# LSEC Fellowships for Undergraduate and Graduate Students

Each year LSEC supports several Carnegie Mellon undergraduates interested in participating in LSEC projects and gain valuable research experience. Such participation can take place over the summer or during the academic year. If appropriate progress is made, projects beginning in the summer can be extended through (parts of) the following academic year, and projects begun in the fall can be extended through the spring and summer.

LSEC Fellows can elect to receive either course credit for independent research or a stipend. Fellows have reserved workspace in the lab, computing and programming support, and access to all LSEC resources. Projects can be an elaboration of one entry from the list below, or a project of the student's choice. Applicants must have an appropriate faculty sponsor for their projects, and we highly recommend collaborating with a faculty member on the application.

**There will be two due dates for the Spring and Fall terms.** The first is an early submission date; applications submitted by this date will be decided in time for work to commence by the beginning of term. The second is a late date; applications submitted by this date will be decided shortly after the late date, subject to availability of funds.

For Spring and Fall terms, the early submission will be two weeks before the start of classes; the late date will be one week after the start of classes.

**There will be only one due date for the Summer term.** The submission date will be four weeks before the end of classes of the Spring term; the expectation is that a student is working at least half-time for three months.

**Support for graduate students.** Such support is given for research projects pursued during the summer (NOT during the regular academic year).

LSEC Fellowships are also intended to help support presentations at conferences; applications for conference support may be made at any time. Applications should be submitted to Joseph Ramsey by email, or by hardcopy to his departmental address:

Dr. Joseph Ramsey

LSEC Fellowships, c/o Dept. of Philosophy

135 Baker Hall

Carnegie Mellon University

Pittsburgh, PA 15213

The applications should include:

- Name, Student Number, Primary Major
- Name of Faculty Sponsor
- Project proposal (approx. 2 pages including a short abstract)
- Resume
- Time Frame for Project (e.g., Summer, Fall, etc.)

## Suggestions for Research Projects

The list below presents broader research frames only - we encourage you to contact a faculty sponsor for a project (within such a frame) you are interested in carrying out.

**Causal and Statistical Reasoning** (Contacts: Richard Scheines, Clark Glymour, or Peter Spirtes)

*Implementing and testing algorithms for predicting the effects of policy interventions from non-experimental data*. Social scientists typically cannot do experiments, and are thus forced to make causal inferences from observational data and background knowledge. Spirtes, Glymour and Scheines (1993) have developed algorithms to take observational data and background knowledge and output a class of causal models that explain the data. An excellent project would be implemented some of these algorithms and to test them on real and simulated data. (Contact: Peter Spirtes)*Simulating Causal Systems.*Simulating data from a causal model constructed by the user has proved crucial in developing algorithms for causal inference, but our simulation environment is quite limited. Extending its functionality and giving it a more imaginative interface would help the project. (Contact: Richard Scheines)*Educational Modules*. One branch of the causal reasoning project is educational. The Dept. of Education has funded us to build web-based software to teach causal reasoning with statistical data. We are now constructing modules that have interactive Java applets to teach these concepts, and have a number of projects that would benefit from an undergraduate research project. (Contact: Richard Scheines or Clark Glymour)*Detecting Anomalies in Space Shuttle Launches*. We have the complete mission control launch data for 4 shuttle launches. (Contact: Joseph Ramsey or Clark Glymour)

