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Analysis of mixed natural and symbolic language input in mathematical dialogs

Magdalena Wolska, Ivana Kruijff-Korbayová
2004 Proceedings of the 42nd Annual Meeting on Association for Computational Linguistics - ACL '04  
Discourse in formal domains, such as mathematics, is characterized by a mixture of telegraphic natural language and embedded (semi-)formal symbolic mathematical expressions.  ...  We present language phenomena observed in a corpus of dialogs with a simulated tutorial system for proving theorems as evidence for the need for deep syntactic and semantic analysis.  ...  However, little is known about the use of natural language in dialog setting in formal domains, such as mathematics, due to the lack of empirical data.  ... 
doi:10.3115/1218955.1218959 dblp:conf/acl/WolskaK04 fatcat:h6d7ebjmqndu3lpt6kxoasccym

Resource-Bounded Modelling and Analysis of Human-Level Interactive Proofs [chapter]

Christoph Benzmüller, Marvin Schiller, Jörg Siekmann
2010 Resource-Adaptive Cognitive Processes  
Experiment 2 A second experiment investigated mathematical domain reasoning tasks and linguistic phenomena in tutorial dialogues.  ...  Processing natural language with embedded mathematical content, however, is a highly challenging task by itself.  ... 
doi:10.1007/978-3-540-89408-7_13 dblp:series/cogtech/BenzmullerSS11 fatcat:j4f5thad3bb7hk3imgg3enxl6m

Assertion Application in Theorem Proving and Proof Planning

Quoc Bao Vo, Christoph Benzmüller, Serge Autexier
2003 International Joint Conference on Artificial Intelligence  
The experimental system will engage in a dialogue in natural language (and perhaps other modes of communication) and help a student to understand and produce mathematical proofs.  ...  We discuss the connection to proof planning and motivate an application in a project aiming at a tutorial dialogue system for mathematics.  ... 
dblp:conf/ijcai/VoBA03 fatcat:u2nwkyxt25fstpstgu7f2izdnq


P Freyd
2004 Electronical Notes in Theoretical Computer Science  
the calculus-and machine-oriented representation format of the domain reasoner.  ...  A particular challenge in this project is to bridge the gap between the human-oriented proof representation format with under-specification used in the proof manager of the tutorial dialogue system and  ...  Conclusion In the DIALOG project we investigate tutorial natural language dialogue on mathematical proofs.  ... 
doi:10.1016/s1571-0661(04)00011-8 fatcat:gosirtiqfffh5l4mygulbpadre

Verification of human-level proof steps in mathematics education

Dominik Dietrich, Mark Buckley
2008 Teaching Mathematics and Computer Science  
Automated mathematics tutorial systems need support from a reasoning module which can verify the correctness of students' contributions.  ...  We present a domain-independent method for automatically verifying correct proof steps and detecting standard reasoning errors.  ...  Tutorial dialogue on mathematical proofs The framework in which our research is being carried out is the Dialog project [5] , which has the final goal of natural tutorial dialogue between a student and  ... 
doi:10.5485/tmcs.2008.0184 fatcat:gaoyapojdrhankkq24u6xu3isu

Assertion-level Proof Representation with Under-Specification

Serge Autexier, Christoph Benzmüller, Armin Fiedler, Helmut Horacek, Bao Quoc Vo
2004 Electronical Notes in Theoretical Computer Science  
the calculus-and the machine-oriented representation format of the domain reasoner.  ...  A particular challenge in this project is to bridge the gap between the human-oriented proof representation format with under-specification used in the proof manager of the tutorial dialogue system and  ...  Conclusion In the DIALOG project we investigate tutorial natural language dialogue on mathematical proofs.  ... 
doi:10.1016/j.entcs.2003.12.026 fatcat:2p7bi5ass5euviuf3ycruwcv6e

Towards an Intelligent Tutor for Mathematical Proofs

Serge Autexier, Dominik Dietrich, Marvin Schiller
2012 Electronic Proceedings in Theoretical Computer Science  
Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment.  ...  The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.  ...  The data was collected in an experiment where thirty-seven students interacted with a mock-up of a natural language dialog tutoring system for mathematical proofs.  ... 
doi:10.4204/eptcs.79.1 fatcat:xyvxfeicwbaxfb3wfd2oaagnbq

Proof step analysis for proof tutoring - a learning approach to granularity

Marvin Schiller, Dominik Dietrich, Christoph Benzmüller
2008 Teaching Mathematics and Computer Science  
The task of this module is to evaluate proof steps as typically uttered by students in tutoring sessions on mathematical proofs.  ...  We present a proof step diagnosis module based on the mathematical assistant system Ωmega.  ...  Acknowledgements We would like to thank Bruce McLaren for his input and comments on initial drafts of this paper. We thank an anonymous referee for helpful comments.  ... 
doi:10.5485/tmcs.2008.0183 fatcat:gfhc35gbgfa5dlm4bue7mwoxwe

