## System Description: A Dialogue Manager Supporting Natural Language Tutorial Dialogue on Proofs (2005)

Venue: | UITP 2005 PRELIMINARY VERSION |

Citations: | 1 - 0 self |

### BibTeX

@MISC{Buckley05systemdescription:,

author = {Mark Buckley and Christoph Benzmüller},

title = { System Description: A Dialogue Manager Supporting Natural Language Tutorial Dialogue on Proofs},

year = {2005}

}

### OpenURL

### Abstract

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.

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Citation Context ...General [2]. It provides a uniform interface for ATPs which is adaptable to the user's expertise level and hides the interface with the ATP at hand behind a generic proof scripting language. AUTOMATH =-=[8,9]-=-, Mizar 5 and Isabelle/Isar [35] use an approach where input and output are expressed in a formal mathematical language which is both human and machine understandable. Although these languages are hum... |

86 | Proof General: A generic tool for proof development
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Citation Context ... moment, no ATP fully supports this type of natural interface, but there has been much research in this direction. One system which abstracts away from the standard interface of ATPs is Proof General =-=[2]-=-. It provides a uniform interface for ATPs which is adaptable to the user's expertise level and hides the interface with the ATP at hand behind a generic proof scripting language. AUTOMATH [8,9], Miza... |

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Citation Context ...m interface for ATPs which is adaptable to the user's expertise level and hides the interface with the ATP at hand behind a generic proof scripting language. AUTOMATH [8,9], Mizar 5 and Isabelle/Isar =-=[35]-=- use an approach where input and output are expressed in a formal mathematical language which is both human and machine understandable. Although these languages are human readable, they have a formal ... |

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Citation Context ...cication in the representation of the proof step uttered by the student. In doing this the proof manager ideally accesses mathematical knowledge stored in MBase [19] and the user model in ActiveMath =-=[21]-=-, and also deploys a domain reasoner, usually a theorem prover. These tasks for the proof manager are very ambitious; somesrst solutions are presented in [3,18,34]. The proof manager receives the unde... |

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Citation Context ...though these languages are human readable, they have a formal style | using keywords and strict structure | which is far from natural language or textbook-style proofs. The grammatical framework (GF) =-=[27]-=- attempts to remedy this by allowing the user to dene in a -calculus a concrete input/output language on top of the abstract syntax of the mathematical expressions. The result is a context-free gram... |

65 |
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Citation Context ...personal banking applications, whereas the dialogue manager for Dialog must supportsexible information exchange in both directions. The solution we decided on is the Information State Update approach =-=[32]-=-. In this approach the dialogue manager maintains a description of the state of the discourse and its participants, which then forms a framework for communication between the external modules associat... |

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Citation Context ...General [2]. It provides a uniform interface for ATPs which is adaptable to the user's expertise level and hides the interface with the ATP at hand behind a generic proof scripting language. AUTOMATH =-=[8,9]-=-, Mizar 5 and Isabelle/Isar [35] use an approach where input and output are expressed in a formal mathematical language which is both human and machine understandable. Although these languages are hum... |

51 |
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Citation Context ...es are hard{ wired and system{driven. Such methods are not sucient for Dialog because of our interest insexible, natural tutorial dialogues. The form-lling approach, such as in the AUTOTUTOR system =-=[15]-=-, is more adaptable thansnite-state. The information that the system seeks is stored in slots in a form which is incrementallyslled until the required amount of information is reached. This allows the... |

46 | MBase: Representing knowledge and context for the integration of mathematical software systems
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Citation Context ...ries to resolve ambiguity and underspecication in the representation of the proof step uttered by the student. In doing this the proof manager ideally accesses mathematical knowledge stored in MBase =-=[19]-=- and the user model in ActiveMath [21], and also deploys a domain reasoner, usually a theorem prover. These tasks for the proof manager are very ambitious; somesrst solutions are presented in [3,18,34... |

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Citation Context ...Benzmuller the presentation component of Nuprl [16], which uses a content planner to select information to be included and a surface realiser to choose words and output sentences. Similarly, PROVERB =-=[17]-=- and its successor P.rex [10] use a pipeline architecture of macroplanning, microplanning and surface realisation to generate proofs comparable to those found in mathematical textbooks. The Dialog pro... |

42 |
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Citation Context ...log project. 1.1 Approaches to Dialogue Management There are a number of candidate approaches to dialogue management which could be suitable for Dialog. Finite-state methods, such as the CSLU toolkit =-=[20,30]-=-, are suited to situations where a certain set of data must be collected by an agent in order to carry out some action, or where the number of possible dialogues is relatively small. Such systems are ... |

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Citation Context ... described in detail in Section 3. The design of the dialogue manager is based on the Information State Update approach used in the Siridus [25] and Trindi [26] projects, and implemented in TrindiKit =-=[31]-=-. The Information State (IS) is a central data structure storing information about the current state of the dialog and about the internal states of modules participating in the dialogue. It is divided... |

