Director: Professor Spirtes

Office: Baker Hall 135D

Email: ps7z[at]andrew.cmu.edu

The Logic and Computation curriculum takes advantage of the preparation provided by the Dietrich College General Education Program in mathematics, philosophy, psychology, and statistics. It is flexible in that it permits students to focus on any of a number of areas including (but not limited to):

- computer science;
- language and information technology;
- artificial intelligence and cognitive science;
- logic and the foundations of mathematics;
- methodology and philosophy of science.

Students in the program take a common core of courses in logic, methodology, and computer science, together with an associated seminar in their senior year. The individual focus is achieved by selecting a sequence of four advanced and closely related courses. It is in this area of focus (or specialization) that students write their senior thesis under the supervision of a faculty member. A number of sample curricula are presented below.

The resulting education in logic, analytic philosophy, mathematics, statistics, and computer science enables students to pursue professional careers or graduate study. The analytic and communication skills developed in the major support a wide range of career choices, including those among the fields of technology, business, and law. Fields of graduate study for which students are well prepared include, for example, computer science, cognitive science, philosophy, logic, and linguistics.

Students who are interested in pursuing this major, or who are pursuing it already, should take note of the Cognitive Science major in the Department of Psychology. That major is so closely related that it is not difficult to pursue it as an additional major, and it provides an intellectually exciting complement.

Logic and Computation is a B.S. degree. In their freshman and sophomore years, students are expected to take three courses that provide preparation in computer science, mathematics, and statistics: 15-110 Principles of Computing, 21-127 Concepts of Mathematics, 36-201 Statistical Reasoning and Practice. 80-211 Logic and Mathematical Inquiry is part of the major's Core Requirements, but should be taken no later than the spring of the sophomore year. This also applies to the computer science sequence 15-121 and 15-150/15-211.

NOTE: Students should complete the prerequisites before their junior year. It is strongly recommended that students take 80-211 Logic and Mathematical Inquiry no later than the spring of their sophomore year and, if possible, also 15-121 and 15-150 /15-211 . However, with suitable planning and advice from the program director, it is possible to complete the program in two years, beginning in the junior year.

The course requirements for the major consist of seven core courses (including one seminar) and four electives. The core courses provide comprehensive background in logic, computability, and analytic philosophy. 80-310 Logic and Computation and 80-150 Nature of Reason must be taken no later than the fall of the junior year. Four advanced electives are chosen in the area of focus, and should support independent research towards fulfilling the senior thesis requirement. In their senior year, students present and discuss their research in 80-511 Thesis Seminar.

15-112 Fundamentals of Programming and Computer Science (12 units)

21-127 Concepts of Mathematics (10 units)

36-201 Statistical Reasoning and Practice (9 units)

80-150 Nature of Reason (9 units)

80-211 Logic and Mathematical Inquiry (9 units)

80-310 Logic and Computation (9 units)

80-311 Computability and Incompleteness (9 units)

15-122 Principles of Imperative Computation (10 units)

15-150 Principles of Functional Programming (10 units)

80-511 Thesis Seminar (9 units)

Bearing in mind prerequisites, Logic and Computation majors must complete four advanced courses in areas that use logical and computational tools, such as philosophy, computer science, linguistics, mathematical logic, psychology, or statistics. The sequence of courses, mostly at the 300-level, must be selected in consultation with the program director.

**Sample 1.** A student interested in Computer Science might take
the following courses:

80-315 Modal Logic

80-413 Category Theory

15-312 Foundations of Programming Languages

15-317 Constructive Logic

**Sample 2.** A student interested in Language and Information
Technology might take the following courses:

80-280 Linguistic Analysis

80-281 Language and Thought

80-381 Meaning in Language

80-383 Language in Use

80-580 Seminar on the Philosophy of Language

**Sample 3.** A student interested in Artificial Intelligence
and Cognitive Science might take the following courses:

80-313 Philosphical Logic

80-314 Logic and Artificial Intelligence

80-315 Modal Logic

80-411 Proof Theory

85-412 Cognitive Modeling

**Sample 4.** A student interested in Logic and the Foundations
of Mathematics might consider the following courses:

80-254 Analytic Philosophy

80-312 Philosophy of Mathematics

80-365 Ramsey

80-411 Proof Theory

80-413 Category Theory

**Sample 5.** A student interested in Methodology might consider
the following courses:

80-220 Philosophy of Science

80-221 Philosophy of Social Science

80-321 Causation, Law, and Social Policy

36-309 Experimental Design for Behavioral and Social Sciences

Logic and Computation Degree Requirements (min.) 360 units

The Logic and Computation major is also suitable as a second major for students in H&SS or for students in other colleges within the university. Non-Dietrich College students interested in an additional major in Logic and Computation need to take only those courses in the Dietrich College General Education Program that are prerequisites to courses required in the major; all other Dietrich College General Education requirements are waived for these students. Depending on the student's back-ground, the requirements of the second major in Logic and Computation can be fulfilled with as few as five additional courses. However, the department limits the courses that may be ‘double counted'; the core courses in the Philosophy department may not be double counted.

The Department of Philosophy also offers a graduate M.S. degree in Logic and Computation, which culminates with the writing of a master's thesis. It is ordinarily a two-year program, but students in the Logic and Computation major are able to complete the additional requirements in one year. Interested students are invited to contact the department for further information and apply to the program in their senior year. Details can be found on the department's homepage: http://hss.cmu.edu/philosophy/

The following links are for students currently enrolled in the program.