https://w3id.org/np/RAXsiMCaDC1SVENBEf3Coawoeosjo15IcyvDG-GLITyK4/Head https://w3id.org/np/RAXsiMCaDC1SVENBEf3Coawoeosjo15IcyvDG-GLITyK4 http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAXsiMCaDC1SVENBEf3Coawoeosjo15IcyvDG-GLITyK4/assertion https://w3id.org/np/RAXsiMCaDC1SVENBEf3Coawoeosjo15IcyvDG-GLITyK4 http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAXsiMCaDC1SVENBEf3Coawoeosjo15IcyvDG-GLITyK4/provenance https://w3id.org/np/RAXsiMCaDC1SVENBEf3Coawoeosjo15IcyvDG-GLITyK4 http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAXsiMCaDC1SVENBEf3Coawoeosjo15IcyvDG-GLITyK4/pubinfo https://w3id.org/np/RAXsiMCaDC1SVENBEf3Coawoeosjo15IcyvDG-GLITyK4 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAXsiMCaDC1SVENBEf3Coawoeosjo15IcyvDG-GLITyK4/assertion https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/dc/terms/title AutoMathKG: The automated mathematical knowledge graph based on LLM and vector database https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/describes https://neverblink.eu/ontologies/llm-kg/methods#AutoMathKG https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/describes https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeCompletion https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/describes https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeFusion https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/describes https://neverblink.eu/ontologies/llm-kg/methods#MathLLM https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/describes https://neverblink.eu/ontologies/llm-kg/methods#MathVD1 https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/describes https://neverblink.eu/ontologies/llm-kg/methods#MathVD2 https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#BoxE https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#CoT https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#Gemma7bit https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#HoLE https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#KG2E https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#Llama27b https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#LoRA https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#MathGloss https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#MathGraph https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#MathKG https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#NaturalProofs https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#PoT https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#RGCN https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#SBERT https://doi.org/10.48550/arXiv.2505.13406 http://purl.org/spar/cito/discusses https://neverblink.eu/ontologies/llm-kg/methods#TransE https://doi.org/10.48550/arXiv.2505.13406 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#Entity https://neverblink.eu/ontologies/llm-kg/methods#AutoMathKG http://purl.org/dc/terms/subject https://neverblink.eu/ontologies/llm-kg/categories#SynergizedReasoning https://neverblink.eu/ontologies/llm-kg/methods#AutoMathKG http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#AutoMathKG http://www.w3.org/2000/01/rdf-schema#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. https://neverblink.eu/ontologies/llm-kg/methods#AutoMathKG http://www.w3.org/2000/01/rdf-schema#label AutoMathKG https://neverblink.eu/ontologies/llm-kg/methods#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 http://purl.org/dc/terms/subject https://neverblink.eu/ontologies/llm-kg/categories#LLMAugmentedKGCompletion https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeCompletion http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeCompletion http://www.w3.org/2000/01/rdf-schema#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. https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeCompletion http://www.w3.org/2000/01/rdf-schema#label Automatic knowledge completion https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeCompletion https://neverblink.eu/ontologies/llm-kg/hasTopCategory https://neverblink.eu/ontologies/llm-kg/top-categories#LLMAugmentedKG https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeFusion http://purl.org/dc/terms/subject https://neverblink.eu/ontologies/llm-kg/categories#LLMAugmentedKGConstruction https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeFusion http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeFusion http://www.w3.org/2000/01/rdf-schema#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. https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeFusion http://www.w3.org/2000/01/rdf-schema#label Automatic knowledge fusion https://neverblink.eu/ontologies/llm-kg/methods#AutomaticKnowledgeFusion https://neverblink.eu/ontologies/llm-kg/hasTopCategory https://neverblink.eu/ontologies/llm-kg/top-categories#LLMAugmentedKG https://neverblink.eu/ontologies/llm-kg/methods#BoxE http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#BoxE http://www.w3.org/2000/01/rdf-schema#label BoxE https://neverblink.eu/ontologies/llm-kg/methods#CoT http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#CoT http://www.w3.org/2000/01/rdf-schema#label CoT https://neverblink.eu/ontologies/llm-kg/methods#Gemma7bit http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#Gemma7bit http://www.w3.org/2000/01/rdf-schema#label Gemma-7b-it https://neverblink.eu/ontologies/llm-kg/methods#HoLE http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#HoLE http://www.w3.org/2000/01/rdf-schema#label HoLE https://neverblink.eu/ontologies/llm-kg/methods#KG2E http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#KG2E http://www.w3.org/2000/01/rdf-schema#label KG2E https://neverblink.eu/ontologies/llm-kg/methods#Llama27b http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#Llama27b http://www.w3.org/2000/01/rdf-schema#label Llama-2-7b https://neverblink.eu/ontologies/llm-kg/methods#LoRA http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#LoRA http://www.w3.org/2000/01/rdf-schema#label LoRA https://neverblink.eu/ontologies/llm-kg/methods#MathGloss http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#MathGloss http://www.w3.org/2000/01/rdf-schema#label MathGloss https://neverblink.eu/ontologies/llm-kg/methods#MathGraph http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#MathGraph http://www.w3.org/2000/01/rdf-schema#label MathGraph https://neverblink.eu/ontologies/llm-kg/methods#MathKG http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#MathKG http://www.w3.org/2000/01/rdf-schema#label Math-KG https://neverblink.eu/ontologies/llm-kg/methods#MathLLM http://purl.org/dc/terms/subject https://neverblink.eu/ontologies/llm-kg/categories#SynergizedReasoning https://neverblink.eu/ontologies/llm-kg/methods#MathLLM http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#MathLLM http://www.w3.org/2000/01/rdf-schema#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. https://neverblink.eu/ontologies/llm-kg/methods#MathLLM http://www.w3.org/2000/01/rdf-schema#label Math LLM https://neverblink.eu/ontologies/llm-kg/methods#MathLLM https://neverblink.eu/ontologies/llm-kg/hasTopCategory https://neverblink.eu/ontologies/llm-kg/top-categories#SynergizedLLMKG https://neverblink.eu/ontologies/llm-kg/methods#MathVD1 http://purl.org/dc/terms/subject https://neverblink.eu/ontologies/llm-kg/categories#SynergizedKnowledgeRepresentation https://neverblink.eu/ontologies/llm-kg/methods#MathVD1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#MathVD1 http://www.w3.org/2000/01/rdf-schema#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. https://neverblink.eu/ontologies/llm-kg/methods#MathVD1 http://www.w3.org/2000/01/rdf-schema#label MathVD1 https://neverblink.eu/ontologies/llm-kg/methods#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 http://purl.org/dc/terms/subject https://neverblink.eu/ontologies/llm-kg/categories#SynergizedKnowledgeRepresentation https://neverblink.eu/ontologies/llm-kg/methods#MathVD2 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://purl.org/spar/fabio/Workflow https://neverblink.eu/ontologies/llm-kg/methods#MathVD2 http://www.w3.org/2000/01/rdf-schema#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. 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