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Citation Context ...e languages that can be dened are relatively restricted. Other approaches concentrate solely on a more natural output from the ATP, and leave input in the machine-oriented formalism. The systems Coq =-=[7]-=- and Theorema [6] have output components which use schema-based techniques to achieve a pseudo-natural language proof presentation. A further step towards natural langauge output is to apply technique... |

24 | A 3-tier planning architecture for managing tutorial dialogue
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Citation Context ...le student utterances, it is a much more viable approach to begin a tutorial dialogue with a sketchy high-level dialogue plan which places as few as possible constraints on the course of the dialogue =-=[37]-=-. We see the provision forsexible dialogue planning as an important addition to the dialogue manager. Meta-level control To achieve a moresexible and adaptable control over rulesring, we believe a met... |

21 | Tutorial dialogs on mathematical proofs
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Citation Context ...logue on proofs, information state update 1 Introduction In this paper we present and discuss the design and implementation of the dialogue manager for the demonstrator system of the Dialog project 3 =-=[5,23,24]-=-. This system was built for demonstration purposes by the Dialog team 4 at Saarland University for the review of the Collaborative Research Centre 378. The goal of the Dialog project is to investigate... |

19 | Verbalization of high-level formal proofs
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Citation Context ...put is to apply techniques from the area of natural language generation to produce texts. This approach is used in 5 http://www.mizar.org 2 Buckley and Benzmuller the presentation component of Nuprl =-=[16]-=-, which uses a content planner to select information to be included and a surface realiser to choose words and output sentences. Similarly, PROVERB [17] and its successor P.rex [10] use a pipeline arc... |

17 | Dialog-driven adaptation of explanations of proofs
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(Show Context)
Citation Context ...component of Nuprl [16], which uses a content planner to select information to be included and a surface realiser to choose words and output sentences. Similarly, PROVERB [17] and its successor P.rex =-=[10]-=- use a pipeline architecture of macroplanning, microplanning and surface realisation to generate proofs comparable to those found in mathematical textbooks. The Dialog project diers from the approach... |

16 | Assertion-level proof representation with under-speci
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Citation Context ...ed in the utterance, in an ad-hoc LISP-like representation (LU, standing for Proof Language with Underspecication). This is a language in the spirit of the proof representation language described in =-=[3]-=-, but designed for the inter-module communication requirements of the Dialog project: f LM = @h1(holds ^ <criterion>(d1 ^ deMorgan-Regel-2) ^ <patient>(f1 ^ formula)) LU = (input (label 1 1) (formula ... |

14 |
A dialogue move taxonomy for tutorial dialogues
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Citation Context ...plain that utterance. Each of the functions of an utterance are encoded in the dimensions of its dialogue move. The taxonomy of dialogue moves used in Dialog is described in 5 Buckley and Benzmuller =-=[33]-=-; it is an adaptation and extension of the DAMSL taxonomy [1]. DAMSL is a standard and application{independent annotation scheme for dialogue tagging, and the taxonomy used in Dialog is therefore tail... |

13 |
Automating hinting in mathematical tutorial dialogue
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(Show Context)
Citation Context ...l concept addressed in the utterance (in this case intersection), and hypCon, the hypotaxis of the concept, expressing a kind of interdenability. 3.6 Tutorial Manager The job of the tutorial manager =-=[13]-=- is to use pedagogical knowledge to decide on how to give hints to the user, and this decision is based on the proof step category (correct, irrelevant, etc), the expected step, a naive student model ... |

13 | Assertion application in theorem proving and proof planning
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Citation Context ...ase [19] and the user model in ActiveMath [21], and also deploys a domain reasoner, usually a theorem prover. These tasks for the proof manager are very ambitious; somesrst solutions are presented in =-=[3,18,34]-=-. The proof manager receives the underspecied proof step which was extracted from the user's utterance by the input analyser. This is encoded in the proof representation language LU [3] (LU in the ou... |

12 |
Coupling CCG with Hybrid Logic Dependency Semantics
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Citation Context ...ermines its linguistic meaning and proof content. Input is syntactically parsed using the openCCG parser [22], and its linguistic meaning is represented using Hybrid Logic Dependence Semantics (HLDS) =-=[4]-=-. Input: The user's utterance in a string (see st input in the output of the GUI above). Output: A structure containing the linguistic meaning (LM) represented in HLDS and the underspecied proof step... |

11 |
An annotated corpus of tutorial dialogs on mathematical theorem proving
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- 2004
(Show Context)
Citation Context ...n hierarchical structure. In this way a single dialogue move can account for the many functions that an utterance may have. Consider example (2) from the corpus of the Dialog Wizard-of-Oz experiments =-=[36]-=- (translated from German): (2) \Can you explain that in more detail?" This utterance is a request for information, it refers back to a previous utterance (the anaphor \that") which the system made, an... |

