[Data Quality] 23 Cyclic rdfs:subClassOf Relationships + 9 Orphan Nodes in OntoMathPRO v8

[park-kyungchan]

Summary

During our migration of OntoMathPRO v8 to Neo4j graph database, we identified 32 data quality issues:

• 23 cyclic rdfs:subClassOf relationships (causing circular hierarchies)
• 9 orphan nodes (missing parent relationships)

Impact: These issues prevent direct DAG (Directed Acyclic Graph) implementation, which is essential for graph databases and ontology reasoning systems.

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Issue #1: Cyclic rdfs:subClassOf Relationships (23 cycles)

Severity

HIGH - Prevents proper hierarchy traversal and reasoning

Description

Cycles occur when rdfs:subClassOf relationships form circular paths, violating the DAG property required for proper ontology hierarchies.

Example cycle:

• A rdfs:subClassOf B
• B rdfs:subClassOf C
• C rdfs:subClassOf A ← Cycle!

Detected Major Cycles

1. E34 Cycle (Length: 5)

   • Path: E34 → E1660 → E4830 → E5122 → E6214 → E34
   • Concepts: Mathematical knowledge object chain

2. E2844 Cycle (Length: 3)

   • Path: E2844 → E1660 → E34 → E2844
   • Concepts: Element of mathematical analysis chain

3. Matrix Cycle (Length: 4)

   • Path: MatrixOperation → SquareMatrix → DiagonalMatrix → MatrixOperation

Plus 20 more cycles (mostly 2-node bidirectional relationships)

Reproduction Steps

Using Protégé:

1. Open `ontomathpro_v8.owl` in Protégé
2. Select "Tools" → "Reasoner" → "HermiT"
3. Run "Start Reasoner"
4. Navigate to E34 class
5. Expand "SubClass Of" hierarchy
6. Observe circular reference

Using Neo4j Cypher (after import):
```cypher
MATCH path = (n:ObjectType)-[:GENERALIZES*]->(n)
RETURN [node in nodes(path) | node.name] as cycle_path,
length(path) as cycle_length
ORDER BY cycle_length DESC
```

Recommended Fix

For the E34 cycle specifically, we recommend removing E34 → E1660 relationship:

Rationale:

• "Mathematical knowledge object" (E34) should NOT be subclass of "Value" (E1660)
• Counter-examples: Theorem, Operator, Formula are not values
• Keeping E1660 → E34 (Value is-a Mathematical knowledge object) is semantically correct

General approach:

1. Analyze semantic correctness of each rdfs:subClassOf in the cycle
2. Remove the weakest relationship (least semantically justified)
3. Re-validate hierarchy

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Issue #2: Orphan Nodes (9 nodes)

Severity

MEDIUM - Reduces hierarchy completeness

Description

9 nodes have no parent relationships due to encoding/naming mismatches in the OWL file.

Detected Orphans

Emden-Fowler Family (5 nodes):

• `Emden–FowlerEquation` (expected parent: E1897)
• `Emden–FowlerTypeEquation`
• `EmdenEquation`
• `Thomas–FermiEquation`
• `Euler–Poisson–DarbouxEquation`

Root Cause: Encoding mismatch (`â` vs `-`)

ElementMatrices Family (4 nodes):

• `ElementMatriсesTheory` (Cyrillic 'с')
• `DeterminantMatrix`
• `MatrixOperation`
• `TraceMatrix`

Root Cause: Cyrillic character in parent name (`с` instead of `c`)

Recommended Fix

1. Normalize encoding: Convert all em-dashes to regular hyphens
2. Fix Cyrillic characters: Replace Cyrillic 'с' with Latin 'c' in `ElementMatricesTheory`
3. Add missing relationships:
   ```xml
   <owl:Class rdf:about="EmdenEquation">
   <rdfs:subClassOf rdf:resource="Emden-FowlerEquation"/>
   </owl:Class>
   ```

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Impact Analysis

Current State

• Total Classes: 4,052
• With cycles: 23 classes affected
• Orphaned: 9 classes
• Effective completeness: ~99.2%

Consequences

• ❌ Cannot be used in Neo4j without manual fixes
• ❌ Reasoners may produce incorrect inferences
• ❌ Hierarchy visualization tools fail
• ❌ SPARQL queries return incomplete results

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Full Details

For complete analysis including all 23 cycles, reproduction scripts, and detailed recommendations, see our full report:

Repository: [Our internal analysis repository]
Report File: `palantir/docs/ontomathpro_issues_report.md`

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Environment

• OntoMathPRO Version: v8 (`ontomathpro_v8.owl`)
• Detection Method: Neo4j graph database migration + Python OWL parsing
• Analysis Date: 2025-11-08
• Reporter: Math Ontology Migration Team

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We're happy to provide additional details or collaborate on fixes. Thank you for maintaining this valuable resource!