Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

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

Philosophy of Computer Science: An Introductory Course

There are many branches of philosophy called “the philosophy of X,” where X = disciplines ranging from history to physics. The philosophy of artificial intelligence has a long history, and there are many courses and texts with that title. Surprisingly, the philosophy of computer science is not nearly as well-developed. This article proposes topics that might constitute the philosophy of computer science and describes a course covering those topics, along with suggested readings and assignments

Arena: A General Evaluation Platform and Building Toolkit for Multi-Agent Intelligence

Learning agents that are not only capable of taking tests, but also innovating is becoming a hot topic in AI. One of the most promising paths towards this vision is multi-agent learning, where agents act as the environment for each other, and improving each agent means proposing new problems for others. However, existing evaluation platforms are either not compatible with multi-agent settings, or limited to a specific game. That is, there is not yet a general evaluation platform for research on multi-agent intelligence. To this end, we introduce Arena, a general evaluation platform for multi-agent intelligence with 35 games of diverse logics and representations. Furthermore, multi-agent intelligence is still at the stage where many problems remain unexplored. Therefore, we provide a building toolkit for researchers to easily invent and build novel multi-agent problems from the provided game set based on a GUI-configurable social tree and five basic multi-agent reward schemes. Finally, we provide Python implementations of five state-of-the-art deep multi-agent reinforcement learning baselines. Along with the baseline implementations, we release a set of 100 best agents/teams that we can train with different training schemes for each game, as the base for evaluating agents with population performance. As such, the research community can perform comparisons under a stable and uniform standard. All the implementations and accompanied tutorials have been open-sourced for the community at https://sites.google.com/view/arena-unity/

Causal simulation and sensor planning in predictive monitoring

Two issues are addressed which arise in the task of detecting anomalous behavior in complex systems with numerous sensor channels: how to adjust alarm thresholds dynamically, within the changing operating context of the system, and how to utilize sensors selectively, so that nominal operation can be verified reliably without processing a prohibitive amount of sensor data. The approach involves simulation of a causal model of the system, which provides information on expected sensor values, and on dependencies between predicted events, useful in assessing the relative importance of events so that sensor resources can be allocated effectively. The potential applicability of this work to the execution monitoring of robot task plans is briefly discussed