The Lattice of Case and Agentivity Scott Grimm The typological literature has demonstrated that semantic parameters such as agentivity, affectedness, and object individuation affect the realization of case-marking. Yet, explicitly connecting case-marking with semantics has proven elusive. This thesis proposes a feature-based representation of agentivity properties, loosely based on Dowty's proto-role theory, which is reformulated in terms of privative opposition and hierarchically organized via a lattice. The resulting agentivity lattice is used as a theoretical construct by which the semantics of case and case systems can be articulated. The general meaning of a case can be specified with respect to a region of the lattice. As opposed to other approaches which resort to listing the properties and qualities of a case, the region of the lattice gives a structured set of properties, which are couched in a context of opposition to other properties. Practical results include treatments of many language-particular semantic uses of case, such as case alternations, which have resisted proper analyses under more syntactic approaches to case. A further advantage of this approach is its ability to model the interaction among multiple semantic parameters, such as agentivity, animacy and definiteness. The investigation begins in Chapter 2, discussing the general principles of case-marking with reference to how case-marking is realized in a variety of languages and how case-markers are formed via the process of grammaticalization. Chapter 3 constructs a hierarchical representation of the semantic properties at work in argument structures, i.e., agentivity, patientivity, etc., via a lattice, which is the core theoretical contribution of this study. Chapter 4 discusses a number of typological generalizations predicted by the lattice and accounts for the different systems of core case-marking, i.e, the marking of subjects and objects, including a treatment of Differential Object Marking. The lattice is then used throughout Chapter 5 to provide an explanatory model of non-canonical case marking in particular languages, that is, phenomena such as case alternations (Hindi, Russian) and case attraction (Ancient Greek). Chapter 6 considers the relation of this study to, and presents several challenges for, varieties of formal semantics. The final chapter draws conclusions and discusses some problems for further research.