On Categories of Nested Conditions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929456142090240 |
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| author | Rensink, Arend Corradini, Andrea |
| author_facet | Rensink, Arend Corradini, Andrea |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06196 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Categories of Nested Conditions Rensink, Arend Corradini, Andrea Logic in Computer Science 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. |
| title | On Categories of Nested Conditions |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2408.06196 |