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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Official URL: http://link.springer.com/chapter/10.1007%2F978-3-5...
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.
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