KOS-TL (Knowledge Operation System Type Logic)

2026-01-03

arXiv.org

AI Summary

This work addresses the longstanding challenge of bridging the gap between static symbolic logic and dynamic system execution, which has hindered the development of executable autonomous knowledge systems. The authors propose a novel three-layer architecture grounded in dependent type theory, uniquely integrating Davidsonian event semantics with Martin-Löf type theory. Central to this framework is the notion of “proof-carrying knowledge,” ensuring that every step in the evolution of knowledge states is accompanied by formal validity evidence. Leveraging an event-driven mechanism ⟨Σ, Ev, Δ⟩, bidirectional refinement, and operational semantics, the system enables coherent co-evolution from physical signals to logical evidence. Metatheoretic verification guarantees progress and consistency, and empirical evaluations in industrial provenance and cross-border financial compliance demonstrate the system’s ability to avoid deadlocks and support verifiable, intelligent autonomous operations.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Data transparency and provenance

Abstract

This paper introduces KOS-TL (Knowledge Operation System Type Logic), a novel constructive framework designed to provide a rigorous logical foundation for autonomous and executable knowledge systems. Traditional knowledge representation models often suffer from a gap between static symbolic logic and dynamic system execution. To bridge this divide, KOS-TL leverages Dependent Type Theory to unify data, logic, and proof into a singular computational substrate.The architecture of KOS-TL is organized into three hierarchical layers: the Core Layer, which defines the static type universe and constructive primitives; the Kernel Layer, which governs state evolution through an event-driven mechanism characterized by the triple $\langle \Sigma, \textsf{Ev}, \Delta \rangle$; and the Runtime Layer, responsible for the bidirectional refinement of physical signals into logical evidence. We formally define the operational semantics of the system and prove key meta-theoretical properties, including Progress and Evolutionary Consistency, ensuring that the system remains logically self-consistent and free from stuck states during continuous state transitions.By integrating Davidsonian event semantics with Martin-L\"of type theory, KOS-TL enables the construction of"proof-carrying knowledge,"where every state change in the knowledge base is accompanied by a formal witness of its validity. We demonstrate the practical utility of this logic through application examples in industrial traceability and cross-border financial compliance. Our results suggest that KOS-TL provides a robust, formally verifiable basis for the next generation of intelligent, autonomous operating systems.

Problem

• knowledge representation
• symbolic logic
• system execution
• logical consistency
• autonomous knowledge systems

Innovation

• Dependent Type Theory
• Proof-Carrying Knowledge
• Event-Driven Semantics
• Operational Semantics
• Constructive Logic