Eliciting implicit assumptions of proofs in the MIZAR Mathematical Library by property omission

When formalizing proofs with interactive theorem provers, it often happens that extra background knowledge (declarative or procedural) about mathematical concepts is employed without the formalizer explicitly invoking it, to help the formalizer focus on the relevant details of the proof. In the contexts of producing and studying a formalized mathematical argument, such mechanisms are clearly valuable. But we may not always wish to suppress background knowledge. For certain purposes, it is important to know, as far as possible, precisely what background knowledge was implicitly employed in a formal proof. In this note we describe an experiment conducted on the MIZAR Mathematical Library of formal mathematical proofs to elicit one such class of implicitly employed background knowledge: properties of functions and relations (e.g., commutativity, asymmetry, etc.).Comment: 11 pages, 3 tables. Preliminary version presented at the 3rd Workshop on Modules and Libraries for Proof Assistants (MLPA-11), affiliated with the 2nd Conference on Interactive Theorem Proving (ITP-2011), Nijmegen, the Netherland

Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora

Deliberation, Representation, Equity

"What can we learn about the development of public interaction in e-democracy from a drama delivered by mobile headphones to an audience standing around a shopping center in a Stockholm suburb? In democratic societies there is widespread acknowledgment of the need to incorporate citizens’ input in decision-making processes in more or less structured ways. But participatory decision making is balancing on the borders of inclusion, structure, precision and accuracy. To simply enable more participation will not yield enhanced democracy, and there is a clear need for more elaborated elicitation and decision analytical tools. This rigorous and thought-provoking volume draws on a stimulating variety of international case studies, from flood risk management in the Red River Delta of Vietnam, to the consideration of alternatives to gold mining in Roșia Montană in Transylvania, to the application of multi-criteria decision analysis in evaluating the impact of e-learning opportunities at Uganda's Makerere University. Editors Love Ekenberg (senior research scholar, International Institute for Applied Systems Analysis [IIASA], Laxenburg, professor of Computer and Systems Sciences, Stockholm University), Karin Hansson (artist and research fellow, Department of Computer and Systems Sciences, Stockholm University), Mats Danielson (vice president and professor of Computer and Systems Sciences, Stockholm University, affiliate researcher, IIASA) and Göran Cars (professor of Societal Planning and Environment, Royal Institute of Technology, Stockholm) draw innovative collaborations between mathematics, social science, and the arts. They develop new problem formulations and solutions, with the aim of carrying decisions from agenda setting and problem awareness through to feasible courses of action by setting objectives, alternative generation, consequence assessments, and trade-off clarifications. As a result, this book is important new reading for decision makers in government, public administration and urban planning, as well as students and researchers in the fields of participatory democracy, urban planning, social policy, communication design, participatory art, decision theory, risk analysis and computer and systems sciences.

Deliberation, Representation, Equity: Research Approaches, Tools and Algorithms for Participatory Processes

In democratic societies there is widespread acknowledgment of the need to incorporate citizens’ input in decision-making processes in more or less structured ways. But participatory decision making is balancing on the borders of inclusion, structure, precision and accuracy. To simply enable more participation will not yield enhanced democracy, and there is a clear need for more elaborated elicitation and decision analytical tools. This rigorous and thought-provoking volume draws on a stimulating variety of international case studies, from flood risk management in the Red River Delta of Vietnam, to the consideration of alternatives to gold mining in Roșia Montană in Transylvania, to the application of multi-criteria decision analysis in evaluating the impact of e-learning opportunities at Uganda's Makerere University. This book is important new reading for decision makers in government, public administration and urban planning, as well as students and researchers in the fields of participatory democracy, urban planning, social policy, communication design, participatory art, decision theory, risk analysis and computer and systems sciences

