Dr.Doodle: A Diagrammatic Theorem Prover

Winterstein, Daniel; Bundy, Alan; Gurr, Corin A.

doi:10.1007/978-3-540-25984-8_24

Cited by 12 publications

(9 citation statements)

References 8 publications

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“…DIAMOND is focused on the domain of natural number arithmetic, proving results like the sum of the first n odd natural numbers is n 2 , and the reasoning is semiautomatic [27]. A natural extension of DIAMOND is to a continuous domain, and Winterstein et al present animated diagrammatic reasoning rules for use in a real analysis setting [57,58].…”

Section: Related Work On Automated Diagrammatic Reasoningmentioning

confidence: 99%

Automated Theorem Proving in Euler Diagram Systems

et al. 2007

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Diagrammatic reasoning has the potential to be important in numerous application areas. This paper focuses on the simple, but widely used, Euler diagrams that form the basis of many more expressive logics. We have implemented a diagrammatic theorem prover, called Edith, which has access to four sound and complete sets of reasoning rules for Euler diagrams. Furthermore, for each rule set we develop a sophisticated heuristic to guide the search for a proof. This paper is about understanding how the choice of reasoning rule set affects the time taken to find proofs. Such an understanding will influence reasoning rule design in other logics. Moreover, this work specific to Euler diagrams directly benefits the many logics based on Euler diagrams. We investigate how the time taken to find a proof depends not only on the proof task but also on the reasoning system used. Our evaluation allows us to predict the best choice of reasoning system, given a proof task, in terms of time taken, and we extract a guide for defining reasoning rules for other logics in order to minimize time requirements.

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Section: Related Work On Automated Diagrammatic Reasoningmentioning

confidence: 99%

Automated Theorem Proving in Euler Diagram Systems

et al. 2007

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“…-It is very natural in geometry to illustrate a proof by a diagrammatic representation, and sometimes a diagram can even be seen as a high level description of a proof [7,23,29,38,39,40]. But sometimes a diagram can be misleading.…”

Section: Introductionmentioning

confidence: 99%

A Graphical User Interface for Formal Proofs in Geometry

Narboux

2007

J Autom Reasoning

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“…Still, the intuitive nature of diagrams motivated the design of formal diagrammatic reasoning systems -for example, spider diagrams [6] and constraint diagrams [3]. Consequently, some purely diagrammatic theorem provers have been developed, Diamond [8], Edith [10] and Dr.Doodle [13] are some examples.…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous Proofs: Spider Diagrams Meet Higher-Order Provers

Urbas

Jamnik

2011

Interactive Theorem Proving

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Abstract. We present an interactive heterogeneous theorem proving framework, which performs formal reasoning by arbitrarily mixing diagrammatic and sentential proof steps. We use Isabelle to enable formal reasoning with either traditional sentences or spider diagrams. We provide a mechanisation of the theory of abstract spider diagrams and establish a formal link between diagrammatic concepts and the existing theories in Isabelle/HOL.

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Dr.Doodle: A Diagrammatic Theorem Prover

Cited by 12 publications

References 8 publications

Automated Theorem Proving in Euler Diagram Systems

Automated Theorem Proving in Euler Diagram Systems

A Graphical User Interface for Formal Proofs in Geometry

Heterogeneous Proofs: Spider Diagrams Meet Higher-Order Provers

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