Dependent Types (DTT) & Logic for AI Agent Ready Knowledge Graphs
$20.00
Minimum price
$45.00
Suggested price
Dependent Types (DTT) & Logic for AI Agent Ready Knowledge Graphs
About the Book
About This Book
This book explores the intersection of formal logic, type theory, and knowledge representation, arguing for a fundamental shift from traditional RDF/OWL-based approaches to type-theoretic foundations for knowledge graphs and AI systems.
Overview
We stand at a critical juncture in knowledge representation. While RDF and OWL have served as foundational technologies for the semantic web, their limitations become increasingly apparent as we build more sophisticated AI systems requiring complex reasoning, contextual knowledge, and formal guarantees. This book presents a comprehensive exploration of how dependent type theory, higher-order logic, and advanced programming language concepts can revolutionize knowledge representation.
Drawing parallels between Russell's Paradox in set theory and current limitations in knowledge graphs, we demonstrate why moving beyond first-order logic is not just beneficial but necessary for the next generation of AI systems. The book combines theoretical foundations with practical implementations, showing how languages like Twelf, Beluga, ELPI, and TypeDB point toward a more expressive and reliable future for knowledge representation.
Key Topics
Foundational Concepts
- Dependent Type Theory: Types that depend on values, enabling precise specification of data relationships and constraints
- Higher-Order Logic: Quantification over predicates and functions for meta-level reasoning
- Logical Frameworks: LF and contextual modal type theory as foundations for formal systems
- Unification Theory: From Prolog's first-order unification to higher-order pattern unification
Programming Languages and Systems
- Lambda Prolog and ELPI: Higher-order logic programming for knowledge representation
- Twelf: Logical framework for encoding deductive systems and ontologies
- Beluga: Programming with contextual types and first-class contexts
- F*: Functional programming with dependent types for verified software
- TypeDB: Polymorphic database design with concept modeling
Knowledge Representation Evolution
- Beyond RDF Triples: Moving from binary relations to hypergraphs and metagraphs
- Ontology Verification: Formal validation of consistency, satisfiability, and structural properties
- Context-Sensitive Knowledge: Representing knowledge that varies by time, location, or perspective
- Constraint Integration: Unifying ontology definition with data validation
Advanced Applications
- AI Memory Systems: Type-theoretic approaches to artificial agent memory
- Personal Knowledge Graphs: Scalable, privacy-preserving knowledge for edge AI
- Hypergraph Ontologies: Native representation of n-ary relationships
- Scientific Knowledge Modeling: Formal approaches to evolving scientific understanding
Chapter Topics
- Introduction: The Problem We Have vs. The Problem We Understand
- Russell's Paradox and Knowledge Representation
- From Set Theory to Type Theory
- First-Order Logic and Its Limitations
- Higher-Order Logic for Knowledge Graphs
- Dependent Types: A New Paradigm for Ontologies
- Lambda Prolog and ELPI: Logic Programming Meets Types
- Twelf for Hypergraph Ontology
- Beluga: Programming with Contexts
- F: Verified Knowledge Systems*
- TypeDB: Polymorphic Databases for AI
- Understanding Unification: From Prolog to Higher-Order Logic
- Emergent Intelligence in AI Agents and Knowledge Graphs
- Personal Knowledge Graphs and Edge AI
- Implementation Strategies and Practical Considerations
Target Audience
This book is designed for:
- Researchers in knowledge representation, semantic web, and formal methods
- AI Engineers building systems that require sophisticated knowledge modeling
- Graduate Students in computer science, particularly those studying logic, type theory, or AI
- Software Architects designing knowledge-intensive applications
- Ontology Engineers seeking more expressive and reliable representation frameworks
Prerequisites
Readers should have familiarity with:
- Basic logic and set theory
- Functional programming concepts
- RDF/OWL and semantic web technologies
- Fundamental computer science theory
No prior experience with dependent types or proof assistants is required, though familiarity with these concepts will enhance understanding.
What Makes This Book Different
Unlike traditional treatments of knowledge representation that focus on extending existing technologies, this book advocates for a fundamental paradigm shift. It bridges the gap between theoretical computer science (type theory, formal logic) and practical AI engineering, showing how advanced programming language concepts can solve real-world knowledge representation challenges.
The book emphasizes working implementations and practical examples rather than purely theoretical discussions, demonstrating how these advanced concepts can be applied to build more reliable, expressive, and verifiable knowledge systems.
About the Author
Table of Contents
- About book
- About the Author
- About a cover
- We do not solve the problems we have; we solve the problems we understand.
