Deep Inference for Automated Proof Tutoring?

Benzmüller, Christoph; Dietrich, Dominik; Schiller, Marvin; Autexier, Serge

doi:10.1007/978-3-540-74565-5_34

Cited by 7 publications

(8 citation statements)

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“…This may result in even more alternative proofs if that utterance was ambiguous but it may also rule out certain proof alternatives that are no longer consistent with the student's utterance. More information on the Proof Step Verifier is available in [6].…”

Section: Mathematical Knowledge Management In ωMega 259mentioning

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: Mathematical Knowledge Management In ωMega 259mentioning

confidence: 99%

Organization, Transformation, and Propagation of Mathematical Knowledge in Ωmega

et al. 2008

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“…A prototypical implementation of such a component was implemented using proof reconstruction in Ω mega CoRE (as presented in Benzmüller et al. ) and the framework presented here, and this was prototypically integrated within the ActiveMath platform for the intelligent e‐learning of mathematics (Melis & Siekmann, ). Via a simple interface, formulas can be submitted stepwise, and the results of analyzing each step with respect to correctness and granularity are shown to the user.…”

Section: Criterion‐based Modeling Of Proof Granularitymentioning

confidence: 99%

“…Benzmüller et al. ), which enables inference applications deeply inside formulas. It has been argued (cf.…”

Section: Introductionmentioning

confidence: 99%

“…Benzmüller et al. ) that proofs in this framework are closer to mathematical practice compared with proofs in more machine‐oriented but popular calculi such as resolution, or even the classic natural deduction calculus. Within a tutorial system such as developed in the Dialog project, the dynamic reconstruction approach enables students to experiment with various ways (i.e., solution paths and step sizes) to approach the same proof.…”

Section: Introductionmentioning

confidence: 99%

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Granularity Analysis for Mathematical Proofs

Schiller

2013

Topics in Cognitive Science

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Mathematical proofs generally allow for various levels of detail and conciseness, such that they can be adapted for a particular audience or purpose. Using automated reasoning approaches for teaching proof construction in mathematics presupposes that the step size of proofs in such a system is appropriate within the teaching context. This work proposes a framework that supports the granularity analysis of mathematical proofs, to be used in the automated assessment of students' proof attempts and for the presentation of hints and solutions at a suitable pace. Models for granularity are represented by classifiers, which can be generated by hand or inferred from a corpus of sample judgments via machine-learning techniques. This latter procedure is studied by modeling granularity judgments from four experts. The results provide support for the granularity of assertion-level proofs but also illustrate a degree of subjectivity in assessing step size.

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“…In [12] we report on a case study in which we applied our ΩMEGA based assessment module with a depth-limit of four assertion level steps to 17 dialogues from the second DIALOG corpus; these 17 dialogues contain a total of 147 proof steps. All the steps within a dialogue were passed to the assessment module sequentially until a step that is labelled as correct cannot be verified, in which case we move on to the next dialogue.…”

Section: Proof Management Correctness Analysis and Content Underspecmentioning

confidence: 99%