NM-DEKL$^3_\infty$: A Three-Layer Non-Monotone Evolving Dependent Type Logic

Peng Chen

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arXiv · 2603.01366

NM-DEKL$^3_\infty$: A Three-Layer Non-Monotone Evolving Dependent Type Logic

Peng Chen

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Abstract

We present a new dependent type system, NM-DEKL$^3_\infty$ (Non-Monotone Dependent Knowledge-Enhanced Logic), for formalising evolving knowledge in dynamic environments. The system uses a three-layer architecture separating a computational layer, a constructive knowledge layer, and a propositional knowledge layer. We define its syntax and semantics and establish Soundness and Equational Completeness; we construct a syntactic model and prove that it is initial in the category of models, from which equational completeness follows. We also give an embedding into the $\mu$-calculus and a strict expressiveness inclusion (including the expressibility of non-bisimulation-invariant properties).

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Peng Chen. 2026-03-02. NM-DEKL$^3_\infty$: A Three-Layer Non-Monotone Evolving Dependent Type Logic. https://arxiv.org/abs/2603.01366

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