Exploring Logic Courses at College Park

Logic, a discipline developed by mathematicians and philosophers, has found applications in various fields, including computer science, economics, law, linguistics, and psychology. Logic courses at College Park offer students the opportunity to delve into the intricacies of modern symbolic logic and its practical applications.

Core Concepts and Techniques

A logic course provides students with a thorough treatment of the basic concepts and techniques of modern symbolic logic, through classical first-order logic with identity. The courses concentrate on the construction of natural deduction proofs and on the evaluation of logical statements in semantic models. Along the way, students study some of the concepts from set theory (sets, functions, relations) used in the definition of semantic models for logical systems. Some courses may also introduce some alternative, or non-classical logics.

Course Design and Structure

"Logic & Proofs" is designed for students from a broad range of disciplines, from mathematics and computer science to drama and creative writing. It is also designed for someone who would like to get a real insight into modern symbolic logic. The course is highly interactive and engaging and brings a fresh perspective to classical material. These features make it possible for any student to master the material - by supporting their individual learning. After all, students in such introductory courses have quite diverse backgrounds and strikingly different perspectives on the courses’ formal aspects.

The presentation is multi-modal: each chapter is introduced by a concise lecture that formulates its central notions and techniques and motivates its learning objectives. In the main text, each central concept is also introduced by a brief lecture; each important technique is examined and used in a particular example. That kind of discussion is followed by interactive learning environments, namely, “Did I get this?” exercises that are essentially multiple-choice problems, and “Learn by doing” exercises that are genuine cognitive tutors.

The course material is carefully scaffolded and has been iteratively improved - using the feedback of both the many students who have taken the course and their instructors. Each chapter features review materials and assignments that include both quizzes and lab problems. The quizzes and practice questions provide fully automated feedback to students. The practice derivation problems offer support by the Dynamic Tutor.

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The LogicLab

The central logical skills are developed in the LogicLab lab environment mentioned earlier. Here, their learning is supported by an intelligent automated tutor. This Proof Tutor helps students, on demand and dynamically, to think through arguments in a systematic and strategic fashion. In the semantic truth-table and truth-tree problems, students practice techniques for a semantic analysis of formulae and arguments. They begin with “chasing truth up the tree of grammar”, in Quine’s vivid language; then they complete truth-tables and build truth-trees for sentential and predicate formulae involving identity. Of course, there is also the task of first checking whether a particular string of symbols is a formula of the language of sentential or predicate logic; that is done in an appropriate interface.

In the course itself, all these tasks are “fixed” in the OLI framework. That is why a Standalone LogicLab has been built; it is fully independent of the OLI platform. In the Standalone LogicLab, Independent Learners and students, but also instructors, at academic institutions can formulate and explore their own logical problems.

Course Options

Logic courses at College Park offer various options to cater to different needs and learning styles. These include:

Full Course (Semester System): Designed for a 13+ week semester, this course includes identity as a core chapter and offers functions as an additional topic.
Full Course (Semester System, Predicate Logic Focus): Also designed for a 13+ week semester, this version focuses on predicate logic in the core topics, with both identity and functions available as additional topics.

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Reduced Course (Quarter System): A slightly reduced course designed for a 10-week quarter system, including identity as a core chapter and with functions as an additional topic.
Sentential Logic Only: This option focuses solely on sentential logic.

The exams included in these versions are optional and can be removed from the course syllabus or left in as optional practice activities. Instructors can also request alterations to the selection of core vs. additional material to suit their needs.

Some versions of the material make all lab problems available to students at all times, while others restrict access based on completion of in-chapter activities and review problems.

Open & Free Courses

Open & Free OLI courses enable independent learners to study a subject on their own terms, at their leisure. Self-guided. Self-paced. Self-supported.

Active Learning and Engagement

Active student participation is not only encouraged, but required. At some institutions, Logic & Proofs is used as the main resource for a course with traditional weekly lectures, as well as meetings with a TA. At yet other institutions, Logic & Proofs has been offered as a fully self-paced course, with online and drop-in instructor and/or TA support, but without regular class meetings. In all three modes of use, Logic & Proofs has been found pedagogically effective.

Logic & Proofs for Individual Learners

Logic & Proofs is available for individual learners in two different modes. The first mode is the completely free version. This version does not include the chapter assignments or any exams; it is to be used for a detailed, free exploration of modern logic and this novel approach to logic instruction.

Then there is, secondly, the certificate version that carries a small registration fee of $80. Here the individual student has access to the full course content of Logic & Proofs (but without Instructor or TA support, and not including any exams). As in the free version, the chapters’ practice problems allow, when involving the construction of proofs, appeals to the Proof Tutor. The assignments do not; they give students the opportunity to demonstrate the mastery of their logical skills. Finally, in the certificate version, the learner has also access to the standalone version of the LogicLab, i.e., a free-standing application that has all the features of the online version.

At CMU, 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.

Instructor Options and Choices

For instructors wishing to try out or start using Logic & Proofs, there are several versions of the material available in the OLI Course Builder, accessible via an instructor's account on OLI:

The full course, designed for the semester system (13+ weeks), including identity as a core chapter and with functions available as an additional topic. This version includes three midterms and one final exam.
The full course, designed for the semester system (13+ weeks), including predicate logic only in the core topics, with both identity and functions available as additional topics. This version includes three midterms and one final exam.
A slightly reduced course, designed for the quarter system (10 weeks), including identity as a core chapter and with functions available as an additional topic. Chapters omitted in the core material are made available for reference in the additional topics. This version includes one midterm and one final exam
Sentential logic only. This version includes a final exam.

The exams included in these versions are optional. They can be removed from the course syllabus in the Course Builder, or left in but not assigned, instead serving as optional practice activities. We also have available versions of the material that include different numbers of exams, with the exam timing being somewhat different. Please contact us for details if you are interested in the possibility of using a different exam suite.

For instructors wishing to include functions as a core topic, or make any other alterations to the selection of core vs additional material, we are able to accommodate most such requests (given advance notice), and are happy to work with you to determine the best selection of core material to suit your needs.

The versions of the material mentioned above make all lab problems available to students at all times. We also offer precondition versions with the same content and exam options as those above that restrict access to lab problems as follows: students must complete in-chapter lab activities to unlock the chapter review problems, and must complete the review problem sets (by finishing at least one problem in each set) in order to unlock the chapter lab assignment.

Preparing for the LSAT

For students aiming to pursue law school, logic courses can be invaluable in preparing for the Law School Admission Test (LSAT). Courses like the TestMasters DC LSAT course offer comprehensive preparation, focusing on systematic techniques and authentic materials. Students have reported significant score improvements through such courses.

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