On Categories of Nested Conditions

Arend Rensink; Andrea Corradini

doi:10.1007/978-3-031-75783-9_16

On Categories of Nested Conditions

Arend Rensink, Andrea Corradini

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

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Abstract

Nested conditions are used, among other things, as a graphical way to express first order formulas ruling the applicability of a graph transformation rule to a given match. In this paper, we propose (for the first time) a notion of structural morphism among nested conditions, consistent with the entailment of the corresponding formulas. This reveals a structural weakness of the existing definition of nested conditions, which we overcome by proposing a new notion of span-based nested conditions, embedding the original ones. We also introduce morphisms for the latter, showing that those form a richer structure by organising the various models in a number of categories suitably related by functors.

Original language	English
Title of host publication	Principles of Verification: Cycling the Probabilistic Landscape
Subtitle of host publication	Essays Dedicated to Joost-Pieter Katoen on the Occasion of His 60th Birthday, Part I
Editors	Nils Jansen, Sebastian Junges, Benjamin Lucien Kaminski, Christoph Matheja, Thomas Noll, Tim Quatmann, Mariëlle Stoelinga, Matthias Volk
Place of Publication	Cham, Switzerland
Publisher	Springer
Pages	393-418
Number of pages	26
ISBN (Electronic)	978-3-031-75783-9
ISBN (Print)	978-3-031-75782-2
DOIs	https://doi.org/10.1007/978-3-031-75783-9_16
Publication status	Published - 2025

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	15260
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Keywords

2025 OA procedure
Graph Transformation, Nested Condition, Entailment, Category Theory

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10.1007/978-3-031-75783-9_16

978-3-031-75783-9_16-1Final published version, 527 KBLicence: Taverne

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Rensink, A., & Corradini, A. (2025). On Categories of Nested Conditions. In N. Jansen, S. Junges, B. L. Kaminski, C. Matheja, T. Noll, T. Quatmann, M. Stoelinga, & M. Volk (Eds.), Principles of Verification: Cycling the Probabilistic Landscape: Essays Dedicated to Joost-Pieter Katoen on the Occasion of His 60th Birthday, Part I (pp. 393-418). (Lecture Notes in Computer Science; Vol. 15260). Springer. https://doi.org/10.1007/978-3-031-75783-9_16

Rensink, Arend ; Corradini, Andrea. / On Categories of Nested Conditions. Principles of Verification: Cycling the Probabilistic Landscape: Essays Dedicated to Joost-Pieter Katoen on the Occasion of His 60th Birthday, Part I. editor / Nils Jansen ; Sebastian Junges ; Benjamin Lucien Kaminski ; Christoph Matheja ; Thomas Noll ; Tim Quatmann ; Mariëlle Stoelinga ; Matthias Volk. Cham, Switzerland : Springer, 2025. pp. 393-418 (Lecture Notes in Computer Science).

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Rensink, A & Corradini, A 2025, On Categories of Nested Conditions. in N Jansen, S Junges, BL Kaminski, C Matheja, T Noll, T Quatmann, M Stoelinga & M Volk (eds), Principles of Verification: Cycling the Probabilistic Landscape: Essays Dedicated to Joost-Pieter Katoen on the Occasion of His 60th Birthday, Part I. Lecture Notes in Computer Science, vol. 15260, Springer, Cham, Switzerland, pp. 393-418. https://doi.org/10.1007/978-3-031-75783-9_16

On Categories of Nested Conditions. / Rensink, Arend; Corradini, Andrea.
Principles of Verification: Cycling the Probabilistic Landscape: Essays Dedicated to Joost-Pieter Katoen on the Occasion of His 60th Birthday, Part I. ed. / Nils Jansen; Sebastian Junges; Benjamin Lucien Kaminski; Christoph Matheja; Thomas Noll; Tim Quatmann; Mariëlle Stoelinga; Matthias Volk. Cham, Switzerland: Springer, 2025. p. 393-418 (Lecture Notes in Computer Science; Vol. 15260).

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

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AB - Nested conditions are used, among other things, as a graphical way to express first order formulas ruling the applicability of a graph transformation rule to a given match. In this paper, we propose (for the first time) a notion of structural morphism among nested conditions, consistent with the entailment of the corresponding formulas. This reveals a structural weakness of the existing definition of nested conditions, which we overcome by proposing a new notion of span-based nested conditions, embedding the original ones. We also introduce morphisms for the latter, showing that those form a richer structure by organising the various models in a number of categories suitably related by functors.

KW - 2025 OA procedure

KW - Graph Transformation, Nested Condition, Entailment, Category Theory

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BT - Principles of Verification: Cycling the Probabilistic Landscape

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A2 - Junges, Sebastian

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Rensink A, Corradini A. On Categories of Nested Conditions. In Jansen N, Junges S, Kaminski BL, Matheja C, Noll T, Quatmann T, Stoelinga M, Volk M, editors, Principles of Verification: Cycling the Probabilistic Landscape: Essays Dedicated to Joost-Pieter Katoen on the Occasion of His 60th Birthday, Part I. Cham, Switzerland: Springer. 2025. p. 393-418. (Lecture Notes in Computer Science). Epub 2024 Nov 13. doi: 10.1007/978-3-031-75783-9_16

On Categories of Nested Conditions

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