This report is a compilation of papers by the PATR group in the Artificial Intelligence Center at SRI International reporting on ongoing research on both practical and theoretical issues concerning grammar formalisms. The current formalism being simultaneously designed, implemented and used by the group, PATR-II, is based on unification of directed-graph structures. Unification is thus a theme both of our research, and of the papers reproduced in this volume. These papers provide an overview of the design of PATR-II (Chapter 1), a discussion of the use of disjunction and negation in unification-based feature systems (Chapter 2), and a theoretical framework for unification-based grammar formalisms which is founded on the domain-theoretic techniques of Data Scott (Chapter 3). All three chapters are versions of papers presented at the Tenth International Conference on Computational Linguistics at Stanford University, Stanford, California during July 2 through 7, 1984. The research was initially part of the KLAUS (Knowledge Learning and Using System) project at SRI, set up with the intention of experimenting with mathematically well-founded alternatives to the DIALOGIC natural-language processing system. The more theoretical research was made possible in part by a gift from the Systems Development Foundation and was conducted as part of a coordinated research effort with the Computer Language subprogram at the Center for the Study of Language and Information, Stanford University. The PATR group at SRI is a rather liquid group of researchers which has included, at various times, John Bear, Lauri Karttunen, Fernando Pereira, Jane Robinson, Stan Rosenschein, Stuart Shieber, Susan Stucky, Mabry Tyson, and Hans Uszkoreit. The research reported here is a direct result of their aid and interaction. However, they should not be blamed for any errors in the present work, nor should the opinions expressed herein be construed as indicative of their personal predilections.