Mathematical Linguistics

Welcome to Mathematical Linguistics, a course covering the mathematics you need to know for Formal Linguistics. This course won’t be as rigorous as a math course, but you will be able to use all of this information and apply it to linguistics. If you have any questions or suggestions, please email them to



Introduction and Overview

Foundation of Mathematics

Basics of Set Theory
Power Sets
Set Operations
Set Laws
Ordered Pairs and Relations
Composition of Functions
Properties of Relations
Equivalence Relations and Partitions

Propositional Logic, Predicate Logic, and Compositional Semantics

Introduction to Propositional Logic and Truth Tables
Tautologies, Contradictions, and Contingencies
Logical Equivalence
Compositional Semantics with Propositional Logic
Compositional Semantics with Propositional Logic Examples
Introduction to Predicate Logic and Translation
Predicate Logic Syntax
Quantifier Raising and Logical Form
Compositional Semantics with Predicates
Compositional Semantics with Pronouns

Formal Languages and Automata

Introduction to Formal Languages and Finite State Machines
Formal Definition of Finite State Machines and Regular Operators
Regular Operations on Finite State Machines
Regular Expressions
Pumping Lemma for Regular Languages
Human Language is not Regular
Context-Free Grammar
Chomsky Normal Form
Pumping Lemma for Context-Free Languages
Context-Sensitive Grammar
Tree-Adjoining Grammar

Abstract Algebra

Algebras and Operations
Identity Elements, Inverse Elements, and Zero Elements
Subgroups, Semigroups, and Monoids
Integral Domains and Well-Ordering
Posets and Duality
Lattices and Semilattices
Filters and Ideals
Boolean Algebra



Mathematical Linguistics – Exam 1 (Foundations of Mathematics, Propositional Logic, and Compositional Semantics)
Mathematical Linguistics – Exam 1 Solutions
Mathematical Linguistics – Exam 2 (Predicate Logic and Compositional Semantics)
Mathematical Linguistics – Exam 2 Solutions
Mathematical Linguistics – Exam 3 (Formal Languages and Automata)
Mathematical Linguistics – Exam 3 Solutions
Mathematical Linguistics – Exam 4 (Abstract Algebra)
Mathematical Linguistics – Exam 4 Solutions