KOS-TL (Knowledge Operation System Type Logic)

• URL: http://arxiv.org/abs/2601.01143v1
• Date: Sat, 03 Jan 2026 10:15:48 GMT
• Title: KOS-TL (Knowledge Operation System Type Logic)
• Authors: Peng Chen,
• Abstract summary: This paper introduces KOS-TL (Knowledge Operation System Type Logic), a novel constructive framework for autonomous and executable knowledge systems.<n>By integrating Davidsonian event semantics with Martin-Lf 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.<n>Our results suggest that KOS-TL provides a robust, formally verifiable basis for the next generation of intelligent operating systems.
• Score: 3.848983210046659
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\langle Σ, \textsf{Ev}, Δ\rangle$; 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-Löf 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.

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