Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.561880
Title: Using diagrammatic reasoning for theorem proving in a continuous domain
Author: Winterstein, Daniel
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2005
Availability of Full Text:
Access from EThOS:
Full text unavailable from EThOS. Please try the link below.
Access from Institution:
Abstract:
This project looks at using diagrammatic reasoning to prove mathematical theorems. The work is motivated by a need for theorem provers whose reasoning is readily intelligible to human beings. It should also have practical applications in mathematics teaching. We focus on the continuous domain of analysis - a geometric subject, but one which is taught using a dry algebraic formalism which many students find hard. The geometric nature of the domain makes it suitable for a diagram-based approach. However it is a difficult domain, and there are several problems, including handling alternating quantifiers, sequences and generalisation. We developed representations and reasoning methods to solve these. Our diagram logic isn't complete, but does cover a reasonable range of theorems. It utilises computers to extend diagrammatic reasoning in new directions – including using animation. This work is tested for soundness, and evaluated empirically for ease of use. We demonstrate that computerised diagrammatic theorem proving is not only possible in the domain of real analysis, but that students perform better using it than with an equivalent algebraic computer system.
Supervisor: Bundy, Alan. ; Gurr, Corin. ; Jamnik, Mateja. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.561880  DOI: Not available
Keywords: Diagrammatic Reasoning ; Theorem Proving ; Continuous Domain
Share: