@prefix this: <https://w3id.org/np/RAXsiMCaDC1SVENBEf3Coawoeosjo15IcyvDG-GLITyK4> .
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@prefix np: <http://www.nanopub.org/nschema#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix prov: <http://www.w3.org/ns/prov#> .
@prefix npx: <http://purl.org/nanopub/x/> .
sub:Head {
   this: np:hasAssertion sub:assertion ;
    np:hasProvenance sub:provenance ;
    np:hasPublicationInfo sub:pubinfo ;
    a np:Nanopublication .
}
sub:assertion {
   <https://doi.org/10.48550/arXiv.2505.13406> dct:title "AutoMathKG: The automated mathematical knowledge graph based on LLM and vector database" ;
    <http://purl.org/spar/cito/describes> <https://neverblink.eu/ontologies/llm-kg/methods#AutoMathKG> , <https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeCompletion> , <https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeFusion> , <https://neverblink.eu/ontologies/llm-kg/methods#MathLLM> , <https://neverblink.eu/ontologies/llm-kg/methods#MathVD1> , <https://neverblink.eu/ontologies/llm-kg/methods#MathVD2> ;
    <http://purl.org/spar/cito/discusses> <https://neverblink.eu/ontologies/llm-kg/methods#BoxE> , <https://neverblink.eu/ontologies/llm-kg/methods#CoT> , <https://neverblink.eu/ontologies/llm-kg/methods#Gemma7bit> , <https://neverblink.eu/ontologies/llm-kg/methods#HoLE> , <https://neverblink.eu/ontologies/llm-kg/methods#KG2E> , <https://neverblink.eu/ontologies/llm-kg/methods#Llama27b> , <https://neverblink.eu/ontologies/llm-kg/methods#LoRA> , <https://neverblink.eu/ontologies/llm-kg/methods#MathGloss> , <https://neverblink.eu/ontologies/llm-kg/methods#MathGraph> , <https://neverblink.eu/ontologies/llm-kg/methods#MathKG> , <https://neverblink.eu/ontologies/llm-kg/methods#NaturalProofs> , <https://neverblink.eu/ontologies/llm-kg/methods#PoT> , <https://neverblink.eu/ontologies/llm-kg/methods#RGCN> , <https://neverblink.eu/ontologies/llm-kg/methods#SBERT> , <https://neverblink.eu/ontologies/llm-kg/methods#TransE> ;
    a prov:Entity .
  <https://neverblink.eu/ontologies/llm-kg/methods#AutoMathKG> dct:subject <https://neverblink.eu/ontologies/llm-kg/categories#SynergizedReasoning> ;
    a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:comment "AutoMathKG is an overarching system that provides an automatically updatable mathematical knowledge graph. It integrates LLMs for KG construction and updates, and uses the KG and its vector database (MathVD) to enhance a specialized LLM's mathematical reasoning capabilities, thus mutually benefiting both components within a unified framework." ;
    rdfs:label "AutoMathKG" ;
    <https://neverblink.eu/ontologies/llm-kg/hasTopCategory> <https://neverblink.eu/ontologies/llm-kg/top-categories#SynergizedLLMKG> .
  <https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeCompletion> dct:subject <https://neverblink.eu/ontologies/llm-kg/categories#LLMAugmentedKGCompletion> ;
    a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:comment "This mechanism utilizes the specialized Math LLM to supplement incomplete proofs or solutions for new mathematical entities within the knowledge graph. By generating missing facts, it directly enhances the completeness and quality of the KG using LLM capabilities." ;
    rdfs:label "Automatic knowledge completion" ;
    <https://neverblink.eu/ontologies/llm-kg/hasTopCategory> <https://neverblink.eu/ontologies/llm-kg/top-categories#LLMAugmentedKG> .
  <https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeFusion> dct:subject <https://neverblink.eu/ontologies/llm-kg/categories#LLMAugmentedKGConstruction> ;
    a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:comment "This mechanism employs MathVD for fuzzy search and LLMs (via in-context learning) to determine whether to merge new input entities with existing similar candidates or add them as new entities. This process directly contributes to the construction and maintenance of the KG by addressing entity discovery, coreference resolution, and relationship integration." ;
    rdfs:label "Automatic knowledge fusion" ;
    <https://neverblink.eu/ontologies/llm-kg/hasTopCategory> <https://neverblink.eu/ontologies/llm-kg/top-categories#LLMAugmentedKG> .
