Book Chapter10.1007/11618027_9
A generic modular data structure for proof attempts alternating on ideas and granularity
Serge Autexier,Christoph Benzmüller,Dominik Dietrich,Andreas Meier,Claus-Peter Wirth +4 more
- 15 Jul 2005
- pp 126-142
TL;DR: A parameterized proof data structure for the management of proofs is described, which supports and bridges the gap between abstract level proof explanation and low-level proof verification.
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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 low-level 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.
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Citations
•Journal Article
Proof development with ΩMEGA
Jörg H. Siekmann,Christoph Benzmüller,Vladimir Brezhnev,Lassaad Cheikhrouhou,Armin Fiedler,Andreas Franke,Helmut Horacek,Michael Kohlhase,Andreas Meier,Erica Melis,Markus Moschner,Immanuel Normann,Martin Pollet,Volker Sorge,Carsten Ullrich,Claus-Peter Wirth,Jürgen Zimmer +16 more
TL;DR: An overview of the architecture of the OMEGA system is presented and some of its novel features are sketched, including methods to develop proofs at a knowledge-based level.
30
PlatΩ: A Mediator between Text-Editors and Proof Assistance Systems
TL;DR: A generic mediator, called [email protected], between text-editors and proof assistants is presented, which automatically generates the corresponding formal representation for a proof assistant, in this case @Wmega.
21
•Journal Article
Towards Explicative Inference for OWL.
TL;DR: This article proposes a framework based on inference rules and proof tactics for OWL ontologies to present inferences in a suitable and adaptable way to human users, and to predict whether certain inferences are harder to understand than others.
Synthesizing proof planning methods and Ω-ants agents from mathematical knowledge
Serge Autexier,Dominik Dietrich +1 more
- 11 Aug 2006
TL;DR: This paper presents techniques to automatically synthesize proof planning methods and Ω-Ants-agents from assertions such that they can be actively used by these systems and enables a user to effectively use these systems without having to know the peculiarities of coding methods and agents.
ΩMEGA: Resource-Adaptive Processes in an Automated Reasoning System.
Serge Autexier,Christoph Benzmüller,Dominik Dietrich,Jörg H. Siekmann +3 more
- 01 Jan 2011
TL;DR: The ΩMEGA project and its predecessor, the MKRP-system, grew out of the principal dissatisfaction with the methodology and lack of success of the search-based "logic engines" of the 1960s and 1970s as discussed by the authors.
15
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Interactive Theorem Proving and Program Development
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Isabelle: A Generic Theorem Prover
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TL;DR: This book discusses theories, terms and types, tactics, and theorems of Isabelle Theories as well as its application to proof management.
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