10 | Supporting Progressive Refinement of Wizard-of-Oz Experiments - Fiedler, Gabsdil - 2002 |

7 |
Draft of DAMSL: Dialogue act markup
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- 1997
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Citation Context ...e encoded in the dimensions of its dialogue move. The taxonomy of dialogue moves used in Dialog is described in 5 Buckley and Benzmuller [33]; it is an adaptation and extension of the DAMSL taxonomy =-=[1]-=-. DAMSL is a standard and application{independent annotation scheme for dialogue tagging, and the taxonomy used in Dialog is therefore tailored to account for the types of moves found in tutorial dial... |

7 |
Automating hinting in an intelligent tutorial system
- Fiedler, Tsovaltzi
- 2003
(Show Context)
Citation Context .... This can be minimal feedback (\min"), didactic (\did"), in which answers and explanations are constantly provided by the tutor, or socratic (\soc"), where hints are used to achieve self-explanation =-=[12]-=-. Input: The tutorial mode, the task dimension of the user's dialogue move, which is determined by the dialog move recogniser, and the proof step information, which is the whole output from the domain... |

6 | Interactive theorem proving with tasks
- Hubner, Autexier, et al.
(Show Context)
Citation Context ...ase [19] and the user model in ActiveMath [21], and also deploys a domain reasoner, usually a theorem prover. These tasks for the proof manager are very ambitious; somesrst solutions are presented in =-=[3,18,34]-=-. The proof manager receives the underspecied proof step which was extracted from the user's utterance by the input analyser. This is encoded in the proof representation language LU [3] (LU in the ou... |

5 |
A framework for information-state based dialogue (demo abstract
- Fliedner, Bobbert
- 2003
(Show Context)
Citation Context ...ch full both of these tasks, and in this paper we concentrate on the second notion of dialogue management { the development platform for dialogue applications. The dialogue manager is built on Rubin =-=[14]-=-, a platform for developing dialogue management applications from CLT company, which is described in section 4. 3 Modules connected to the Dialog System As shown in the diagram of the system in Figure... |

4 | Omega: Computer supported mathematics
- Siekmann, Benzmuller
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(Show Context)
Citation Context ...ibes a dialogue move which is concerned with resolving the domain task. 3.4 Proof Manager The proof manager is the mediator between the dialogue manager and the mathematical proof assistantsmega{Core =-=[28]-=-. The proof manager replays and stores the status of the partial proof which has been built by the student so far, and based on this partial proof, it analyses the soundness and relevance of a next pr... |

4 |
Supporting progressive re of Wizard-ofOz experiments
- Fiedler, Gabsdil
- 2002
(Show Context)
Citation Context .... Architecture 1.2 The Sample Dialogue The Dialog demonstrator has been developed to illustrate the functionality of the Dialog system at hand of a few dialogues from the project's Wizardof-Oz corpus =-=[11]-=-. Here we concentrate on dialog did16k. The task that the student is asked to prove is theorem (1) ( where K stands for the complement operation). (1) K((A[B)\(C[D)) = (K(A)\K(B))[(K(C)\K(D)) The exam... |

3 |
Natural language proofs in nested cells representation
- Buchberger
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(Show Context)
Citation Context ...can be dened are relatively restricted. Other approaches concentrate solely on a more natural output from the ATP, and leave input in the machine-oriented formalism. The systems Coq [7] and Theorema =-=[6]-=- have output components which use schema-based techniques to achieve a pseudo-natural language proof presentation. A further step towards natural langauge output is to apply techniques from the area o... |

3 |
Dialog: Tutorial dialog with an assistance system for mathematics (2004), project report
- Pinkal, Siekmann, et al.
(Show Context)
Citation Context ...logue on proofs, information state update 1 Introduction In this paper we present and discuss the design and implementation of the dialogue manager for the demonstrator system of the Dialog project 3 =-=[5,23,24]-=-. This system was built for demonstration purposes by the Dialog team 4 at Saarland University for the review of the Collaborative Research Centre 378. The goal of the Dialog project is to investigate... |

3 |
Dialog: Natural language-based interaction with a mathematics assistance system Buckley and Benzmuller (2004), project proposal
- Pinkal, Siekmann, et al.
(Show Context)
Citation Context ...logue on proofs, information state update 1 Introduction In this paper we present and discuss the design and implementation of the dialogue manager for the demonstrator system of the Dialog project 3 =-=[5,23,24]-=-. This system was built for demonstration purposes by the Dialog team 4 at Saarland University for the review of the Collaborative Research Centre 378. The goal of the Dialog project is to investigate... |