On Categories of Nested Conditions

Arend Rensink; Andrea Corradini

doi:10.48550/arXiv.2408.06196

On Categories of Nested Conditions

Arend Rensink
, Andrea Corradini

Formal Methods and Tools

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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
Publisher	ArXiv.org
Number of pages	30
DOIs	https://doi.org/10.48550/arXiv.2408.06196
Publication status	Published - 12 Aug 2024

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cs.LO

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10.48550/arXiv.2408.06196Licence: CC BY-NC-SA

2408.06196v1Final published version, 380 KBLicence: CC BY-NC-SA

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On Categories of Nested Conditions
Rensink, A. & Corradini, A., 13 Nov 2024, Principles of Verification: Cycling the Probabilistic Landscape: Essays Dedicated to Joost-Pieter Katoen on the Occasion of His 60th Birthday, Part I. Jansen, N., Junges, S., Kaminski, B. L., Matheja, C., Noll, T., Quatmann, T., Stoelinga, M. & Volk, M. (eds.). Cham, Switzerland: Springer, p. 393-418 26 p. (Lecture Notes in Computer Science; vol. 15260).
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On Categories of Nested Conditions

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On Categories of Nested Conditions

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