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

1. Introduction: The Problem We Have vs. The Problem We Understand
2. Russell's Paradox and Knowledge Representation
3. From Set Theory to Type Theory
4. First-Order Logic and Its Limitations
5. Higher-Order Logic for Knowledge Graphs
6. Dependent Types: A New Paradigm for Ontologies
7. Lambda Prolog and ELPI: Logic Programming Meets Types
8. Twelf for Hypergraph Ontology
9. Beluga: Programming with Contexts
10. F: Verified Knowledge Systems*
11. TypeDB: Polymorphic Databases for AI
12. Understanding Unification: From Prolog to Higher-Order Logic
13. Emergent Intelligence in AI Agents and Knowledge Graphs
14. Personal Knowledge Graphs and Edge AI
15. 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

Volodymyr Pavlyshyn

@volland84

Hey I am Volodymyr 

Seasoned Developer's Journey from COBOL to Web 3.0, SSI, Privacy First Edge AI, and Beyond

 As a seasoned developer with over 20 years of experience, I have worked with various programming languages, including some that are considered "dead," such as COBOL and Smalltalk. However, my passion for innovation and embracing cutting-edge technology has led me to focus on the emerging fields of Web 5.0, Self-Sovereign Identity (SSI),AI Agents, Knowledge Graphs, Agentiic memory systems, and the architecture of a decentralized world that empowers data democratization.

A firm believer in the potential of agent systems and the concept of a "soft" internet, I am dedicated to exploring and promoting these transformative ideas. In addition to writing, I also enjoy sharing my knowledge and insights through videoblogging. Most of my Medium posts serve as supplementary content to the videos on my YouTube channel, which you can explore here: https://www.youtube.com/c/VolodymyrPavlyshyn. 

Join me on this exciting journey as we delve into the future of technology and the possibilities it holds.