A Systematic Literature Review of Intelligent Tutoring Systems with Dialogue in Natural Language

Jose Paladines, Jaime Ramirez
2020 IEEE Access  
Dialog interprets a mixture of natural language and mathematical expressions through a domain reasoner that requires deep syntactic and semantic analysis to obtain a formal representation of the steps  ...  To detect these misconceptions, the system relies on a domain reasoner that evaluates the soundness, granularity (acceptable size of the proof) and relevance (useful with respect to the goal) of the proof  ... 
doi:10.1109/access.2020.3021383 fatcat:cw5bz6ytdnegfhyj3v2wcy3a7i

ΩMEGA: Resource-Adaptive Processes in an Automated Reasoning System [chapter]

Serge Autexier, Christoph Benzmüller, Dominik Dietrich, Jörg Siekmann
2010 Resource-Adaptive Cognitive Processes  
More specifically, the DIALOG project studies natural language-based tutorial dialogs when teaching how to prove a theorem.  ...  Evaluation We tested our proof-step checking component on a little less than 20 tutorial dialogs from a Wizard-of-Oz experiment, where students had to solve exercises on binary relations.  ... 
doi:10.1007/978-3-540-89408-7_17 dblp:series/cogtech/AutexierBDS11 fatcat:t6vlyxgwcbe45ctq7oy3mlb7sy

Argumentation in Explanations to Logical Problems [chapter]

Armin Fiedler, Helmut Horacek
2001 Lecture Notes in Computer Science  
Explaining solutions to logical problems is one of the areas where argumentation in natural language plays a prominent role.  ...  One crucial reason for the difficulty in pursuing this issue in a systematic manner when relying on formal inference systems lies in the discrepancy between machine-oriented reasoning and human-adequate  ...  Second, the transformed proof is verbalized in natural language.  ... 
doi:10.1007/3-540-45545-0_109 fatcat:6ajsfmynd5dihbdg3rxycqli7i

Organization, Transformation, and Propagation of Mathematical Knowledge in Ωmega

Serge Autexier, Christoph Benzmüller, Dominik Dietrich, Marc Wagner
2008 Mathematics in Computer Science  
Moreover, it naturally decomposes the global and complex reasoning and truth maintenance task into local reasoning and truth maintenance tasks inside the system components.  ...  Mathematical assistance systems and proof assistance systems in general have traditionally been developed as large, monolithic systems which are often hard to maintain and extend.  ...  Ωmega is furthermore exploited as a domain reasoner in the proof tutoring environment Dialog [8] .  ... 
doi:10.1007/s11786-008-0054-6 fatcat:qoxkghx6c5epfjjaw5oykgfjjy

Computer supported mathematics with Ωmega

Jörg Siekmann, Christoph Benzmüller, Serge Autexier
2006 Journal of Applied Logic  
The shift from search based methods to more abstract planning techniques however opened up a paradigm for mathematical reasoning on a computer and several systems of that kind now employ a mix of interactive  ...  But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited.  ...  term borrowed from research on the semantics of natural language.  ... 
doi:10.1016/j.jal.2005.10.008 fatcat:bfpsfvprmnfnddfvwwx5cqbjiq

Supporting the formal verification of mathematical texts

Claus Zinn
2006 Journal of Applied Logic  
In fact, we argue that the expert language of mathematics is the natural choice for achieving efficient mathematician-machine interaction.  ...  Our empirical approach, the analysis of carefully authored textbook proofs, forces us to focus on the language and the reasoning pattern that mathematician use when presenting proofs to colleagues and  ...  Saarland University's DIALOG project The DIALOG project aims at supporting proof construction with natural-language tutorial dialogue.  ... 
doi:10.1016/j.jal.2005.10.010 fatcat:kx4okcs3ijhcbd7iw7ugmscrrm

Preface - Emerging Technologies and Landmark Systems for Learning Mathematics and Science: Dedicated to the Memory of Erica Melis - Part 1

Bruce M. McLaren, Sergey Sosnovsky, Vincent Aleven
2014 International Journal of Artificial Intelligence in Education  
Once confronted with an error, a student engages in a tutorial dialog with the system, trying to explain the reason for the incorrect simulator behavior.  ...  Erica recognized the difficulty that many students have in understanding and constructing mathematical proofs and took an interest in tutoring and assisting students in this task.  ... 
doi:10.1007/s40593-014-0021-0 fatcat:trz755nqwnegjdot2dhvbczbcy
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