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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.

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