Deliberation, Representation, Equity

"What can we learn about the development of public interaction in e-democracy from a drama delivered by mobile headphones to an audience standing around a shopping center in a Stockholm suburb? In democratic societies there is widespread acknowledgment of the need to incorporate citizens’ input in decision-making processes in more or less structured ways. But participatory decision making is balancing on the borders of inclusion, structure, precision and accuracy. To simply enable more participation will not yield enhanced democracy, and there is a clear need for more elaborated elicitation and decision analytical tools. This rigorous and thought-provoking volume draws on a stimulating variety of international case studies, from flood risk management in the Red River Delta of Vietnam, to the consideration of alternatives to gold mining in Roșia Montană in Transylvania, to the application of multi-criteria decision analysis in evaluating the impact of e-learning opportunities at Uganda's Makerere University. Editors Love Ekenberg (senior research scholar, International Institute for Applied Systems Analysis [IIASA], Laxenburg, professor of Computer and Systems Sciences, Stockholm University), Karin Hansson (artist and research fellow, Department of Computer and Systems Sciences, Stockholm University), Mats Danielson (vice president and professor of Computer and Systems Sciences, Stockholm University, affiliate researcher, IIASA) and Göran Cars (professor of Societal Planning and Environment, Royal Institute of Technology, Stockholm) draw innovative collaborations between mathematics, social science, and the arts. They develop new problem formulations and solutions, with the aim of carrying decisions from agenda setting and problem awareness through to feasible courses of action by setting objectives, alternative generation, consequence assessments, and trade-off clarifications. As a result, this book is important new reading for decision makers in government, public administration and urban planning, as well as students and researchers in the fields of participatory democracy, urban planning, social policy, communication design, participatory art, decision theory, risk analysis and computer and systems sciences.

Deliberation, Representation, Equity: Research Approaches, Tools and Algorithms for Participatory Processes

What can we learn about the development of public interaction in e-democracy from a drama delivered by mobile headphones to an audience standing around a shopping center in a Stockholm suburb? In democratic societies there is widespread acknowledgment of the need to incorporate citizens’ input in decision-making processes in more or less structured ways. But participatory decision making is balancing on the borders of inclusion, structure, precision and accuracy. To simply enable more participation will not yield enhanced democracy, and there is a clear need for more elaborated elicitation and decision analytical tools. This rigorous and thought-provoking volume draws on a stimulating variety of international case studies, from flood risk management in the Red River Delta of Vietnam, to the consideration of alternatives to gold mining in Roșia Montană in Transylvania, to the application of multi-criteria decision analysis in evaluating the impact of e-learning opportunities at Uganda's Makerere University. Editors Love Ekenberg (senior research scholar, International Institute for Applied Systems Analysis [IIASA], Laxenburg, professor of Computer and Systems Sciences, Stockholm University), Karin Hansson (artist and research fellow, Department of Computer and Systems Sciences, Stockholm University), Mats Danielson (vice president and professor of Computer and Systems Sciences, Stockholm University, affiliate researcher, IIASA) and Göran Cars (professor of Societal Planning and Environment, Royal Institute of Technology, Stockholm) draw innovative collaborations between mathematics, social science, and the arts. They develop new problem formulations and solutions, with the aim of carrying decisions from agenda setting and problem awareness through to feasible courses of action by setting objectives, alternative generation, consequence assessments, and trade-off clarifications. As a result, this book is important new reading for decision makers in government, public administration and urban planning, as well as students and researchers in the fields of participatory democracy, urban planning, social policy, communication design, participatory art, decision theory, risk analysis and computer and systems sciences

A Holmes and Doyle Bibliography, Volume 5: Periodical Articles--Secondary References, Alphabetical Listing

This bibliography is a work in progress. It attempts to update Ronald B. De Waal’s comprehensive bibliography, The Universal Sherlock Holmes, but does not claim to be exhaustive in content. New works are continually discovered and added to this bibliography. Readers and researchers are invited to suggest additional content. Volume 5 includes "passing" or "secondary" references, i.e. those entries that are passing in nature or contain very brief information or content

A Holmes and Doyle Bibliography, Volume 6: Periodical Articles, Subject Listing, By De Waal Category

This bibliography is a work in progress. It attempts to update Ronald B. De Waal’s comprehensive bibliography, The Universal Sherlock Holmes, but does not claim to be exhaustive in content. New works are continually discovered and added to this bibliography. Readers and researchers are invited to suggest additional content. Volume 6 presents the periodical literature arranged by subject categories (as originally devised for the De Waal bibliography and slightly modified here)

A Holmes and Doyle Bibliography, Volume 9: All Formats—Combined Alphabetical Listing

This bibliography is a work in progress. It attempts to update Ronald B. De Waal’s comprehensive bibliography, The Universal Sherlock Holmes, but does not claim to be exhaustive in content. New works are continually discovered and added to this bibliography. Readers and researchers are invited to suggest additional content. This volume contains all listings in all formats, arranged alphabetically by author or main entry. In other words, it combines the listings from Volume 1 (Monograph and Serial Titles), Volume 3 (Periodical Articles), and Volume 7 (Audio/Visual Materials) into a comprehensive bibliography. (There may be additional materials included in this list, e.g. duplicate items and items not yet fully edited.) As in the other volumes, coverage of this material begins around 1994, the final year covered by De Waal's bibliography, but may not yet be totally up-to-date (given the ongoing nature of this bibliography). It is hoped that other titles will be added at a later date. At present, this bibliography includes 12,594 items