The program builds upon Carnegie Mellon's unique strengths in logic and its applications to computer science. Internationally recognized faculty, frequent workshops, colloquia, seminar series, and excellent computing facilities contribute to an ideal environment for both theoretical and applied research. Graduates of the program have gone on to prominent positions in industry and academe. Carnegie Mellon ranks highly in logic and related fields; see the university-maintained summary of rankings of various departments and programs at Carnegie Mellon.
Areas of strength include:
automated theorem proving
category theory and categorical logic
constructive mathematics
formal verification
foundations of decision theory
foundations of programming languages
logics of programs
lambda calculus
learning theory
model theory
proof theory
set theory
temporal and modal logics
theory of computing
type theory
Related research at Carnegie Mellon includes algorithms, artificial intelligence, combinatorial optimization, computational complexity, computational linguistics, operations research, and programming systems. See also the logic bibliography maintained at Carnegie Mellon.
Peter Andrews Professor of Mathematics mathematical logic, automated theorem proving, type theory
Horacio Arlo Costa Associate Professor of Philosophy philosophical logic, epistemology, knowledge representation
Jeremy Avigad Professor of Philosophy and Mathematical Sciences mathematical logic, proof theory, automated theorem proving, history and philosophy of mathematics
Steve Awodey Professor of Philosophy category theory, logic, philosophy of mathematics, history of logic and analytic philosophy
Lenore Blum Distinguished Career Professor of Computer Science computational complexity, real computation
Stephen Brookes Professor of Computer Science mathematical semantics of programming languages
Edmund Clarke FORE Systems Professor of Computer Science and Professor of Electrical and Computer Engineering automatic verification of computer hardware and software
James Cummings Associate Professor of Mathematical Sciences mathematical logic, set theory
David Danks Associate Professor of Philosophy causal learning, cognitive science, philosophy of psychology, philosophy of science
Clark Glymour Alumni University Professor of Philosophy philosophy of science, causal modeling, cognitive science, machine learning
Rami Grossberg Associate Professor of Mathematical Sciences mathematical logic, model theory
Robert Harper Professor of Computer Science type theory, logical frameworks, programming languages
Kevin Kelly Professor of Philosophy epistemology, philosophy of science, learning theory, computability, Ockham's razor
Peter Lee Professor of Computer Science foundations of programming languages, proof carrying code
Frank Pfenning Professor of Computer Science and Philosophy programming languages, logic and type theory, logical frameworks, automated deduction, trustworthy computing
André Platzer Assistant Professor of Computer Science logics of hybrid systems, logics of programs, automated theorem proving, proof theory, automatic verification, and hybrid systems verification
John Reynolds Professor of Computer Science semantics of programming languages
Richard Scheines Professor of Philosophy, Machine Learning, and Human Computer Interaction graphical and statistical causal inference, philosophy of social science, foundations of causation, educational technology
Ernest Schimmerling Associate Professor of Mathematical Sciences mathematical logic, set theory
Dana Scott Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic (Emeritus) mathematical logic, model theory, set theory, foundations of logic and mathematics, symbolic mathematical computation
Teddy Seidenfeld H. A. Simon Professor of Philosophy, Statistics, and Machine Learning foundations of statistics, decision theory
Wilfried Sieg Patrick Suppes Professor of Philosophy philosophy of mathematics, proof theory, automated proof search, history of modern logic, computability theory
Mandy Simons Associate Professor of Philosophy philosophy of language, formal semantics and pragmatics of natural language
Peter Spirtes Professor of Philosophy and Machine Learning graphical and statistical causal inference, causation in the social sciences, philosophy of physics
Richard Statman Professor of Computer Science and Mathematical Sciences mathematical logic, theory of computation, lambda calculus, combinatory logic
The three PAL departments offer many beginning, intermediate and advanced graduate logic courses. Beginning courses are repeated every year with more or less the same content each time whereas the topics covered in intermediate and advanced courses vary. Courses that are offered on a regular or semiregular basis include:
15-812 Semantics of Programming Languages
15-814 Type Systems for Programming Languages
15-819 Hardware and Software Verification
21-600 Mathematical Logic I
21-602 Set Theory I
21-603 Model Theory I
21-700 Mathematical Logic II
21-702 Set Theory II
21-703 Model Theory II
21-800 Advanced Topics in Logic
21-804 Math Logic Seminar
21-805 Lambda Calculus
80-610 Logic and Computation
80-615 Modal Logic
80-611 Computability and Incompleteness
80-612 Philosophy of Mathematics
80-618 Computability and Proof Search
80-619 Computability and Learnibility
80-711 Proof Theory
80-713 Category Theory
80-813 Seminar on Philosophy of Mathematics
80-820 Categorical Logic
One can read off departments from course numbers according to:
15-xxx Computer Science
21-xxx Mathematical Sciences
80-xxx Philosophy
Before each semester, a list of courses and descriptions for the upcoming term is published here.