Preliminaries

Abstract

In this preliminary chapter we will focus on four different subjects. First, we present rules. They will be used throughout this work for defining functions in an elegant and simple way. In the second section the standard notions for first-order logic are introduced [CL73]. This introduction is quite short, we merely present the notations we shall need. As the standard notations for logic are used, readers familiar with this topic may skip the second section. Since a large part of the indexing techniques rely on tree-like structures, we state some notions describing graphs and trees in the third section. Finally, we describe the way algorithms are presented.