- Introduction to Lene Rachel Andersen
- Understanding of the Problem
- Misunderstanding Makes It Worse
- Complexity and Complex Problems
- Emotional Comfort for Complex Problems
- New Education: The Place of Bildung and Ego Development
- Philosophy as a Key to Understanding: Epistemology, Reasoning, Logic, and Ethics
- How to Build Organizations That Understand
- Conclusion
- Emergent Intelligence: How More Becomes Different in Architecture of AI Agents and Knowledge Graphs
- The Scaling Problem in Software
- Knowledge Graphs: The Ultimate Emergent Structure
- Broken Symmetry in Software Architecture
- AI Agents and Memory: Emergence of Digital Consciousness
- Hierarchical Organization of Software Complexity
- Conclusion: The New Whole
- Evolution of Knowledge Graphs and AI Agents
- Static Graphs
- Dynamic Graphs
- Temporal Graphs
- Event Graphs
- LLMs in Graph Construction
- Dynamic Graphs and Entity/Relation Extraction with LLMs
- Temporal Graphs and Temporal Context Extraction
- Event Graphs and Event Context Extraction
- Event Graphs and Episodic Memory for AI Agents
- Conclusion
- Metagraphs and Hypergraphs for complex AI agent memory and RAG
- Knowledge graphs and not just graphs
- Strings not things
- Knowledge Graphs are not enough, and Tripples is not enough.
- Temporal aware Semantic and Episodic memory for AI agents
- Hypergraphs as rescue
- Named Graphs and Graph of Graphs for Multi-model and multilingual data
- Humman-like memories for AI Agent with Metagraph
- The Semantic Hypergraph (SH) Model: A Deep Dive into Representing Linguistic Meaning
- Understanding Hypergraphs: Beyond Pairwise Connections
- Core Concepts of Semantic Hypergraphs: Weaving Meaning
- The SH Type System: A Grammar for Semantic Roles
- Atomic Types (Atoms)
- Non-Atomic Types (Inferable)
- Argument Roles: Enhancing Semantic Precision
- Knowledge Representation in Semantic Hypergraphs: Illustrative Examples
- Goals, Advantages, and Potential Applications of the SH Model
- Relation to Other Knowledge Representation Formalisms (A Comparative Perspective)
- Challenges and Future Directions
- Conclusion: Charting a Course for Deeper Semantic Understanding
- Metagraphs as Homoiconic Structures: Revolutionizing Knowledge Representation
- Understanding Homoiconicity in Knowledge Structures
- Metagraphs: Beyond Traditional Graph Representations
- The Synthesis: Metagraphs as Homoiconic Structures
- 1. Schema as Data
- 2. Operations as Graph Elements
- 3. Recursive Self-Description
- 4. Emergent Semantic Layers
- Practical Applications
- Knowledge Engineering and Ontology Management
- Adaptive AI Systems
- Complex Systems Modeling
- Data Integration and Federated Knowledge
- Intelligent Business Process Management
- Implementation Challenges and Approaches
- Computational Efficiency
- Representational Clarity
- Future Directions
- Cognitive Architectures
- Distributed Knowledge Commons
- Neurosymbolic Integration
- Conclusion
- Beyound Knowledge Graphs for AI - Why we need Something different
- Beyond Binary Relations: The Memory Project Revelations
- When Simple Graphs Meet Complex Reality
- Hitting the Wall: The Limitations of Binary Relations
- The Emergence of Complex Hierarchies
- The Complexity of Construction Rules
- The Inadequacy of First-Order Logic
- The Path Forward: From Theory to Implementation
- Why Logic
- The Foundational Role of Logic in Knowledge Representation
- Beyond Validation: Logic as Computational Foundation
- The Limits of First-Order Approaches
- The Path Forward: Higher-Order Logic and Type Theory
- Logical Frameworks
- The Architecture of Formal Reasoning
- From Theory to Practice: Framework Implementation
- Framework Selection and Trade-offs
- First Order Logic
- The Structure of First-Order Logic
- First-Order Logic in Knowledge Graphs
- The Power of First-Order Reasoning
- Limitations in AI Agent Memory Systems
- Bridging to Higher-Order Frameworks
- Higher Order Logic
- The Architecture of Higher-Order Logic
- Higher-Order Logic in Knowledge Representation
- Implementation Challenges and Solutions
- Higher-Order Logic in Practice: ELPI and Lambda Prolog
- Contextual Reasoning and Hypothetical Knowledge
- Integration with Type-Theoretic Approaches
- Type Theory
- The Curry-Howard Correspondence
- Types as Specifications
- Computational Content and Constructive Logic
- The Progression to Dependent Types
- Simple Type Theory
- The Type Hierarchy and Classification
- Type-Directed Knowledge Organization
- Simple Types in Knowledge Graph Systems
- Implementation in Programming Language Foundations
- Limitations and Extensions
- The Bridge to Dependent Types
- Dependent Type Theory
- The Foundation: Types Depending on Values
- Dependent Types in Knowledge Representation
- The Pi and Sigma Type Constructors
- Dependent Types and Proof-Relevant Programming
- Practical Challenges and Solutions
- Implementation Strategies in Knowledge Systems
- Dependent Types and Hypergraph Ontologies
- Quasi Dependent Types
- Restricted Dependency Mechanisms
- Practical Applications in Knowledge Systems
- Integration Strategies for Knowledge Graphs
- Balancing Expressiveness and Tractability
- Future Directions and Research Opportunities
- Dependent Types: A New Paradigm for Ontologies and Knowledge Graphs
- What is Dependent Type Theory (DTT)?
