Purpose: This paper proposes CatRO (Categorical Referent Ontology), a category-theoretic formalization of staged concept formation that addresses the symbol grounding problem.
Methods: CatRO formalizes the transformation from observational data to concepts as three staged processes: observation (OBS-P) as a functor, individualization (IND-P) as a natural transformation, and universalization (UNV-P) as classification based on Conceptual Spaces. We introduce a Pattern Datum hierarchy (OMD, SPD, PP…
Read morePurpose: This paper proposes CatRO (Categorical Referent Ontology), a category-theoretic formalization of staged concept formation that addresses the symbol grounding problem.
Methods: CatRO formalizes the transformation from observational data to concepts as three staged processes: observation (OBS-P) as a functor, individualization (IND-P) as a natural transformation, and universalization (UNV-P) as classification based on Conceptual Spaces. We introduce a Pattern Datum hierarchy (OMD, SPD, PPD, EPD) as explicit intermediate representations and demonstrate correspondence with the DOLCE top-level ontology through the Quality Space framework.
Results: This formalization mathematically guarantees structure preservation while providing ``gray box'' interpretability---the structural traceability of transformation processes is ensured even when the specific content of intermediate representations cannot be fully described in natural language. Two illustrative examples---``Two Apples'' and ``Pendulum Motion''---demonstrate the framework's operation.
Conclusions: CatRO contributes to bridging formal ontology and machine learning by providing a theoretical foundation for explainable concept formation.
