# Knowledge Graphs ## Overview Knowledge graphs are structured representations of information that encode entities, their properties, and the relationships between them as a graph. They provide a powerful framework for organizing, querying, and reasoning about complex knowledge domains. In the context of [[knowledge_base/cognitive/active_inference|active inference]] and cognitive modeling, knowledge graphs serve as external knowledge structures that complement internal [[knowledge_base/mathematics/generative_models|generative models]], enabling agents to navigate and reason about structured information spaces. ## Core Structure ### Entities and Relations A knowledge graph $\mathcal{G} = (E, R, T)$ consists of: - **Entities** ($E$): Nodes representing objects, concepts, or events - **Relations** ($R$): Edge types representing relationships - **Triples** ($T \subseteq E \times R \times E$): Directed edges $(h, r, t)$ connecting head entity $h$ to tail entity $t$ via relation $r$ ### Formal Representation ``` (Active_Inference, is_a, Theoretical_Framework) (Free_Energy_Principle, underlies, Active_Inference) (Belief_Updating, implements, Active_Inference) ``` ### Schema and Ontology - **Classes**: Hierarchical categorization of entities - **Properties**: Attributes and relationships - **Constraints**: Rules governing valid relationships - **Ontologies**: Formal specifications of conceptualizations ## Knowledge Graph Operations ### Querying - **Graph traversal**: Navigate relationships between entities - **Pattern matching**: Find subgraph patterns - **SPARQL/Cypher**: Formal query languages - **Semantic search**: Meaning-based retrieval ### Reasoning - **Transitive closure**: Infer indirect relationships - **Rule-based reasoning**: Apply logical rules - **Embedding-based reasoning**: Learn latent representations - **Link prediction**: Predict missing relationships ### Construction - **Information extraction**: Extract entities and relations from text - **Entity resolution**: Identify and merge duplicate entities - **Knowledge fusion**: Combine knowledge from multiple sources - **Crowdsourcing**: Human-in-the-loop curation ## Connection to Active Inference ### Epistemic Actions Knowledge graph exploration as [[knowledge_base/mathematics/epistemic_value|epistemic action]]: - Querying reduces uncertainty about the environment - Navigation follows expected information gain - Structure learning discovers new relationships ### Generative Models Over Graphs Agents can maintain generative models of knowledge graph structure: $p(G | \theta) = \prod_{(h,r,t) \in T} p(t | h, r, \theta)$ enabling prediction of missing links and anomaly detection. ### Multi-Agent Knowledge Systems The [[code/Things/KG_Multi_Agent/README|KG Multi-Agent]] system demonstrates: - Distributed knowledge extraction across multiple agents - Coordinated graph construction via swarm intelligence - Collective knowledge synthesis from unstructured data ## Applications ### Research and Education - [[knowledge_base/cognitive/research_education|Research documentation]] and literature management - Concept mapping and learning pathway navigation - Cross-reference tracking and knowledge synthesis ### Information Systems - Semantic search engines - Question answering systems - Recommendation systems - Data integration platforms ### Scientific Discovery - Drug discovery and biomedical research - Materials science knowledge management - Climate science data integration ## Network Properties Knowledge graphs exhibit properties studied in [[network_theory|network theory]]: - **Scale-free degree distributions**: Few highly connected hub entities - **Small-world properties**: Short path lengths between entities - **Community structure**: Clusters of related concepts - **Hierarchical organization**: Multi-level abstractions ## Related Concepts - [[network_theory]] - Network analysis foundations - [[complex_systems]] - Systems-level perspectives - [[knowledge_base/mathematics/graphical_models]] - Probabilistic graph models - [[knowledge_base/mathematics/information_theory]] - Information measures - [[knowledge_base/cognitive/social_cognition]] - Social knowledge structures - [[knowledge_base/cognitive/research_education]] - Research applications ## References - Hogan, A. et al. (2021). Knowledge Graphs. ACM Computing Surveys - Ji, S. et al. (2021). A Survey on Knowledge Graphs: Representation, Acquisition, and Applications - Ehrlinger, L. & Wolfram, W. (2016). Towards a Definition of Knowledge Graphs