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A Generic Modular Data Structure for Proof Attempts Alternating on Ideas and Granularity
 Proceedings of MKM’05, volume 3863 of LNAI, IUB
, 2006
"... Abstract. A practically useful mathematical assistant system requires the sophisticated combination of interaction and automation. Central in such a system is the proof data structure, which has to maintain the current proof state and which has to allow the flexible interplay of various components i ..."
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Abstract. A practically useful mathematical assistant system requires the sophisticated combination of interaction and automation. Central in such a system is the proof data structure, which has to maintain the current proof state and which has to allow the flexible interplay of various components including the human user. We describe a parameterized proof data structure for the management of proofs, which includes our experience with the development of two proof assistants. It supports and bridges the gap between abstract level proof explanation and lowlevel proof verification. The proof data structure enables, in particular, the flexible handling of lemmas, the maintenance of different proof alternatives, and the representation of different granularities of proof attempts. 1
Mathematical Domain Reasoning Tasks in Natural Language Tutorial Dialog on Proofs
, 2005
"... We study challenges that are imposed to mathematical domain reasoning in the context of natural language tutorial dialog on mathematical proofs. The focus is on proof step evaluation: (i) How can mathematical domain reasoning support the resolution of ambiguities and underspecified parts in proof st ..."
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Cited by 7 (6 self)
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We study challenges that are imposed to mathematical domain reasoning in the context of natural language tutorial dialog on mathematical proofs. The focus is on proof step evaluation: (i) How can mathematical domain reasoning support the resolution of ambiguities and underspecified parts in proof steps uttered by a student? (ii) How can mathematical domain reasoning support the evaluation of a proof step with respect to the criteria soundness, granularity, and relevance?
System Description: A Dialogue Manager Supporting Natural Language Tutorial Dialogue on Proofs
 UITP 2005 PRELIMINARY VERSION
, 2005
"... The Dialog project investigates flexible natural language tutorial dialogue on mathematical proofs. Since the medium of communication is natural language dialogue, and since tutorial dialogues are by nature both flexible and unpredictable, it is essential to include a sophisticated, dedicated dialog ..."
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Cited by 2 (0 self)
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The Dialog project investigates flexible natural language tutorial dialogue on mathematical proofs. Since the medium of communication is natural language dialogue, and since tutorial dialogues are by nature both flexible and unpredictable, it is essential to include a sophisticated, dedicated dialogue manager to handle the interaction between student and the system modules. In this paper we present the design and implementation of the dialogue manager for the demonstrator system of the Dialog project. The dialogue manager forms the interface between the user and the system modules, including the automated theorem prover Ωmega–Core, the tutorial module and the linguistic analysis module.
A Dialogue Manager supporting Natural Language Tutorial Dialogue on Proofs
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 2006
"... The Dialog project investigates flexible natural language tutorial dialogue on mathematical proofs. Due to the flexible and unpredictable nature of tutorial dialogue in natural language it is essential to include a sophisticated, dedicated dialogue manager to handle the interaction between student a ..."
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Cited by 1 (1 self)
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The Dialog project investigates flexible natural language tutorial dialogue on mathematical proofs. Due to the flexible and unpredictable nature of tutorial dialogue in natural language it is essential to include a sophisticated, dedicated dialogue manager to handle the interaction between student and the system modules. In this paper we present the design and implementation of the dialogue manager for the demonstrator system of the Dialog project. The dialogue manager forms the interface between the user and the system modules, including the automated theorem prover Ωmega–Core, the tutorial module and the linguistic analysis module. We also give an evaluation of Rubin, the development platform for the dialogue manager.
Work address: FB Computerlinguistik
, 2001
"... 3.2 State of the Art at the Time of the Proposal and Original Research ..."
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