Learn Logic & Formal Reasoning

Explore our comprehensive educational materials to deepen your understanding of logic, Boolean algebra, and formal reasoning.

Your reading progress

How much logic do you already know?

We'll suggest where to start. Every guide stays available whichever you choose.

0 of 16 guides read

Start withIntroduction to Logic

Mark a guide as read when you finish it and we'll suggest what to read next.

Introduction Guides

Start your journey with our foundational guides covering the core concepts and principles of formal logic.

Whether you're a student, educator, or professional, these comprehensive tutorials will help you master the fundamentals of logical reasoning, from basic propositional logic to advanced predicate calculus and Boolean algebra.

  1. Step 1 of 16Beginner3 min read

    Introduction to Logic→

    A comprehensive introduction to the study of logic, its branches, historical context, and applications across various disciplines.

  2. Step 2 of 16Beginner2 min read

    Introduction to Propositional Calculus→

    Learn about propositions, truth tables, logical operators, and how to construct and evaluate logical expressions in propositional logic.

  3. Step 3 of 16Beginner7 min read

    Truth Tables→

    Master the fundamentals of truth tables, learn how to construct them for any logical expression, and use them to analyze logical equivalences and validate arguments.

  4. Step 4 of 16Beginner18 min read

    Logical Fallacies→

    Learn to identify and avoid common errors in reasoning, from informal fallacies like ad hominem and straw man arguments to formal fallacies in deductive reasoning.

  5. Step 5 of 16Beginner5 min read

    History of Logic→

    Journey through the evolution of logic from Aristotle's syllogisms to Gödel's incompleteness theorems, exploring how four brilliant minds shaped the foundations of rational thought.

  6. Step 6 of 16Intermediate9 min read

    Semantic Tableaux→

    How a proof works and how to build one: signed formulas, the ten decomposition rules, closing a branch, and reading a countermodel off one that stays open.

  7. Step 7 of 16Intermediate3 min read

    Introduction to Boolean Algebra→

    Discover the mathematical foundations of Boolean algebra, its laws and theorems, and its applications in digital systems and computer science.

  8. Step 8 of 16Intermediate20 min read

    Logic Gates & Digital Circuits→

    Explore how Boolean logic is implemented in hardware through logic gates (AND, OR, NOT, NAND, NOR, XOR) and how these gates combine to form digital circuits that power modern computing.

  9. Step 9 of 16Intermediate6 min read

    Karnaugh Maps→

    Simplify Boolean expressions by eye: how the grid is ordered, how to group the ones and the zeros, and how to read the minimal form off the map.

  10. Step 10 of 16Intermediate5 min read

    Introduction to Predicate Logic→

    Explore predicate logic (first-order logic), which extends propositional logic with predicates, quantifiers, and the ability to reason about objects and their properties.

  11. Step 13 of 16Advanced5 min read

    Introduction to Modal Logic→

    Learn about modal logic, including necessity and possibility operators, possible worlds semantics, axiom systems, and applications in philosophy, computer science, and AI.

Logic in Practice

Discover how logic is applied in real-world fields and technologies. These guides explore the practical applications of logical reasoning in artificial intelligence, programming, mathematics, philosophy, and linguistics.

  1. Step 11 of 16Intermediate9 min read

    Logic in Programming→

    Learn how Boolean logic, operators, and logical reasoning are essential to writing code, from control flow and conditionals to program verification and testing.

  2. Step 12 of 16Intermediate6 min read

    Logic in Mathematics→

    Understand how logic forms the foundation of mathematics, from proof techniques and mathematical induction to set theory, quantifiers, and the philosophy of mathematical truth.

  3. Step 14 of 16Advanced7 min read

    Logic in Artificial Intelligence→

    Explore how logic forms the foundation of AI systems, from knowledge representation and inference engines to machine learning and natural language processing.

  4. Step 15 of 16Advanced6 min read

    Logic in Philosophy→

    Explore the deep relationship between logic and philosophy, covering the philosophy of logic, modal systems, argument analysis, paradoxes, and the nature of logical truth.

  5. Step 16 of 16Advanced7 min read

    Logic in Linguistics→

    Discover how formal logic illuminates natural language structure and meaning, from compositional semantics and quantification to presupposition, modality, and computational linguistics.

Why Learn Logic?

Logic is the foundation of rational thinking and is essential in many fields including mathematics, computer science, philosophy, and artificial intelligence. Understanding logic helps you analyze arguments, write better code, prove mathematical theorems, and make sound decisions based on evidence and reasoning.

Key Benefits of Learning Logic

  • Enhance critical thinking and problem-solving abilities
  • Build a strong foundation for computer science and mathematics
  • Improve analytical reasoning in everyday decision-making
  • Develop skills essential for careers in technology, research, and academia

Ready to Get Started?

Ready to put your knowledge into practice? Try our interactive exercises to reinforce what you've learned, or use the logic calculator to experiment with different logical expressions and see real-time results.

Frequently Asked Questions

Find answers to common questions about using the Logic Calculator

Where should I start if I am new to logic?

Start with the guides. They are ordered as a reading path rather than an alphabetical list, and the index shows each guide's step number and the level it assumes. Telling the site how much logic you already know moves your starting point to the first guide at that level; the guides before it stay on the index as background reading.

What do the beginner, intermediate and advanced labels on the guides mean?

They say how much logic a guide assumes you already have, not how hard it is to read. The reading path never goes backwards through the levels, so once you have picked one you can read forward from your starting point without landing on a guide that depends on one you skipped.

Does the site remember which guides I have read?

Yes, in this browser. Marking a guide as read updates the progress count on the index and the 'up next' suggestion at the end of each guide, which points at the first guide after this one you have not read yet. Nothing is sent anywhere, and clearing your site data resets it.

Should I read the guides or do the exercises first?

Read enough of a guide to recognise the notation, then practise. The exercises are grouped by the same topics the guides cover, so the usual rhythm is a guide, then exercises in that category, then the next guide once the answers start coming easily.

What is the difference between propositional logic and Boolean algebra?

Propositional logic focuses on the relationships between propositions using logical operators, while Boolean algebra is a mathematical structure dealing with binary values (true/false or 1/0). Both are supported by this calculator and use similar operators.

See all questions