Screenshot of a subformulae activity in the course.

Logic & Proofs[Enter Course]


Logic is a remarkable discipline. It is deeply tied to mathematics and philosophy, as correctness of argumentation is particularly crucial for these abstract disciplines. Logic systematizes and analyzes steps in reasoning: correct steps guarantee the truth of their conclusion given the truth of their premise(s); incorrect steps allow the formulation of counterexamples, i.e., of situations in which the premises are true, but the conclusion is false.

Recognizing (and having conceptual tools for recognizing) the correctness or incorrectness of steps is crucial in order to critically evaluate arguments, not just in philosophy and mathematics, but also in ordinary life. This skill is honed by working in two virtual labs. In the ProofLab you learn to construct complex arguments in a strategically guided way, whereas in the TruthLab the emphasis is on finding counterexamples systematically.

Who should take this course?

This is an introductory course designed for students from a broad range of disciplines, from mathematics and computer science to drama and creative writing. The highly interactive presentation makes it possible for any student to master the material. Concise multimedia lectures introduce each chapter; they discuss, in detail, the central notions and techniques presented in the text, but also articulate and motivate the learning objectives for each chapter.

Open & Free Version

The Open & Free, Logic & Proofs course includes the first five chapters of Logic & Proofs, providing a basic introduction to sentential logic. A full version of Logic & Proofs, including both sentential and predicate logic, is also available without technical or instructor support to independent users, for a small fee. No credit is awarded for completing either the Open & Free, Logic & Proofs course or the full, unsupported Logic & Proofs course.

Academic Version

Academic use of Logic & Proofs provides a full course on modern symbolic logic, covering both sentential and predicate logic, with identity. Optional suites of exams are available for use in academic sections.

Additional Course Details

Topics Covered:
The notions of statement and argument; Logical analysis of informal arguments; Syntax and semantics of: sentential logic, predicate logic, and identity; Natural deduction-style proofs, with an emphasis on effective and strategic proof construction; and Truth-trees, with an emphasis on systematic construction of counterexamples from completed trees.
Estimated Time to Complete Course:
This is a semester long course, taking one week to cover each of the 12 core chapters of the material. That includes the homework assignments at the end of each chapter.
The course can also be used as an accelerated, 4 to 6 week introduction to or review of logic, at the rate of two to three chapters per week (possibly omitting some chapters or sections), to be followed by additional topics for the remainder of the semester.
Additional Software or Materials Required:
You will need Flash and Java installed. Flash is required for both the multimedia lectures and the many interactive learning activities; Java is required for the TruthLab and ProofLab. These programs are free. More detailed information is provided in the course under “Test and Configure Your System.”
Maintenance Fee (per student):
Free for independent learners; $80 for academic students.

In-Depth Description

Logic & Proofs is an introduction to modern symbolic logic, covering sentential and predicate logic (with identity). The course is highly interactive and engaging. It brings a fresh perspective to classical material by focusing on developing two crucial logical skills: strategic construction of proofs and the systematic search for counterexamples.

Concise multimedia lectures introduce each chapter of the course and discuss in detail central notions and techniques presented in the text. The introductory lectures articulate and motivate the learning objectives for each chapter.


The two crucial logical skills are developed via numerous exercises in two lab environments:

In the ProofLab, the main workbench of Logic & Proofs, students practice proof construction in a natural deduction framework. Their learning is supported by an intelligent and dynamic automated tutor. This tutor helps students, in a dialogue, to think through arguments in a strategic and systematic fashion.

In the TruthLab, the semantic counterpart to the ProofLab, students practice techniques for semantic analysis of formulae and arguments. They begin with chasing truth up a parse tree, then complete truth-tables, and ultimately learn to build truth-trees for predicate formulae involving identity. The emphasis is on reading off counterexamples to invalid arguments from completed trees.


Each chapter features both review materials and homework assignments, including quizzes and lab problems. The end-of-chapter quizzes and practice questions provide fully automated feedback to the student; the ample practice lab problems offer tutoring, while the problems in the chapter’s lab assignment do not, providing students with the opportunity to demonstrate mastery of the skills developed in completing the practice problems.


At Carnegie Mellon and elsewhere, Logic & Proofs is offered as a semester-long introductory logic course. In addition to working through the online material at a specified rate (approximately one chapter per week), the class meets in small groups once a week for an instructor-led discussion session. Active student participation is not only encouraged, but required.

At some institutions, Logic & Proofs has been offered as a fully self-paced course, with online and drop-in instructor and TA support, but without regular class meetings. At yet other institutions, Logic & Proofs is used as the main resource for a course with traditional weekly lectures, as well as meetings with a TA. In all three modes of use, Logic & Proofs has been found pedagogically effective. See the relevant research by Schunn and Patchan at the AProS project site.

The course has been taken (from September 2004 to June 2012) by more than 5,000 students for credit at various institutions including Carnegie Mellon, Carnegie Mellon Qatar, IUPUI, Francisco Marroquín University (Guatemala), Haverford College, University of British Columbia, University of Nevada in Las Vegas, Kent State University, College of Lake County. The course is is now also being offered through Stanford’s EPGY Program to high-school students.