The Laboratory for Symbolic and Educational Computing

1. Overview
2. LSEC Projects
3. Resources
4. LSEC Fellowships

1. Overview

The Laboratory for Symbolic and Educational Computing (LSEC) is part of the Philosophy Department at Carnegie Mellon University. It was founded in 1996 by Wilfried Sieg, who co-directed it with Richard Scheines until June 30, 2005. Teddy Seidenfeld and Sieg are the current co-directors; Joseph Ramsey, the Department´s Director of Computing, has been providing direction and supervision for LSEC computational projects since 1998.

The Department's research orientation is heavily interdisciplinary. The disciplines, which are important for LSEC range from mathematical logic through the philosophy of science to decision and game theory. Modern philosophy has formulated many of the foundational questions germane to mathematics and the sciences and has answered several of them. Decision theory, game theory, logic, statistical causal inference and the theory of computation have all advanced significantly as a result of recent philosophical research.

Within this broad interdisciplinary context, the mission of LSEC is threefold:

• To advance research by the implementation and examination of central algorithms;
• To turn such advances into useful computational tools that will support researchers;
• To use the tools as part of computer taught courses that are highly interactive and completely web-based.

Current research and educational projects are described next.

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2. LSEC Projects

Here is a list of current research and educational projects that are currently pursued in LSEC.

• AProS
• Tetrad
• Isabelle
• Web-based Course: Causal and Statistical Reasoning
• Web-based Course: Empirical Research Methods (under development)
• Web-based Course: Logic & Proofs
• Web-based Course: Functions & Computation (under development)

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3. Resources

Computational Resources

The lab is equipped with several high end PCs, and laser printers, and substantial hard disk space. Computational support by the College and University (H&SS Computing Services, Computing Services) is outstanding.

Intellectual Resources

Joseph Ramsey, the Department´s Director of Computing, and Davin Lafon, LSEC´s Principal Research Programmer, the graduate students in Logic, Computation & Methodology, and the Department's faculty provide a wealth of computational experience.

Institutional Connections

LSEC is connected to several other labs and centers at Carnegie Mellon. The Department of Machine Learning combines faculty from Philosophy, Statistics, Computer Science, Robotics, and Language Technologies with a common interest in practically computable methods to learn from data. The Human-Computer Interaction Institute (HCII), has faculty from Philosophy, Computer Science, Design, the Software Engineering Institute, and Psychology with expertise in designing, implementing, and evaluating user interfaces, educational software, and computer mediated interaction in general.  The development of web-based courses is being pursued in the context of Carnegie Mellon´s Open Learning Initiative (OLI); there are also close interactions with the Pittsburgh Science of Learning Center (PSLC) and the Program in Interdisciplinary Educational Research (PIER).

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4. LSEC Fellowships for Undergraduates

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 of $12/hour. 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.

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 at jdramsey@andrew.cmu.edu

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 Undergraduate 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 elementary set theory and computability theory. 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 we the goal is to develop elementary set theory beginning with Zermelo’s axioms and ending with the famous theorems of Cantor and Cantor-Bernstein. It is a systematic development that introduces and explores in particular the central concept of a set theoretic function.
• 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 results to be shown are the Halting Problem and the unsolvability of the decision problem for predicate logic; after that the incompleteness theorems of Gödel are the focus of the presentation.

Rational Choice (Contacts: Teddy Seidenfeld or Horacio Arló-Costa)

• 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. (Contact Teddy Seidenfeld or Horacio Arló-Costa ).
• Neural models of choice. Patients with lesions to the ventromedial prefrontal cortex (VMPFC) exhibit both deficiencies in decision-making and in social tasks. There is no available unified explanation of these deficiencies; although recent work by McClelland and Maia (CMU) as well as Fellows and Farah (U. Penn) indicates that VMPFC mediates reversal learning (this evidence questions the usual interpretation of experiments like the so-called Iowa Task). This has lead many to think that these patients’ difficulties in the social domain might be due to their inability to rapidly and flexibly update their representation of social reinforcers. Thus the idea is that patients who have impairments in the rapid updating of stimulus-reinforcement contingencies would be expected to have social difficulties. In collaboration with NIH we are carrying experiments whose main goal is to provide a bridge between the laboratory findings regarding reversal-learning deficits and the real-life observations regarding social difficulties, by showing that VMPFC patients may be unable to adapt their behavior when the behavior of someone with whom they are interacting changes. This is done by implementing a sequential version of the so-called trust game, where patients play against a computer program (without knowing that this is the case). Work in this area may involve experimental design, data analysis, and design of computer interfaces and algorithms as well as analytic work concerning the sequential game itself (Contact: Horacio Arló-Costa ).

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