On Categories of Nested Conditions
Logic in Computer Science
2024-08-13 v1
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.
Cite
@article{arxiv.2408.06196,
title = {On Categories of Nested Conditions},
author = {Arend Rensink and Andrea Corradini},
journal= {arXiv preprint arXiv:2408.06196},
year = {2024}
}