First-Order Logic, also called predicate logic or predicate calculus, extends propositional Logic with functions, relations, and quantification over individuals.

Recall our informal summary Predicate Logic Informally, as well as lecture06 on formal treatment of propositional logic. We next give such precise treatment to first-order logic. In future lectures we cover questions of automation for first-order logic.

Announcement: mathematical logic course (in French) this semester.

First-Order Logic Syntax

First-Order Logic Semantics

First-Order Theories

Substitutions for First-Order Logic

Evaluating Formulas in Finite Structures

Graphs as Interpretations

Isomorphism of Interpretations

Continued in lecture10.

• Calculus of Computation Textbook, Chapter 2 and Section 3.1