A normal form for Euler diagrams with shading

FISH, ANDREW, John, Chris and TAYLOR, JOHN (2008) A normal form for Euler diagrams with shading In: Proceedings of the 5th International Conference on the Theory and Application of Diagrams, Herrsching, Germany, 19-21 September, 2008.

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Abstract

In logic, there are various normal forms for formulae; for example, disjunctive and conjunctive normal form for formulae of propositional logic or prenex normal form for formulae of predicate logic. There are algorithms for ‘reducing’ a given formula to a semantically equivalent formula in normal form. Normal forms are used in a variety of contexts including proofs of completeness, automated theorem proving, logic programming etc. In this paper, we develop a normal form for unitary Euler diagrams with shading. We give an algorithm for reducing a given Euler diagram to a semantically equivalent diagram in normal form and hence a decision procedure for determining whether two Euler diagrams are semantically equivalent. Potential applications of the normal form include clutter reduction and automated theorem proving in systems based on Euler diagrams.

Item Type: Contribution to conference proceedings in the public domain ( Full Paper)
Subjects: G000 Computing and Mathematical Sciences
DOI (a stable link to the resource): 10.1007/978-3-540-87730-1_20
Faculties: Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Visual Modelling
Depositing User: Converis
Date Deposited: 25 Mar 2010
Last Modified: 07 Aug 2013 03:02
URI: http://eprints.brighton.ac.uk/id/eprint/7062

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