Logic, Computation and Methodology

The Master of Science in Logic, Computation, and Methodology at Carnegie Mellon University is a rigorous postgraduate program designed for students interested in the foundational aspects of computer science, logic, and mathematical reasoning. This interdisciplinary program integrates advanced coursework and research opportunities in formal logic, theoretical computer science, and philosophical methodology, preparing graduates to contribute to both academic research and practical applications in industry. Students engage deeply with topics such as computational logic, proof theory, algorithms, formal semantics, and the philosophy of computation, developing a comprehensive understanding of the principles that underpin modern computing systems and artificial intelligence. The program emphasizes critical thinking, analytical skills, and the ability to rigorously analyze complex systems, making it suitable for students aiming for academic careers or advanced research positions. Designed to foster innovation and inquiry, the curriculum includes courses taught by leading experts in the fields of logic, computer science, and philosophy, encouraging an interdisciplinary perspective that bridges theory and practice. Students also have opportunities to participate in cutting-edge research projects, attend seminars and workshops, and collaborate with faculty on innovative topics. The program prepares graduates for doctoral studies or roles in research, development, and consulting in academia, technology companies, or governmental agencies. Specializations within the program may include formal verification, computational linguistics, cognitive science, or ethics in AI, among others. Overall, the program aims to cultivate a deep understanding of the theoretical foundations of computation, enhance analytical reasoning, and promote the application of logical methods to solve complex problems across diverse domains. Graduates leave the program equipped with the skills and knowledge to advance scientific understanding and technological innovation in an increasingly computational world.

The program's course requirements are designed to provide students with a shared introduction to basic tools of philosophical analysis, a shared background of philosophical issues, significant interdisciplinary competence, and an introduction to research topics in the department.

By default students are presumed to be in the course-based degree option (they will not write a thesis). If a student would like to write a thesis, they must seek approval from one member of the department (the supervisor) and one additional faculty member (the second reader). This permission must be secured prior to the first day of classes of the fourth semester, but students are strongly advised to secure it earlier.

In the requirements below we refer to the "philosophical areas." For the purpose of our requirements philosophical areas are:

• Area 1: Philosophy of Science, Methodology, and Epistemology
• Area 2: Value Theory
• Area 3: History of Philosophy
• Area 4: Philosophy of Mind, Philosophy of Language, Lingusitics, and Metaphysics
• Area 5: Philosophy of Mathematics and Logic

Core requirements

• 80-600 Philosophy Core Seminar I and II (2 semesters): Survey of crucial research in philosophy, logic, and related areas
• 80-610 Formal Logic: The syntax and semantics of first-order logic, and related topics
• 80-618 Topics in Logic I (half semester): The theory of computability, and Gödel's incompleteness theorems
• 80-616 Formal Methods (1.5 semesters): An introduction to contemporary formal frameworks, including Bayes Nets, Decision Theory, Game Theory, and Formal Learning Theory
• Professional development seminar: Students must enroll in the professional development seminar in the spring semester of both years
• Two courses from two different philosophical areas

With approval of the Director of Graduate Studies, other courses in logic may be substituted for 80-610 and 80-618. For example, 80-619 Computability and Learnability may be substituted for 80-618.

Philosophy electives

Course-based option

• Two graduate level courses from any of the five philosophical areas

Thesis option

• Two course of independent thesis research

Interdisciplinary requirement

An interdisciplinary elective, e.g. in logic, computer science, statistics, game theory, linguistics, economics, or psychology, to develop formal skills that will support thesis research. These courses need to be approved by the Director of Graduate Studies. Suitable courses include:

• 10-701 Machine Learning
• 15-211 Fundamental Data Structures and Algorithms
• 21-601 Model Theory I
• 36-625 Probability and Mathematical Statistics I
• 85-719 Introduction to Parallel Distributed Processing
• 85-765 Cognitive Neuroscience

Additional courses

• Two additional graduate level courses

NOTE: A maximum of two directed readings may be used to fulfill the requirements for the course-based masters degree without special permission from the Director of Graduate Studies. Students in the course-based option are encouraged, however, to consider taking at least one directed reading to further delve into an area of a previous course.

• Graduate application
• Sample of original written work
• Personal research statement
• Three (or more) letters of recommendation
• Transcripts from all previously attended colleges or universities
• GRE scores (Institution code: 2074; Department code: 2801)
• TOEFL or IELTS scores for non-native English speaking applicants
• $50 application fee

Scanned versions of official transcripts, GRE score reports, and TOEFL / IELTS scores can be uploaded in lieu of sending paper copies.

Scholarships

The Philosophy Department offers qualified M.S. students up to a 50% tuition fellowship, added to whatever outside fellowships or other tuition awards the student has gained on her or his own. In addition, qualified MS students have the opportunity to serve as teaching assistants or graders for undergraduate courses, for a stipend rate set annually by the department. In the 2015-2016 academic year, by TAing or grading one course per term for each of two terms, an M.S. student earns $8,000 in stipend. In addition, the department provides approximately $1,100 to cover the cost of a Carnegie Mellon health insurance policy

The program in Logic, Computation and Methodology at Carnegie Mellon University offers students a comprehensive exploration of foundational issues in logic, the theoretical underpinnings of computation, and methodologies used in formal reasoning and computer science research. Designed for students interested in the interfaces among philosophy, computer science, and mathematics, this program emphasizes developing a deep understanding of logical systems, algorithms, and the processes involved in formal analysis. Students engage with topics such as propositional and predicate logic, model theory, proof theory, complexity theory, algorithms, and the philosophical implications of formal systems. The curriculum typically includes coursework that covers the formal methods used in artificial intelligence, programming language semantics, and the design of logical frameworks for reasoning about computation.

Throughout the program, students have opportunities to participate in cutting-edge research projects, often collaborating with faculty members who are leaders in their fields. The program aims to equip graduates with the analytical and technical skills necessary for careers in academia, research institutions, or industry roles in software development, formal verification, and artificial intelligence. The education fosters a rigorous mindset for abstract reasoning and problem-solving, preparing students to contribute to the advancement of logic, computation, and related disciplines. The interdepartmental nature of the program allows students to take advantage of resources in Computer Science, Philosophy, and Mathematical Sciences, emphasizing a well-rounded and interdisciplinary approach to understanding computational and logical paradigms. Overall, graduates of the Logic, Computation and Methodology program become equipped to push the boundaries of theoretical computer science and philosophy, applying their knowledge to real-world problems and innovative research questions.