### 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.

Original language | English |
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Title of host publication | Proceedings of the 5th International Conference on the Theory and Application of Diagrams |

Place of Publication | Berlin Heidelberg |

Publisher | Springer-Verlag |

Pages | 206-221 |

Number of pages | 16 |

Volume | 5223 |

ISBN (Electronic) | 9783540877301 |

ISBN (Print) | 9783540877295 |

DOIs | |

Publication status | Published - 1 Jan 2008 |

Event | Proceedings of the 5th international conference on the theory and application of diagrams - Herrsching, Germany, 19-21 September, 2008 Duration: 1 Jan 2008 → … |

### Publication series

Name | Lecture Notes in Computer Science |
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### Conference

Conference | Proceedings of the 5th international conference on the theory and application of diagrams |
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Period | 1/01/08 → … |

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## Cite this

Fish, A., John, C., & Taylor, J. (2008). A normal form for Euler diagrams with shading. In

*Proceedings of the 5th International Conference on the Theory and Application of Diagrams*(Vol. 5223, pp. 206-221). (Lecture Notes in Computer Science). Berlin Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-540-87730-1_20