements a generalization of Dowty's seminal Proto-Role Theory, to induce semantic proto-roles, which we compare to those Dowty proposes.