### Abstract

Previous work has shown how first-order logic can equivalently be expressed through nested graph conditions, also called condition trees, with surprisingly few ingredients. In this paper, we extend condition trees by adding set-based operators such as sums and products, calculated over operands that are themselves characterised by first-order logic formulas. This provides a greatly improved way to specify computations such as: given that the price of a geranium plant equals 2 per flower petal, return the average price of all geraniums with at least one flower. We claim the same level of expressive equivalence as before between (extended) condition trees and a certain class of logic formulas; we show that the latter go beyond what can be expressed in first-order logic. On the practical side, we evaluate the performance and usability of set-based operators by specifying and comparing the example geranium property, with and without set-based operators, in the graph transformation tool GROOVE.

Original language | English |
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Title of host publication | ModelEd, TestEd, TrustEd |

Subtitle of host publication | Essays Dedicated to Ed Brinksma on the Occasion of His 60th Birthday |

Editors | Joost-Pieter Katoen, Rom Langerak, Arend Rensink |

Publisher | Springer |

Pages | 191-213 |

Number of pages | 23 |

Volume | 10500 LNCS |

ISBN (Print) | 9783319682693 |

DOIs | |

Publication status | Published - 2017 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10500 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

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### Cite this

*ModelEd, TestEd, TrustEd: Essays Dedicated to Ed Brinksma on the Occasion of His 60th Birthday*(Vol. 10500 LNCS, pp. 191-213). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10500 LNCS). Springer. https://doi.org/10.1007/978-3-319-68270-9_10

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*ModelEd, TestEd, TrustEd: Essays Dedicated to Ed Brinksma on the Occasion of His 60th Birthday.*vol. 10500 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10500 LNCS, Springer, pp. 191-213. https://doi.org/10.1007/978-3-319-68270-9_10

**How much are your geraniums? Taking graph conditions beyond first Order.** / Rensink, Arend.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - How much are your geraniums? Taking graph conditions beyond first Order

AU - Rensink, Arend

PY - 2017

Y1 - 2017

N2 - Previous work has shown how first-order logic can equivalently be expressed through nested graph conditions, also called condition trees, with surprisingly few ingredients. In this paper, we extend condition trees by adding set-based operators such as sums and products, calculated over operands that are themselves characterised by first-order logic formulas. This provides a greatly improved way to specify computations such as: given that the price of a geranium plant equals 2 per flower petal, return the average price of all geraniums with at least one flower. We claim the same level of expressive equivalence as before between (extended) condition trees and a certain class of logic formulas; we show that the latter go beyond what can be expressed in first-order logic. On the practical side, we evaluate the performance and usability of set-based operators by specifying and comparing the example geranium property, with and without set-based operators, in the graph transformation tool GROOVE.

AB - Previous work has shown how first-order logic can equivalently be expressed through nested graph conditions, also called condition trees, with surprisingly few ingredients. In this paper, we extend condition trees by adding set-based operators such as sums and products, calculated over operands that are themselves characterised by first-order logic formulas. This provides a greatly improved way to specify computations such as: given that the price of a geranium plant equals 2 per flower petal, return the average price of all geraniums with at least one flower. We claim the same level of expressive equivalence as before between (extended) condition trees and a certain class of logic formulas; we show that the latter go beyond what can be expressed in first-order logic. On the practical side, we evaluate the performance and usability of set-based operators by specifying and comparing the example geranium property, with and without set-based operators, in the graph transformation tool GROOVE.

UR - http://www.scopus.com/inward/record.url?scp=85032689383&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-68270-9_10

DO - 10.1007/978-3-319-68270-9_10

M3 - Chapter

SN - 9783319682693

VL - 10500 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 191

EP - 213

BT - ModelEd, TestEd, TrustEd

A2 - Katoen, Joost-Pieter

A2 - Langerak, Rom

A2 - Rensink, Arend

PB - Springer

ER -