**Computational Cognitive Science** (Contact: David Danks)

*How Humans Learn Causal Structure*. We believe that humans learn about causal structure in a different way than our computer algorithms do, but we don't know. Research is needed into how humans learn about causation, and how they might be trained to do so more effectively.*Learning from Distributed Datasets.*Some preliminary algorithms are known for learning about the world from multiple information sources. Potential projects include some combination of implementation, simulation, and extension of those algorithms, as well as multiple real-world applications.*Structure of Human Concept Learning*. Psychological theories of human concept representation have recently been represented using graphical models. Potential projects include developing formal models of concept learning, and testing those models empirically.*Integration of Concept and Causal Learning in Humans.*Causal learning depends on our concepts, and at least some concepts are described by causal structures. However, there are essentially no formal models that integrate these two processes. There are thus numerous open formal and empirical questions about any possible integration.*"Webs" of Causal Knowledge*. People seem to have quite wide-ranging, well-integrated webs of causal knowledge, even though we rarely learn about more than one or two causal relationships at a time. Potential projects include: empirical investigations of the size, coherence, and stability of those webs; and theoretical research on the ways in which people might integrate local learning into the web.*Unsupervised Human Concept Learning*. Most psychological research on concept learning has focused on the supervised case, in which the learner is taught the concept (implicitly or explicitly). In contrast, very little is known about unsupervised learning, in which people must determine the number and structure of concepts for themselves. Potential projects include: the extension of existing concept learning models to the unsupervised case; the translation of machine learning models to the psychological domain; and empirical investigations of the nature of unsupervised concept learning.

**Proof Search and Logical Reasoning** (Contacts: Wilfried Sieg or Joseph Ramsey)

*Automated Proof Search*. We have developed a very effective search method for finding natural proofs in logic. How can these techniques be extended to mathematical arguments? We are in the process of extending the underlying intercalation method to elementary set theory. This involves both interesting mathematical and computational issues.*Logic & Proofs*. The techniques of automated proof search, developed in the project above, are now being taught in a fully web-based course: Logic & Proofs. There are many areas where the logical presentation, examples, interactive learning environments and the graphical interface can be improved. However, the most important educational project is to refine an intelligent, dynamic tutor for proof construction using these techniques.*Educational experiments*. The web-based course provides an ideal setting for carrying out educational experiments; we want to investigate which methods are effective for teaching students basic notions and techniques in logic.*Mental Proofs*. Many powerful algorithms exist for finding proofs in logical systems. Some strive explicitly to use strategies that human experts are thought to employ, but little is known about how novice and experts actually search for proofs.

**Beyond Pure Logic **(Contacts: Wilfried Sieg or Joseph Ramsey)

As an extension of Logic & Proofs, we are developing a course presenting the fundamental Incompleteness and Undeidability Theorems that were first established in the 1930s by Gödel, Church and Turing. The substantive material is sketched below; however, the AProS search for proofs in set theory should also serve as the basis for intelligent tutoring in set theory.

*Elementary set theory*. Here one goal is to develop elementary set theory beginning with the axioms of Zermelo Fraenkel and ending with the famous theorems of Cantor and Cantor-Bernstein. However, apart from this purley set theoretic development, we focus on the REPRESENTATION of parts of mathematical practice in the formal framework of set theory. We do this first for elementary number theory and then for the theory of syntax. That allows us then to prove quite easily Gödel's Incompleteness theorems for set theory.*Computability theory*. The introduction to computability theory involves as the basic concept that of a Turing machine (computation). So we are aiming to implement Turing machines as a web-based application. The main undecidability result to be shown is the Halting Problem. Then we introduce a notion of EFFECTIVE REDUCIBILITY of one problem to another and show that the Halting Problem is reducible to the Decision Problem for Predictive Logic, but also to the Tiling Problem. The unsolvability of the Halting Problem implies directly the unsolvability of the other problems.

**Rational Choice **(Contacts: Teddy Seidenfeld or Kevin Zollman)

*Imprecise Probabilities and values*. The relevant information used in most real decision problems tends to be scarce, vague or even sometimes conflicting. By the same token preferences may also be incomplete. There are nevertheless well known theories of decision that can be applied to situations of this kind where both probabilities and value are imprecise. There is preliminary evidence (gathered through experiments carried by some of our faculty and students) that these theories can accommodate recalcitrant empirical evidence (like the so-called two-color Ellsberg’s paradox). Extensions of this work for non-binary choices in three color Ellsberg situations (as well as real-life versions of these situations) are planned for Spring and Fall 2010. Work includes the design of the experimental set-up, data-analysis, and the development of software.