A normal form for Euler diagrams with shading
Fish, A., Taylor, J. and John, C. (2008) A normal form for Euler diagrams with shading Proceedings of the 5th International Conference on Diagrams 2008, Lecture Notes in Artificial Intelligence, 5223 . pp. 206-221. ISSN 0302-9743
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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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