In setting up a formal system to specify a grammar formalism, the conventional (mathematical) wisdom is to start with primitives (basic primitive structures) as simple as possible and then introduce various operations for constructing more complex structures. An alternate approach is to start with complex (more complicated) primitives, which directly capture some crucial linguistic properties and then introduce some general operations for composing these complex structures. These two approaches provide different domains of locality, i.e., domain over which various types of linguistic dependencies can be specified. This latter approach, characterized as COMPLICATE LOCALLY, SIMPLIFY GLOBALLY (CLSG), pushes non-local dependencies to become local, i.e., they arise in the basic primitive structures to start with.

The CLSG approach has led to some new insights into syntactic description, semantic composition, language generation, statistical processing, and psycholinguistic properties, all these with possible relevance to the cognitive architecture for language. I will describe these results in an introductory manner. I will also briefly talk about the implications of this approach for the characterization of discourse structure. If time permits I will comment on some other formalisms that are intermediate between the two approaches mentioned above.