- OWL’s Logical Foundations and Limitations
- How DTT Enhances Knowledge Modeling
- Using Proof Assistants and Dependently-Typed Languages
- Hypergraphs and Higher-Order Relationships
- Conclusion
- Type Theory, AI Memory and Metagraphs
- Russell’s Paradox
- Set Theory Is Not Wrong, But Has Paradoxes
- RDF Is Not Wrong, But Not Enough
- Meta and Hyper Graphs for AI Memory
- Type Theory for Graph Modeling
- Conclusion
- DataLog and Prolog as AI first Languages
- A Historical Perspective and Future Implications
- The Birth of AI Programming: Lisp and Symbolic Reasoning
- The European Response: Prolog and First-Order Logic
- The Power of Declarative Programming
- Datalog: The Elegant Subset
- Why This History Matters for Modern AI
- The Future of Logic-Based AI
- A Call to Rediscover Logic
- Personal Knowledge Graphs. Semantic Entity Persistence in DataLog. Deductive databases
- Common Logic and power of relations
- DataLog as a GPT like program
- Entities modeling
- Conclusion
- High-Order Logic Languages for Unifying OWL and SHACL
- DataLog and Prolog for Ontology
- OWL and Second-Order Logic Capabilities
- Why We Need HOL for Ontology
- Dependent Type Theory and HOL for Ontology
- HOL and DTT for Hypergraph Ontology
- Conclusion
- TypeDB: A Polymorphic Database for AI Agent Memory and Complex Ontology
- Graph DB and Object Impedance
- Failure of Object Databases
- PERA and Concept Modeling
- Concept Modeling and Concept Graphs
- Concept Modeling and Dependent Types Theory
- Relations and Hypergraph Modeling
- TypeDB and Deductive Capabilities with Rules
- Conclusion
- F*: The Dependently Typed Programming Language for Software Verification
- Origins and Design Philosophy
- Core Features
- Dependent Types
- Effects System
- Proof-Oriented Programming
- Multi-Target Compilation
- Real-World Applications
- Project Everest
- Security-Critical Applications
- Learning Curve and Adoption Challenges
- Comparison with Other Verification Tools
- Future Directions
- Conclusion
- Twelf: Dependent Types and Logic for Knowledge Graph and Ontology Description
- Knowledge Representation in Twelf
- Type-Based Entity Representation
- Relations as Dependent Types
- Ontology Formalization
- Judgment-Based Class Hierarchies
- Constraint Modeling
- Reasoning and Querying
- Inference Rules
- Query Execution
- Advantages for Knowledge Graph Applications
- Comparison with Mainstream Approaches
- Formal Foundations
- Type System Capabilities
- Reasoning Capabilities
- Verification Strength
- Expressivity Trade-offs
- Practical Considerations
- Use Cases
- Twelf for Hypergraph Ontology: A Comprehensive Guide
- Twelf as a Meta-Logical Framework
- Hypergraphs in Ontology
- Integration of Twelf with Hypergraph Ontologies
- Formal Representation Capabilities
- Semantic Hypergraphs for Ontology Modeling
- Knowledge Representation for Complex Domains
- Implementation challenges in these domains include:
- Implementation Techniques and Tools
- Advanced Topics and Future Directions
- Integration with Other Formalisms
- Scalability and Performance
- Applications in Emerging Fields
- Implementing Twelf for Hypergraph Ontology: A Complete Example
- Basic Declarations
- Hypergraph Structure
- Inference Rules
- Querying the Ontology
- Advanced Features: Modular Organization
- Extension: Temporal Aspects
- Conclusion
- Lambda Prolog and ELPI: Advancing Knowledge Graphs and Complex Ontologies
- The Origins and Foundations of Lambda Prolog
- Higher-Order Terms and Unification
- Scoped Logical Variables
- Hypothetical Reasoning
- Strong Typing
- ELPI: Revitalizing Lambda Prolog for Modern Computing
- Performance Breakthrough
- Embeddability by Design
- Constraint Handling Rules
- Knowledge Graphs and Ontologies: The Representational Challenge
- The Limitations of First-Order Approaches
- The Expressivity-Tractability Tradeoff
- ELPI for Advanced Knowledge Representation
- Representing Higher-Order Relationships
- Contextual and Modal Reasoning
- Meta-Ontology and Ontology Evolution
- Constraint-Based Knowledge Validation
- ELPI for Hypergraph Knowledge Representation
- Native Hyperedge Representation
- Hypergraph Traversal and Pattern Matching
- Advanced Applications in Domain-Specific Knowledge Graphs
- Biomedical Knowledge Integration
- Legal and Regulatory Knowledge Graphs
- Scientific Knowledge Discovery
- Implementation Strategies and Challenges
- Integration with Existing Knowledge Infrastructures
- Performance and Scalability Considerations
- Knowledge Acquisition and Maintenance Workflows
- Future Directions and Research Opportunities
- Neural-Symbolic Integration
- Distributed Knowledge and Federated Reasoning
- Human-AI Collaborative Knowledge Engineering
- Conclusion
- Understanding Unification: From Prolog to Higher-Order Logic
- Prolog Unification: The Foundation
- What is Prolog Unification?
