# Background in Logic

• Neil Immerman
Chapter
Part of the Graduate Texts in Computer Science book series (TCS)

## Abstract

Mathematics enables us to model many things abstractly. Group theory, for example, abstracts features of such diverse activities as English changeringing and quantum mechanics. Mathematical logic carries the abstraction one level higher: it is a mathematical model of mathematics. This book shows that the computational complexity of all problems in computer science can be understood via the complexity of their logical descriptions. We begin with a high-level introduction to logic. Although much of the material is well-known, we urge readers to at least skim this background chapter as the concentration on finite and ordered structures, i.e., relational databases, is not standard in most treatments of logic.

## Keywords

Free Variable Function Symbol Boolean Variable Relation Symbol Numeric Relation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Notes

1. 1.
Usually we will take ϕ0 = true, thus letting |I(A)| = |A|k, cf. Remark 1.32.Google Scholar