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

Arend Rensink*

*Corresponding author for this work

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    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 languageEnglish
    Title of host publicationModelEd, TestEd, TrustEd
    Subtitle of host publicationEssays Dedicated to Ed Brinksma on the Occasion of His 60th Birthday
    EditorsJoost-Pieter Katoen, Rom Langerak, Arend Rensink
    PublisherSpringer
    Pages191-213
    Number of pages23
    Volume10500 LNCS
    ISBN (Print)9783319682693
    DOIs
    Publication statusPublished - 2017
    EventSymposium on Model-Ed, Test-Ed, Trust-Ed in honour of Ed Brinksma on the occasion of his 60th birthday, 2017 - Enschede, Netherlands
    Duration: 18 Oct 201718 Oct 2017

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume10500 LNCS
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Conference

    ConferenceSymposium on Model-Ed, Test-Ed, Trust-Ed in honour of Ed Brinksma on the occasion of his 60th birthday, 2017
    CountryNetherlands
    CityEnschede
    Period18/10/1718/10/17

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  • Cite this

    Rensink, A. (2017). How much are your geraniums? Taking graph conditions beyond first Order. In J-P. Katoen, R. Langerak, & A. Rensink (Eds.), 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