Morphology
Classification of word forms
Regularization of derivatives (Axiom-atic, Axiom-atize, etc.).
Examples: Axiom-atic, Axiom-atize, Axiom-ization, Axiom-icity
Framework
Terminology Matrix. The Terminology Matrix organizes the classification and comparison of "Axiom-" into an academic framework.
Terminology Matrix
Name, purpose, and examples for each analytical dimension.
| Dimension | Name | Purpose | Examples |
|---|---|---|---|
| Morphology | Classification of word forms | Regularization of derivatives (Axiom-atic, Axiom-atize, etc.). | Axiom-atic, Axiom-atize, Axiom-ization, Axiom-icity |
| Semantics | Comparison of semantic domains | Definition of Axiom-ness (surface) vs Axiom-aticity (deep). | Axiom-ness, Axiom-aticity |
| Function | Domain analysis | Identifying roles in number theory, physics, and geometry. | Number theory, Physics, Geometry |
| Relation | Ontology construction | Integration across domains via Axiom-omorphism. | Axiom-omorphism |
| Ontology | Ontology and conceptual hierarchy | Formalizing the hierarchy from Axiom-ness to Axiom-odynamics. Meaning integration via RDF/OWL. | OWL, RDF |
| Ontopology | Fusion of ontology and topology | Integrating ontological and topological structure. Describing conceptual proximity and continuity. | Ontology, Topology |
Semantics
Comparison of semantic domains
Definition of Axiom-ness (surface) vs Axiom-aticity (deep).
Examples: Axiom-ness, Axiom-aticity
Function
Domain analysis
Identifying roles in number theory, physics, and geometry.
Examples: Number theory, Physics, Geometry
Relation
Ontology construction
Integration across domains via Axiom-omorphism.
Examples: Axiom-omorphism
Ontology
Ontology and conceptual hierarchy
Formalizing the hierarchy from Axiom-ness to Axiom-odynamics. Meaning integration via RDF/OWL.
Examples: OWL, RDF
Ontopology
Fusion of ontology and topology
Integrating ontological and topological structure. Describing conceptual proximity and continuity.
Examples: Ontology, Topology
Practical Toolkit Construction
Axiom-Namespace
Assign unique IDs and definitions to each derivative term according to ISO standards.
Ensuring concept and designation uniqueness per ISO 1087, ISO 704.
Morphism-Protocol
Describe Axiom-omorphism in a format like Common Logic (ISO/IEC 24707) and define it as a "transformation protocol" from number theory to physics.
Framework for information exchange between logical systems.
Ontology Map
Visualize the hierarchy from Axiom-ness (surface) to Axiom-odynamics (deep) using OWL.
Meaning integration and hierarchy visualization via RDF/OWL.
Definition of Axiom-omorphism (ISO 704 compliant)
An internationally standard-compliant definition based on ISO 704 principles (superordinate concept + delimiting characteristics, substitutability, avoidance of circularity).
Axiom-omorphism
Superordinate concept: A type of structure-preserving mapping.
Delimiting characteristics: A mapping between two or more axiomatic systems that preserves logical structure while correlating propositions from one domain (e.g., number theory) with those of another (e.g., physics, geometry). Can be formalized within the framework of Common Logic (ISO/IEC 24707).
Substitution example: "Axiom-omorphism is a structure-preserving mapping that maps the axiomatic system of number theory to that of physics."