| this paper , following @xcite , presents an approach to grammar description and processing based on the geometry of _ cancellation diagrams _ , a concept which plays a central role in combinatorial group theory @xcite . the focus here is on the geometric intuitions and on relating group - theoretical diagrams to the traditional charts associated with context - free grammars and type-0 rewriting systems . the paper is structured as follows . we begin in section 1 by analyzing charts in terms of constructs called _ cells _ , which are a geometrical counterpart to rules . then we move in section 2 to a presentation of cancellation diagrams and show how they can be used computationally . in section 3 we give a formal algebraic presentation of the concept of _ group computation structure _ , which is based on the standard notions of free group and conjugacy . we then relate in section 4 the geometric and the algebraic views of computation by using the fundamental theorem of combinatorial group theory @xcite . in section 5 we study in more detail the relationship between the two views on the basis of a simple grammar stated as a group computation structure . in section 6 we extend this grammar to handle non - local constructs such as relative pronouns and quantifiers . we conclude in section 7 with some brief notes on the differences between normal submonoids and normal subgroups , group computation versus rewriting systems , and the use of group morphisms to study the computational complexity of parsing and generation . |