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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2604.22530 |
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| _version_ | 1866918466311684096 |
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| author | Peng, Chen |
| author_facet | Peng, Chen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22530 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | DEKL 2.0: Trace-Indexed Knowledge Evolution in Dependent Type Theory Peng, Chen Logic in Computer Science 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. |
| title | DEKL 2.0: Trace-Indexed Knowledge Evolution in Dependent Type Theory |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2604.22530 |