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arXiv · 2604.22530

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

Chen Peng
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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.

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Chen Peng. 2026-04-24. DEKL 2.0: Trace-Indexed Knowledge Evolution in Dependent Type Theory. https://arxiv.org/abs/2604.22530

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