Q&A — Phase 27.1 DomainMapper

[web3guru888]

Frequently Asked Questions

Q1: Why structure mapping instead of embedding similarity?

Embedding similarity captures surface-level patterns (shared vocabulary, statistical co-occurrence). Structure mapping captures relational isomorphisms — the deep structural parallels that make analogies productive. The solar-system/atom analogy works because both share attracts(center, orbiter) + revolves(orbiter, center), not because "sun" and "nucleus" have similar word embeddings.

Q2: How is the one-to-one constraint enforced?

During the merge phase, each entity in the source can map to at most one entity in the target (and vice versa). The greedy merge algorithm maintains a used_source: set and used_target: set. Any match hypothesis that would violate one-to-one is discarded. This prevents degenerate many-to-one mappings.

Q3: What happens when no good mapping exists?

If the best mapping's structural score falls below a configurable threshold (default: 0.2), map_domains returns a DomainMapping with confidence=0.0 and empty transferred_inferences. The caller (typically GeneralizationOrchestrator) interprets this as "domains are too dissimilar for productive transfer."

Q4: How does the LRU cache work?

The mapping cache is keyed on (source.domain_id, target.domain_id). Since DomainSchema is frozen, its identity is stable. The cache uses functools.lru_cache with a configurable maxsize (default: 128). Cache invalidation happens when a domain's schema is updated (detected via schema hash).

Q5: Can DomainMapper handle partial domains?

Yes. If the target domain has fewer entities/relations than the source, the mapping will have unmapped_source entries. These unmapped elements are precisely what transfer_knowledge uses to generate candidate inferences — they represent knowledge the source has that the target might benefit from.

Q6: How does this integrate with ConceptGraph (26.1)?

ConceptGraph provides the raw material: entities as concept nodes, relations as edges. DomainSchema.from_concept_graph(graph, domain_filter) extracts a domain-specific subgraph and wraps it as a DomainSchema. This bridges Phase 26's knowledge representation with Phase 27's transfer machinery.

Q7: What are the computational complexity bounds?

• Local matching: O(|R_s| × |R_t|) where R = relations
• Merge: O(n² log n) for n local matches (greedy with sorting)
• Systematicity scoring: O(d × m) where d = max relation depth, m = matched relations
• Practical: <100ms for domains with <1000 relations on modern hardware

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Issue: #594 | Show & Tell: #599