Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

Synthesizing Probabilistic Invariants via Doob's Decomposition

When analyzing probabilistic computations, a powerful approach is to first find a martingale---an expression on the program variables whose expectation remains invariant---and then apply the optional stopping theorem in order to infer properties at termination time. One of the main challenges, then, is to systematically find martingales. We propose a novel procedure to synthesize martingale expressions from an arbitrary initial expression. Contrary to state-of-the-art approaches, we do not rely on constraint solving. Instead, we use a symbolic construction based on Doob's decomposition. This procedure can produce very complex martingales, expressed in terms of conditional expectations. We show how to automatically generate and simplify these martingales, as well as how to apply the optional stopping theorem to infer properties at termination time. This last step typically involves some simplification steps, and is usually done manually in current approaches. We implement our techniques in a prototype tool and demonstrate our process on several classical examples. Some of them go beyond the capability of current semi-automatic approaches

Extending ACL2 with SMT Solvers

We present our extension of ACL2 with Satisfiability Modulo Theories (SMT) solvers using ACL2's trusted clause processor mechanism. We are particularly interested in the verification of physical systems including Analog and Mixed-Signal (AMS) designs. ACL2 offers strong induction abilities for reasoning about sequences and SMT complements deduction methods like ACL2 with fast nonlinear arithmetic solving procedures. While SAT solvers have been integrated into ACL2 in previous work, SMT methods raise new issues because of their support for a broader range of domains including real numbers and uninterpreted functions. This paper presents Smtlink, our clause processor for integrating SMT solvers into ACL2. We describe key design and implementation issues and describe our experience with its use.Comment: In Proceedings ACL2 2015, arXiv:1509.0552

Multifaceted companion devices: applying the new model of media attendance to smartphone usage

This study inspects the relationship between outcome expectations, habit strength, and smartphone usage by attempting to validate the new model of media attendance (NMMA) (LaRose and Eastin, 2004) , a social-cognitive theory of uses and gratifications. The fast adoption rate of smartphones, and their inherent characteristics as convergent, always-on, always-connected devices, warrant a closer look into user habitualization of this medium. Using a sample of 481 smartphone users selected from a larger panel, we were able to support the NMMA, although surprisingly no significant effect of habit strength on smartphone usage was found. While some uncertainties connected to the method are noted, this suggests a more complex reality, in which habitualization of a convergent media device does not necessarily implicate a significant rise in usage

Sphenomenology --- An Overview, with a Focus on a Higgsino LSP World, and on Eventual Tests of String Theory

In this talk, as requested, I begin with a overview and with some basic reminders about how evidence for supersymmetry in nature might appear -- in particular, how SUSY signatures are never clear so it is difficult to search for them without major theoretical input. Models can be usefully categorized phenomenologically by naming their LSP -- that is, once the LSP is approximately fixed so is the behavior of the observables, and the resulting behavior is generally very different for different LSPs. Next I compare the three main LSP-models (gravitino, bino, higgsino). Hints from data suggest taking the higgsino-LSP world very seriously, so I focus on it, and describe its successful prediction of reported events from the 1996 LEP runs. SUSY signatures in the $\tilde h$ LSP world are very different from those that are usually studied. Then I briefly discuss how to measure the parameters of the effective Lagrangian from collider and decay data. Finally I turn to how data will test and help extract the implications of string theories.Comment: Uses espcrc2.st