Undergraduate Degrees
The Major in Logic and Computation
Director: Professor Arló Costa
Office: Baker Hall 161B
Email: hcosta[at]andrew.cmu.edu
The Logic and Computation curriculum takes advantage of the preparation provided by the H&SS 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.
Curriculum
Logic and Computation is a B.S. degree. In their freshman and sophomore years, students are expected to take four courses that provide preparation in logic, computer science, mathematics, and statistics: Programming Fundamentals (15-111), Concepts of Mathematics (21-127), Statistical Reasoning (36-201), Arguments and Mathematical Inquiry (80-211). This last course is already 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 15-211/212.
NOTE: Students should complete the prerequisites before their junior year. It is strongly recommended that students take Arguments and Mathematical Inquiry no later than the spring of their sophomore year and, if possible, also Fundamental Data Structures and Algorithms and Principles of Programming. 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 six core courses, four electives, and one seminar. The core courses provide comprehensive background in logic, computability, and analytic philosophy. Logic and Computation (80-310) and Minds, Machines, and Knowledge (80-300) 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 the thesis seminar.
Prerequisites (28 units)*15-111 Intermediate/Advanced Programming (10 units)
21-127 Concepts of Mathematics**
36-201 Statistical Reasoning***
*Only the 10 units for 15-111 are unique to the major.
**Can also be used to fulfill the DCR5, Mathematical Reasoning requirement in
the H&SS General Education program.
***This course fulfills the CCR4, Statistical Reasoning requirement in the H&SS
General Education program.
80-211 Arguments and Mathematical Inquiry
80-300 Minds, Machines, and Knowledge
80-310 Logic and Computation
80-311 Computability and Incompleteness
80-511 Thesis seminar
15-211 Fundamental Data Structures and Algorithms**
15-212 Principles of Programming**
*Only 45 units are unique to the major; 15-211 and 15-212 count toward total
units for the General Education Program, DCR6.
**It is recommended that students complete 15-211 and 15-212 in the sophomore
year; H&SS students can use these courses to satisfy their General Education
requirement in the category DCR6, Science and Technology.
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 Curricula
Here are five samples of Logic and Computation curricula (beyond the core courses), each reflecting a different emphasis.Sample 1. A student interested in Computer Science might take
the following courses:
80-315 Modal Logic (or: 80-413 Category Theory)
80-316 Probability and Artificial Intelligence
80-317 Constructive Logic
15-312 Programming Languages: Design and Processing
Sample 2. A student interested in Language and Information
Technology might take the following courses:
80-280 Linguistic Analysis
80-480 Linguistic Theory
80-481 Formal Semantics
11-682 Introduction to Language Technologies
Sample 3. A student interested in Artificial Intelligence
and Cognitive Science might take the following courses:
80-314 Logic in Artificial Intelligence
80-315 Modal Logic (or: 80-318 Mechanized Reasoning; or: 80-319 Machine Learning)
80-316 Probability and Artificial Intelligence
85-411 Cognitive Processes and Problem Solving
Sample 4. A student interested in Logic and the Foundations
of Mathematics might consider the following courses:
80-312 Philosophy of Mathematics (or: 80-254 Analytic Philosophy)
80-318 Mechanized Reasoning: proof search by machine (or: 80-319 Machine Learning)
80-411 Proof Theory (or: 21-229 Set Theory) 80-413 Category Theory
Sample 5. A student interested in Methodology might consider
the following courses:
80-220 Philosophy of Science (or: 80-221 Philosophy of Social Science)
80-319 Machine Learning (or: 80-312 Philosophy of Mathematics)
80-321 Causality and Social Policy
36-309 Experimental Design Logic and Computation
Degree Requirements (min.) 360 units
Logic and Computation as a Second Major
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-H&SS students interested in an additional major in Logic and Computation need to take only those courses in the H&SS General Education Program that are prerequisites to courses required in the major; all other H&SS General Education requirements are waived for these students. Depending on the student's background, 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 M.S. Program in Logic and Computation
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.
Resources for Current Majors
The following links are for students currently enrolled in the program.