  <https://neverblink.eu/ontologies/llm-kg/methods#BoxE> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "BoxE" .
  <https://neverblink.eu/ontologies/llm-kg/methods#CoT> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "CoT" .
  <https://neverblink.eu/ontologies/llm-kg/methods#Gemma7bit> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "Gemma-7b-it" .
  <https://neverblink.eu/ontologies/llm-kg/methods#HoLE> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "HoLE" .
  <https://neverblink.eu/ontologies/llm-kg/methods#KG2E> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "KG2E" .
  <https://neverblink.eu/ontologies/llm-kg/methods#Llama27b> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "Llama-2-7b" .
  <https://neverblink.eu/ontologies/llm-kg/methods#LoRA> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "LoRA" .
  <https://neverblink.eu/ontologies/llm-kg/methods#MathGloss> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "MathGloss" .
  <https://neverblink.eu/ontologies/llm-kg/methods#MathGraph> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "MathGraph" .
  <https://neverblink.eu/ontologies/llm-kg/methods#MathKG> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "Math-KG" .
  <https://neverblink.eu/ontologies/llm-kg/methods#MathLLM> dct:subject <https://neverblink.eu/ontologies/llm-kg/categories#SynergizedReasoning> ;
    a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:comment "Math LLM is a specialized LLM designed with task adapters, retrieval augmentation from AutoMathKG and MathVD, and self-calibration to address various mathematical problems. It exemplifies synergized reasoning by treating the LLM as an agent that interacts with the KGs to conduct complex mathematical deductions and problem-solving." ;
    rdfs:label "Math LLM" ;
    <https://neverblink.eu/ontologies/llm-kg/hasTopCategory> <https://neverblink.eu/ontologies/llm-kg/top-categories#SynergizedLLMKG> .
  <https://neverblink.eu/ontologies/llm-kg/methods#MathVD1> dct:subject <https://neverblink.eu/ontologies/llm-kg/categories#SynergizedKnowledgeRepresentation> ;
    a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:comment "MathVD1 is one of two proposed strategies for constructing a vector database (MathVD) from the AutoMathKG entities. It embeds a single long text concatenating all key information about an entity using SBERT, providing a vector representation of KG knowledge for similarity search, which is crucial for the system's synergized reasoning and knowledge fusion mechanisms." ;
    rdfs:label "MathVD1" ;
    <https://neverblink.eu/ontologies/llm-kg/hasTopCategory> <https://neverblink.eu/ontologies/llm-kg/top-categories#SynergizedLLMKG> .
  <https://neverblink.eu/ontologies/llm-kg/methods#MathVD2> dct:subject <https://neverblink.eu/ontologies/llm-kg/categories#SynergizedKnowledgeRepresentation> ;
    a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:comment "MathVD2 is the second proposed strategy for constructing MathVD. It separately embeds each key information description of an entity using SBERT and then weights and sums these vectors based on their importance. This method contributes to a robust vector representation of KG knowledge, facilitating synergized knowledge representation and retrieval within the AutoMathKG system." ;
    rdfs:label "MathVD2" ;
    <https://neverblink.eu/ontologies/llm-kg/hasTopCategory> <https://neverblink.eu/ontologies/llm-kg/top-categories#SynergizedLLMKG> .
  <https://neverblink.eu/ontologies/llm-kg/methods#NaturalProofs> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "NaturalProofs" .
  <https://neverblink.eu/ontologies/llm-kg/methods#PoT> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "PoT" .
  <https://neverblink.eu/ontologies/llm-kg/methods#RGCN> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "R-GCN" .
  <https://neverblink.eu/ontologies/llm-kg/methods#SBERT> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "SBERT" .
  <https://neverblink.eu/ontologies/llm-kg/methods#TransE> a <http://purl.org/spar/fabio/Workflow> ;
    rdfs:label "TransE" .
}
sub:provenance {
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    prov:wasDerivedFrom <https://doi.org/10.48550/arXiv.2505.13406> .
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