On Categories of Nested Conditions
<|reference_start|>On Categories of Nested Conditions: 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.<|reference_end|>
@article{rensink2024on,
    title={On Categories of Nested Conditions},
    author={Arend Rensink, Andrea Corradini},
    journal={arXiv preprint arXiv:2408.06196},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.06196},
    primaryClass={cs.LO}
}