Knowledge Representation

How knowledge is structured, stored, and accessed fundamentally shapes an AGI system's capabilities. This page covers the major paradigms for knowledge representation.

Why Knowledge Representation Matters

AGI systems must:

• Store facts and relationships
• Perform logical reasoning
• Generalize from examples
• Interface with natural language
• Handle uncertainty and incomplete information

Symbolic Representations

Semantic Networks

• Nodes: Concepts or entities
• Edges: Relationships between concepts
• Inheritance: IS-A hierarchies, property inheritance
• Applications: Conceptual understanding, natural language processing

Frames and Scripts

• Frames: Stereotypical situations with slots and fillers
• Scripts: Sequences of events (restaurant script, airport script)
• Default Reasoning: Assumptions and exceptions
• Applications: Story understanding, commonsense reasoning

Ontologies

• Classes and Instances: Taxonomic organization
• Properties and Relations: Attributes and connections
• Axioms: Logical constraints and rules
• OWL and RDF: Web ontology standards
• Applications: Knowledge graphs, semantic web, domain modeling

Logic-Based Representations

• Predicate Logic: Facts and rules
• Horn Clauses: Computational logic (Prolog)
• Description Logic: Decidable fragments for ontologies
• Non-monotonic Logic: Reasoning with defaults and exceptions

Graph-Based Knowledge

Knowledge Graphs

• Entities: Real-world objects and concepts
• Relations: Typed edges connecting entities
• Triple Stores: Subject-predicate-object storage (e.g., Wikidata, DBpedia)
• Graph Embeddings: TransE, DistMult, ComplEx for link prediction

Property Graphs

• Nodes with Properties: Attributes on entities
• Labeled Edges: Relationship types
• Neo4j and Graph Databases: Querying with Cypher
• Applications: Social networks, recommendation systems

Vector Representations

Word Embeddings

• Word2Vec: CBOW and Skip-gram models
• GloVe: Global vectors for word representation
• FastText: Subword information
• Applications: Similarity, analogy, clustering

Sentence and Document Embeddings

• BERT: Bidirectional transformers
• Sentence-BERT: Sentence-level representations
• Universal Sentence Encoder

Knowledge Graph Embeddings

• TransE: Translation-based embeddings
• RotatE: Rotation in complex space
• Graph Neural Networks: Learning on graph structures

Hybrid Approaches

Neuro-Symbolic Systems

• Neural Networks + Logic: Combining learning and reasoning
• Differentiable Logic: End-to-end training with logical constraints
• Knowledge-Enhanced Models: Injecting structured knowledge into neural models

Atomspace (OpenCog)

• Hypergraph: Generalization of graphs with hyper-edges
• Atoms: Nodes and links as basic units
• TruthValues and AttentionValues: Uncertainty and importance
• Pattern Matching: Flexible query language
• Applications: Hyperon framework's knowledge store

Conceptual Spaces

Gärdenfors Framework

• Quality Dimensions: Features as geometric dimensions
• Convex Regions: Natural categories
• Conceptual Combination: Operations in geometric space
• Applications: Similarity, categorization, metaphor

Distributed Representations

Neural Network Activations

• Hidden Layer Representations: Learned features
• Attention Mechanisms: Dynamic focus
• Emergent Structure: Self-organized representations

Challenges

• Grounding: Connecting symbols to perceptual experience
• Compositionality: Building complex meanings from parts
• Context-Dependence: Meaning shifts with context
• Scalability: Managing millions of facts
• Integration: Combining multiple representation types

Tools and Frameworks

• Protégé: Ontology editor
• OpenCyc: Large-scale ontology
• RDFLib: Python library for RDF
• Neo4j: Graph database
• NetworkX: Graph analysis in Python

Recommended Resources

• Knowledge Representation and Reasoning - Brachman and Levesque
• Semantic Web for the Working Ontologist - Allemang and Hendler
• Artificial Intelligence: A Modern Approach (KR chapters) - Russell and Norvig

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