Structural Morphisms for Nested Conditions - Full Version

2026-08-12

AI Summary

This study addresses the formal representation and preservation of logical relationships among nested conditions in graph transformation rules. To overcome the limitations of existing approaches, which lack precise characterization of structural dependencies between nested conditions, the work introduces condition operators that emulate logical connectives and, for the first time, defines structural morphisms between nested conditions. Within a categorical framework, it establishes criteria under which these morphisms align with logical implication and proves that they preserve implication under a specific semantic interpretation. Furthermore, the paper uncovers the functorial nature and universal properties of the proposed constructions, thereby providing novel formal tools to strengthen the logical foundations of graph transformation systems.

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 first introduce several operators on conditions mimicking logical connectives. Next we propose an original notion of structural morphism among nested conditions, and we identify circumstances under which morphisms are consistent with the entailment of the corresponding conditions. Finally we frame the results in a categorical context, proving functoriality and universality properties of the various operations.

Problem

• nested conditions
• structural morphism
• graph transformation
• logical entailment
• categorical framework

Innovation

• structural morphism
• nested conditions
• graph transformation
• functoriality
• categorical framework