Diagramets

Diagramets are a formalism for encoding relational information with diagrams. A Diagramet consists of nodes representing entities, edges representing relationships, and optional containers that group subdiagrams. Edges may be directed or undirected and can carry labels to specify relation type. Hyperedges enable multi-way relations, allowing compact representation of complex interactions. The goal is readable diagrammatic reasoning with formal analyzability.

Formal model: A Diagramet can be modeled as a finite labeled directed hypergraph with a layout. The set of nodes, edges, and a labeling function form the core. Diagramets may include attributes such as color or weight. Some variants enforce planarity to improve readability; others permit edge crossings and automatic layout.

Construction and transformations: Diagramets are built by adding nodes and edges according to rules. They can be composed by gluing compatible subdiagrams along shared interfaces. Transformation rules rewrite a subdiagram into an equivalent form, enabling diagrammatic reasoning or simplification. Equivalence is defined by structure-preserving isomorphism that respects labels and hierarchy.

Types and examples: Linear Diagramets arrange components on a line; planar Diagramets avoid edge crossings; hierarchical Diagramets use containers to express containment. Annotated Diagramets attach metadata to nodes or edges. A simple example encodes that A causes B and B influences C, with directed, labeled edges.

Applications: Diagramets appear in education for reasoning about relations, knowledge representation, visual programming, and workflow design. They are studied for expressiveness, readability, and interoperability with other diagrammatic formalisms.