Assertion-level Proof Representation with Under-Specification

Autexier, Serge; Benzmüller, Christoph; Fiedler, Armin; Horacek, Helmut; Bao, Vo Nguyen Quoc

doi:10.1016/j.entcs.2003.12.026

Cited by 14 publications

(12 citation statements)

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“…2 (2008) Mathematical Knowledge Management in Ωmega 257 by means to define multiple foci of attention on subformulas that are maintained during the proof. Each task is reduced to a possibly empty set of subtasks by one of the following proof construction steps: (1) the introduction of a proof sketch [3,28], (2) deep structural rules for weakening and decomposition of subformulas, (3) the application of a lemma that can be postulated on the fly, (4) the substitution of meta-variables, and (5) the application of an inference. An eminent feature of the TaskLayer is that inferences cannot only be applied on top-level formulas in a task, but also to subformulas.…”

Section: Tasklayer -The Proof Managermentioning

confidence: 99%

Organization, Transformation, and Propagation of Mathematical Knowledge in Ωmega

et al. 2008

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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. In this article we propose a component network architecture as a means to design and implement such systems. Under this view a mathematical assistance system is an integrated knowledge-based system composed as a network of individual, specialized components. These components manipulate and mutually exchange different kinds of mathematical knowledge encoded within different document formats. Consequently, several units of mathematical knowledge coexist throughout the system within these components and this knowledge changes non-monotonically over time. Our approach has resulted in a lean and maintainable system code and makes the system open for extensions. Moreover, it naturally decomposes the global and complex reasoning and truth maintenance task into local reasoning and truth maintenance tasks inside the system components. The interplay between neighboring components in the network is thereby realized by nonmonotonic updates over agreed interface representations encoding different kinds of mathematical knowledge. Mathematics Subject Classification (2000). 68T30; 68T35.Keywords. Mathematical knowledge management, proof assistants, system architecture.This work has been funded by the DFG Collaborative Research Center on Resource-Adaptive Cognitive Processes, SFB 378, and was supported by grants from Studienstiftung des Deutschen Volkes e.V . 254S. Autexier et al.Math.comput.sci.

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Section: Tasklayer -The Proof Managermentioning

confidence: 99%

Organization, Transformation, and Propagation of Mathematical Knowledge in Ωmega

et al. 2008

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“…The hypothesis that assertion level reasoning [23] plays an essential role in this context has been confirmed. The fact that assertion level reasoning may by highly underspecified in human-constructed proofs, however, is a novel finding [3].…”

Section: B: Mathural Processing and Mathural Generationmentioning

confidence: 99%

“…In the following we assume that the meaning of a student utterance can always be successfully determined by the mathural processing resources available to the tutor system. 3 …”

Section: B: Mathural Processing and Mathural Generationmentioning

confidence: 99%

Resource-Bounded Modelling and Analysis of Human-Level Interactive Proofs

Benzmüller

Schiller

Siekmann

2010

Resource-Adaptive Cognitive Processes

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“…Théry's approach [22] bridges the gap by defining an XML format for manually annotating statements in mathematical papers to link them to formal counterparts, wherein proofs must be supplied; consistency is checked in a prover. Similar approaches include Weak Type Theory [15], MathLang [14]), or the Dialog project [5]. In a sense in the opposite direction, Kohlhase [17] works on the existing mathematical corpus of L A T E X papers and tries to capture their semantic content automatically with additional markup.…”

Section: Related Workmentioning

confidence: 99%

Assisted Proof Document Authoring

Aspinall

Lüth

Wolff

2006

Lecture Notes in Computer Science

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Abstract. Recently, significant advances have been made in formalised mathematical texts for large, demanding proofs. But although such large developments are possible, they still take an inordinate amount of effort and time, and there is a significant gap between the resulting formalised machine-checkable proof scripts and the corresponding human-readable mathematical texts. We present an authoring system for formal proof which addresses these concerns. It is based on a central document format which, in the tradition of literate programming, allows one to extract either a formal proof script or a human-readable document; the two may have differing structure and detail levels, but are developed together in a synchronised way. Additionally, we introduce ways to assist production of the central document, by allowing tools to contribute backflow to update and extend it. Our authoring system builds on the new PG Kit architecture for Proof General, bringing the extra advantage that it works in a uniform interface, generically across various interactive theorem provers.

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Assertion-level Proof Representation with Under-Specification

Cited by 14 publications

References 13 publications

Organization, Transformation, and Propagation of Mathematical Knowledge in Ωmega

Organization, Transformation, and Propagation of Mathematical Knowledge in Ωmega

Resource-Bounded Modelling and Analysis of Human-Level Interactive Proofs

Assisted Proof Document Authoring

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