### Introductory course on logic

#### Patrick Blackburn

This course is an introduction to the basic ideas of classical
logic. Two main themes are emphasized: logic as a representation
language (that is, we will discuss what can and cannot be talked about
in various classical languages) and logic as a tool for reasoning (to
this end, we will introduce the idea of tableaux proofs). At the end
of the course the student should have a good grasp of a number of key
logical concepts, and be ready to tackle the advanced logic course
offered in week two.
Lecture 1. Propositional Calculus. In this lecture we discuss
propositional calculus, the simplest classical logic of all. We
introduce a simple tableau system for reasoning with it, and discuss a
number of key properties, notably decidability and completeness.

Lecture 2. First-Order Languages. In this lecture we start exploring a
more powerful and interesting system: first-order logic. We introduce
the first-order language, discuss their interpretation in relational
structures, and note some examples of the expressive power they offer
us.

Lecture 3. First-Order Tableaux. We extend the tableaux system
introduced in Lecture 1 to a full first-order tableaux system, and
give a number of examples of its use. We also discuss the limitations
of this type of tableaux system for automated reasoning, and
discuss how to fix this.

Lecture 4. The limits of first-order logic. The first part of this
lecture is devoted to the Compactness theorem, and what it has to tell
us about first-order expressivity. The second part of the lecture
discusses other tools for talking about relational structures, notably
second-order logic.