## A blackboard architecture for guiding interactive proofs (1998)

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Venue: | Artificial Intelligence: Methodology, Systems and Applications |

Citations: | 24 - 19 self |

### BibTeX

@INPROCEEDINGS{Benzmüller98ablackboard,

author = {Christoph Benzmüller and Volker Sorge},

title = {A blackboard architecture for guiding interactive proofs},

booktitle = {Artificial Intelligence: Methodology, Systems and Applications},

year = {1998},

pages = {102--114},

publisher = {Springer Verlag}

}

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### Abstract

Abstract. The acceptance and usability of current interactive theorem proving environments is, among other things, strongly influenced by the availability of an intelligent default suggestion mechanism for commands. Such mechanisms support the user by decreasing the necessary interactions during the proof construction. Although many systems offer such facilities, they are often limited in their functionality. In this paper we present a new agent-based mechanism that independently observes the proof state, steadily computes suggestions on how to further construct the proof, and communicates these suggestions to the user via a graphical user interface. We furthermore introduce a focus technique in order to restrict the search space when deriving default suggestions. Although the agents we discuss in this paper are rather simple from a computational viewpoint, we indicate how the presented approach can be extended in order to increase its deductive power. 1

### Citations

567 |
Untersuchungen über das logische Schließen
- Gentzen
- 1935
(Show Context)
Citation Context ...reliminaries In this section we give brief definitions of some concepts we will refer to in the remainder of this paper. We assume that the reader is familiar with the natural deduction calculus (ND) =-=[7]-=-. In\Omega mega [3] as well as in many other interactive theorem proving systems, such as tps [2] or hol [8], theorems are interactively proven by applying ND-rules or tactics, where the latter are es... |

308 |
An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof
- Andrews
- 1986
(Show Context)
Citation Context ...cates and argument functions. While the former denotes conditions the formula of a proof line has to 1 The partial proof is displayed in a linearized representation of the ND-calculus as described in =-=[1]-=-. Each line consists of a unique label, a set of hypotheses, a formula, and a justification. p :p p ; = [x:p is-universal-quantification(x)] ; p p fcg = [x:p matches(scope(x); u)] fu:cg p p fc;tg = [x... |

305 | The Hearsay-II speechunderstanding system: integrating knowledge to resolve uncertainty
- Erman, Hayes-Roth, et al.
- 1980
(Show Context)
Citation Context ...ned independently from the actual command and the user can choose freely among several given suggestions. In contrast to the classical HEARSAY Blackboard architecture used for speech recognition (cf. =-=[5, 6]-=-) our Argument Agents do not depend on an explicit central control system. Instead they can be seen as autonomous entities. Their actions are solely triggered by the type of the Blackboard, that is, t... |

149 |
Blackboard systems
- Engelmore, Morgan
- 1998
(Show Context)
Citation Context ...ncurrent programming techniques by introducing autonomous agents which self-containedly search for default suggestions and which cooperate by exchanging relevant results via a Blackboard architecture =-=[4]-=-. This mechanism is steadily working in the background and dynamically adapting its computational behavior to the state of the proof. It is able to exchange command and argument suggestions with the u... |

104 |
Introduction to HOL
- Gordon, Melham
- 1993
(Show Context)
Citation Context ... this paper. We assume that the reader is familiar with the natural deduction calculus (ND) [7]. In\Omega mega [3] as well as in many other interactive theorem proving systems, such as tps [2] or hol =-=[8]-=-, theorems are interactively proven by applying ND-rules or tactics, where the latter are essentially compounds of ND-rules. In other words, a tactic application abbreviates a purely rule based deriva... |

70 | TPS: A theorem proving system for classical type theory
- Andrews, Bishop, et al.
- 1996
(Show Context)
Citation Context ...n within the proof and does not provide a sophisticated suggestion mechanism in order to minimize the necessary interactions. Current interactive theorem proving systems such as\Omega mega [3] or tps =-=[2]-=- already provide mechanisms for suggesting command arguments or even commands. Usually these mechanisms are rather limited in their functionality as they (i) use a sequential strategy allowing only fo... |

66 | OMEGA: Towards a mathematical assistant
- Benzmüller, Cheikhrouhou, et al.
- 1997
(Show Context)
Citation Context ...user's orientation within the proof and does not provide a sophisticated suggestion mechanism in order to minimize the necessary interactions. Current interactive theorem proving systems such as mega =-=[3]-=- or tps [2] already provide mechanisms for suggesting command arguments or even commands. Usually these mechanisms are rather limited in their functionality as they (i) use a sequential strategy allow... |

55 | G.: Real Theorem Provers Deserve Real UserInterfaces
- Théry, Bertot, et al.
- 1992
(Show Context)
Citation Context ...f. 7 Related Work and Conclusion The necessity to develop (graphical) user interfaces and mechanisms to better support the user within interactive theorem proving environments has been pointed out by =-=[13]-=-. Even though, current theorem proving environments still offer many potentialities for an improvement and still have not adapted all the usable techniques developed for user interfaces in other domai... |

27 |
eds.) Intelligent User Interfaces
- Sullivan, Tyler
- 1991
(Show Context)
Citation Context ...ven though, current theorem proving environments still offer many potentialities for an improvement and still have not adapted all the usable techniques developed for user interfaces in other domains =-=[12]-=-. Focusing techniques are well known from natural language processing and have been suggested as a tool for guidance in Graphical User Interfaces in [9]. In this paper we have discussed a new approach... |

26 | MEGA: Towards a mathematical assistant
- Benzmüller, Cheikhrouhou, et al.
- 1997
(Show Context)
Citation Context ... orientation within the proof and does not provide a sophisticated suggestion mechanism in order to minimize the necessary interactions. Current interactive theorem proving systems such as\Omega mega =-=[3]-=- or tps [2] already provide mechanisms for suggesting command arguments or even commands. Usually these mechanisms are rather limited in their functionality as they (i) use a sequential strategy allow... |

11 |
The design and an example use of Hearsay-III
- Erman, London, et al.
- 1981
(Show Context)
Citation Context ...ned independently from the actual command and the user can choose freely among several given suggestions. In contrast to the classical HEARSAY Blackboard architecture used for speech recognition (cf. =-=[5, 6]-=-) our Argument Agents do not depend on an explicit central control system. Instead they can be seen as autonomous entities. Their actions are solely triggered by the type of the Blackboard, that is, t... |

5 |
Focus in Graphical User Interfaces
- Perez, Sibert
- 1993
(Show Context)
Citation Context ...developed for user interfaces in other domains [12]. Focusing techniques are well known from natural language processing and have been suggested as a tool for guidance in Graphical User Interfaces in =-=[9]-=-. In this paper we have discussed a new approach for an intelligent suggestion of commands as well as their corresponding arguments within the framework of an interactive theorem prover. Both mechanis... |

3 | L\Omega UI: A Distributed Graphical User Interface for the Interactive Proof System\Omega mega. Submitted to the International Workshop on User Interfaces for Theorem Provers
- Siekmann, Hess, et al.
- 1998
(Show Context)
Citation Context ...ons We now sketch how the particular agents interact via the entries on the Blackboard and how the user can interact with the suggestion mechanism via\Omega mega's graphical user interface L\Omega UI =-=[11]-=-. Suppose a user chooses to apply 8E in our example. The choice of the command automatically initializes a corresponding empty Suggestion Blackboard. As only A p ; needs no necessary arguments, it wil... |