Logic & Proofs

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 thesystematic 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.