- The Unification Algorithm
- Detailed Examples
- Implementation Considerations
- Beta Reduction: Function Application in Lambda Calculus
- What is Beta Reduction?
- Formal Definition and Properties
- Connection to Higher-Order Logic
- Examples in Different Contexts
- Beta Reduction in the Paper’s Context
- Higher-Order Unification: The Challenge
- The Fundamental Complexity
- Why Higher-Order Unification is Harder
- The Pattern Fragment
- Key Challenges
- Detection Algorithms
- The Solution Approach
- Practical Implementation
- The Elpi System
- Implementation Architecture
- Key Innovations
- Benefits and Trade-offs
- Real-World Application
- Conclusion
- Beluga for Ontologies and Knowledge Graphs: Bridging Formal Systems and Semantic Knowledge
- Understanding Beluga: A Programming Language for Formal Reasoning
- The Logical Framework Foundation
- Higher-Order Abstract Syntax (HOAS)
- First-Class Contexts and Contextual Objects
- Dependently Typed System
- Inductive Proofs as Programs
- Understanding Ontologies and Knowledge Graphs
- Ontologies: Formal Representations of Knowledge Domains
- Knowledge Graphs: Practical Applications of Ontologies
- The Role of Ontologies in Knowledge Graphs
- Potential Applications of Beluga for Ontologies and Knowledge Graphs
- 1. Formal Verification of Ontology Consistency
- 2. Ontology Evolution and Change Management
- 3. Reasoning with Contextual Knowledge
- 4. Mapping Between Ontologies
- 5. Knowledge Graph Schema Validation
- A Concrete Example: Verifying a Simple Ontology with Beluga
- The University Ontology
- Encoding the Ontology in Beluga
- Verifying Ontology Properties with Beluga
- Validating Cardinality Constraints
- Benefits of the Beluga Approach
- Implementation Challenges and Considerations
- 1. Bridging Different Formalisms
- 2. Scalability Concerns
- 3. Integration with Existing Tools
- 4. Usability for Domain Experts
- Practical Implementation Approach
- 1. Develop a Formal Representation of OWL/RDF Semantics in Beluga
- 2. Create Verification Libraries for Common Ontology Patterns
- 3. Build Interfaces to Existing Knowledge Graph Management Systems
- 4. Implement a Layer of Abstraction for Domain Experts
- Conclusion
- Emulating Dependent Types in Elpi: A Journey into Logic Programming and Type Theory
- What are Dependent Types? A Deeper Dive
- Why Elpi for Emulating Dependent Types? The Unique Advantage
- Emulating Dependent Types in Elpi: A Conceptual and Practical Approach
- Applying This Model to Hypergraph Ontology
- Practical Implications and Next Steps
The Leanpub 60 Day 100% Happiness Guarantee
Within 60 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.
Now, this is technically risky for us, since you'll have the book or course files either way. But we're so confident in our products and services, and in our authors and readers, that we're happy to offer a full money back guarantee for everything we sell.
You can only find out how good something is by trying it, and because of our 100% money back guarantee there's literally no risk to do so!
So, there's no reason not to click the Add to Cart button, is there?
See full terms...
Earn $8 on a $10 Purchase, and $16 on a $20 Purchase
We pay 80% royalties on purchases of $7.99 or more, and 80% royalties minus a 50 cent flat fee on purchases between $0.99 and $7.98. You earn $8 on a $10 sale, and $16 on a $20 sale. So, if we sell 5000 non-refunded copies of your book for $20, you'll earn $80,000.
(Yes, some authors have already earned much more than that on Leanpub.)
In fact, authors have earnedover $14 millionwriting, publishing and selling on Leanpub.
Learn more about writing on Leanpub
Free Updates. DRM Free.
If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).
Most Leanpub books are available in PDF (for computers) and EPUB (for phones, tablets and Kindle). The formats that a book includes are shown at the top right corner of this page.
Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.
Learn more about Leanpub's ebook formats and where to read them
