A Computer Environment for Writing Ordinary Mathematical Proofs

McMath, David; Rozenfeld, Marianna; Sommer, Richard

doi:10.1007/3-540-45653-8_35

Cited by 13 publications

(15 citation statements)

References 4 publications

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“…The need for natural interfaces (both superficial and functional) in automated verification has been recognized to varying degrees by the designers of the Tutch proof checker [1], the Scunak mathematical assistant system [9], the ForTheL language and SAD proof assistant [31], the EPGY Theorem-Proving Environment [21], the ΩMEGA proof verifier [28], and in the work of Sieg and Cittadini [27]. The ontology-oriented, lightweight verification capabilities of the automated assistant are inspired by work in the assembly of large-scale formal and semi-formal ontologies [24].…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Safe compositional network sketches

Bestavros

Kfoury

Lapets

et al. 2010

Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control

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NetSketch is a tool for the specification of constrained-flow networks (CFNs) and the certification of desirable safety properties imposed thereon, conceived to assist system integrators in modeling and design. It provides compositional analysis capabilities based on a strongly-typed domain-specific language (DSL) for describing and reasoning about CFNs and relevant invariants. Users can model or design individual network components and perform manual or automated whole-system analysis of the properties thereof. Users can also assemble many instances of these components into larger networks, relying on NetSketch's less precise but more tractable compositional analysis capabilities. This ability to trade "precision of analysis" for "feasibility of analysis" according to available resources is among the novel features of NetSketch. In earlier work we illustrated how NetSketch is applied to actual domains [6], and provided a formal definition of its underlying formalism [7].While the NetSketch DSL provides automatic compositional analysis capabilities for modeling and designing entire networks, users may need to employ a wider variety of tools and techniques when modeling and designing individual network components. These can include common tools for reasoning about systems of constraints of various classes (such as linear constraints, quadratic constraints, and so on), as well as logical systems and ontologies that deal with concepts relevant to the application domain. We integrate the AARTIFACT [14] lightweight automated assistant for formal reasoning (which has also been applied in proving the soundness of the NetSketch formalism [15]) as a tool for modeling and designing individual network components. We present use cases within the context of an example application of the NetSketch DSL that demonstrate how the automated assistant provides NetSketch users with both an interface for reasoning formally about constraints, and a straightforward way to implicitly employ a rich domain-specific ontology of logical propositions. This allows users to verify common properties of constraints and constraint sets, and to reason about constraint relationships using automatically verifiable algebraic manipulations.

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Section: Related Work and Conclusionmentioning

confidence: 99%

Safe compositional network sketches

Bestavros

Kfoury

Lapets

et al. 2010

Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control

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“…Human users, who are not necessarily ATP experts, are often the source of the initial input to, and the destination of the final output from, ATP tools. Human data formats are often semi-formal, and translation is required to and from a machine usable format, e.g., [Fie01,MRS01]. In an ideal world it would not be necessary for humans to look at the machine usable input and output, nor at intermediate data being passed between tools in a component based system.…”

Section: Introductionmentioning

confidence: 99%

Universität des Saarlandes

2017

Geschichte Der Anorganischen Chemie

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Abstract. This paper describes two data-exchange formats for Automated Theorem Proving (ATP) tools. First, a language for writing the problems that are input to ATP systems, and for writing the solutions that are output from ATP systems, is described. Second, a hierarchy of values for specifying the logical status of an ATP problem, as may be established by an ATP system, is described. These data-exchange formats will support application and research in ATP, and will facilitate communication between ATP tools in distributed and embedded environments.

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“…This hampers their usability within a mathematical tutoring environment. For example, when the theorem prover Otter (McCune, 2003) was used in the EPGY learning environment for checking studentgenerated proof steps, it sometimes verified seemingly large student steps easily, whereas other, seemingly trivial steps were not verified within an appropriate resource limit (McMath et al, 2001). This criticism applies foremost to machine-oriented theorem proving systems, for example, systems based on fine-grained resolution or tableaux calculi.…”

Section: Introductionmentioning

confidence: 99%

Proof Granularity as an Empirical Problem?

Schiller

Benzmüller

2009

Proceedings of the First International Conference on Computer Supported Education

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Abstract:Even in introductory textbooks on mathematical proof, intermediate proof steps are generally skipped when this seems appropriate. This gives rise to different granularities of proofs, depending on the intended audience and the context in which the proof is presented. We have developed a mechanism to classify whether proof steps of different sizes are appropriate in a tutoring context. The necessary knowledge is learnt from expert tutors via standard machine learning techniques from annotated examples. We discuss the ongoing evaluation of our approach via empirical studies.

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A Computer Environment for Writing Ordinary Mathematical Proofs

Cited by 13 publications

References 4 publications

Safe compositional network sketches

Safe compositional network sketches

Universität des Saarlandes

Proof Granularity as an Empirical Problem?

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