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KOS-TL (Knowledge Operation System Type Logic)

Peng Chen

TL;DR

This paper formally defines the operational semantics of the KOS-TL (Knowledge Operation System Type Logic), a novel constructive framework designed to provide a rigorous logical foundation for autonomous and executable knowledge systems, and proves key meta-theoretical properties, including Progress and Evolutionary Consistency.

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.

KOS-TL (Knowledge Operation System Type Logic)

TL;DR

This paper formally defines the operational semantics of the KOS-TL (Knowledge Operation System Type Logic), a novel constructive framework designed to provide a rigorous logical foundation for autonomous and executable knowledge systems, and proves key meta-theoretical properties, including Progress and Evolutionary Consistency.

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 ; 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.
Paper Structure (114 sections, 23 theorems, 81 equations, 1 figure, 11 tables, 1 algorithm)

This paper contains 114 sections, 23 theorems, 81 equations, 1 figure, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The Architecture of KOS-TL
  3. Core Layer Requirements Analysis and Logical Construction
  4. Overall Architecture Description
  5. Key Design Decisions
  6. L1: Kernel (Kernel Layer) — Operational Semantics Domain
  7. Kernel Layer Requirements Modeling: Dynamic Evolution and State Determinism
  8. Design Methodology: Small-Step Operational Semantics and State Machine Model
  9. Overall Architecture Description
  10. Key Design Decisions
  11. L2: Runtime Layer — System Evolution Domain
  12. Requirements Modeling: Physical Fidelity and Environmental Elaboration
  13. Design Methodology: Elaboration and Materialization in Bidirectional Mapping
  14. Overall Architecture Description
  15. Key Design Decisions
  16. ...and 99 more sections

Key Result

Lemma 1

Substitution Lemma If $\Gamma, x:B, \Delta \vdash t : A$ and $\Gamma \vdash u : B$, then $\Gamma, \Delta[u/x] \vdash t[u/x] : A[u/x]$. Here, $\Delta$ is a general context to handle variables defined after $x$ that depend on $x$. In simple cases, $\Delta$ is empty.

Figures (1)

  • Figure 1: KOS-TL Layered Interaction Interface Diagram

Theorems & Definitions (72)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Lemma 1
  • proof
  • ...and 62 more