DEKL 2.0: Trace-Indexed Knowledge Evolution in Dependent Type Theory

2026-04-24

AI Summary

This work addresses the challenge of formalizing the non-monotonic evolution of knowledge along execution traces within dependent type theory while preserving the monotonicity of the underlying proof calculus. To this end, we introduce a novel dependent type framework that treats both finite and infinite execution traces as first-class objects, models knowledge evolution via presheaf semantics, and leverages category-theoretic machinery to support propositional reasoning and fixed-point constructions. The key innovation lies in unifying, for the first time, trace-indexed knowledge evolution, executable traces, typed evidence, and belief revision within a single linguistic framework, with non-monotonicity captured through non-surjective restriction maps. This approach establishes a correspondence between trace reachability and logical completeness, yielding a unified formal system that seamlessly integrates dynamic knowledge evolution with typed logical reasoning.

Technology Category

• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

DEKL 2.0 is a dependent type-theoretic framework for trace-indexed knowledge evolution. Its central claim is that the proof calculus remains monotone under standard structural rules, while non-monotonic behavior arises semantically from trace extension. Finite and infinite traces are first-class objects in the computational universe; knowledge is interpreted as a presheaf over the finite-trace category; and proposition-level reasoning is handled categorically with fixed-point support. We establish trace--reachability correspondence and completeness, characterize non-monotonicity by non-surjective restriction maps, and present a semantic interpretation based on the free category generated by a transition system. The framework unifies executable traces, typed witnesses, and knowledge revision in one dependent language.

Problem

• knowledge evolution
• dependent type theory
• non-monotonic reasoning
• trace semantics
• presheaf semantics

Innovation

• dependent type theory
• trace-indexed knowledge
• non-monotonic reasoning
• presheaf semantics
• categorical logic