Logic for Computer Science and Artificial Intelligence

Chapter 1

Introduction

We briefly analyze the relationship between logic and computer science, by focusing successively on two points of views, in a somewhat natural order. We first underline the importance of logic in the foundations of computer science and how it is used in many computer science domains. Then we explain why logic is useful for computer engineers.

1.1. Logic, foundations of computer science, and applications of logic to computer science

Trying to underline the importance of logic for computer science in the 21st Century is the same as trying to reinvent the wheel. Indeed, in 1969, C.A.R. Hoare wrote:

Computer programming is an exact science, in that all the properties of a program and all the consequences of executing it can, in principle, be found out from the text of the program itself by means of purely deductive reasoning.

More recently, in 1986, Hoare stated that “computers are mathematical machines and computer programs are mathematical expressions”.

Of course, in our defence of logic, we will not make use of arguments relying on Hoare’s renowned expertise, as these arguments may turn out to be fallacious; however, we attempt to shed some light on this kind of sentence and to convince the reader that the importance of logic for computer science is a fact and not a matter of opinion.

Logical concepts have been of prime importance in computer science, and this is still the case nowadays.

Instead of making a potentially tedious enumeration, we shall simply ...