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  "slug": "ultrametric-nested-semantic-graphs-a-language-neutral-meaning-representation",
  "title": "Ultrametric Nested Semantic Graphs: A Language‑Neutral Meaning Representation",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Cross‑lingual semantic parsing and retrieval degrade for agglutinative and polysynthetic languages because a single surface word can encode an entire proposition, making token‑level matching ineffective. The missing component is a language‑neutral representation whose pairwise distances obey a provable consistency law. We define Ultrametric Nested Semantic Graphs (UNSGs) as rooted hierarchical graphs built from constituency parses by adding sibling edges, and we restrict the distance to the leaf set, defining it as the height of the lowest common ancestor (LCA). The distance satisfies the strong triangle inequality, guaranteeing ultrametricity. We correct earlier planarity claims by exhibiting a non‑planar counterexample and qualify the planar‑slope bound to the subclass of planar UNSGs that are nested pseudotrees. Exact combinatorial costs are derived: 58 786 binary bracketings for a 12‑word sentence, 1 860 480 injective node mappings for a 5‑node pattern in a 20‑node graph, and a 500× compression from pairwise distances to tree parameters at n=1,000 nodes. These results provide a mathematically rigorous, language‑neutral foundation for subgraph‑matching retrieval across typologically diverse languages.",
  "abstract_markdown": "Cross‑lingual semantic parsing and retrieval degrade for agglutinative and polysynthetic languages because a single surface word can encode an entire proposition, making token‑level matching ineffective. The missing component is a language‑neutral representation whose pairwise distances obey a provable consistency law. We define **Ultrametric Nested Semantic Graphs (UNSGs)** as rooted hierarchical graphs built from constituency parses by adding sibling edges, and we restrict the distance to the leaf set, defining it as the height of the lowest common ancestor (LCA). The distance satisfies the strong triangle inequality, guaranteeing ultrametricity. We correct earlier planarity claims by exhibiting a non‑planar counterexample and qualify the planar‑slope bound to the subclass of planar UNSGs that are nested pseudotrees. Exact combinatorial costs are derived: $58\\,786$ binary bracketings for a 12‑word sentence, $1\\,860\\,480$ injective node mappings for a 5‑node pattern in a 20‑node graph, and a $500\\times$ compression from pairwise distances to tree parameters at $n=1{,}000$ nodes. These results provide a mathematically rigorous, language‑neutral foundation for subgraph‑matching retrieval across typologically diverse languages.",
  "date": "2026-10-20",
  "first_published": "2026-10-20",
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  "url": "https://papers.qnfo.org/papers/ultrametric-nested-semantic-graphs-a-language-neutral-meaning-representation",
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    "titles": [
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