arXiv:2606.03063v1 Announce Type: cross Abstract: We propose ZX-Calculus (Knowledge Evolution Calculus), a conservative extension of Martin-Lof Dependent Type Theory (MLTT) integrating trace-indexed types, presheaf non-monotone semantics, and constructive AGM belief revision. A Coq mechanisation accompanies the paper (34 complete proofs; zero admits for the two central results). (I) Trace types. FinTrace(s0,sn) is an inductive family of typed execution traces. FinTrace and Star(Step) are isomorphic as path types but not judgementally equal; TraceElim exposes the event label e:Event explicitly,
The continuous evolution of AI and formal verification demands more robust theoretical foundations, pushing research towards integrating complex logical systems.
This work introduces a foundational extension to type theory, potentially enabling more explainable, verifiable, and robust AI systems necessary for critical applications.
The proposed ZX-Calculus offers a new framework for modeling knowledge evolution and belief revision in AI, moving beyond traditional, simpler logical systems.
- · AI safety researchers
- · Formal verification specialists
- · Developers of explainable AI
- · Developers relying solely on ad-hoc AI solutions
It provides a new mathematical framework for understanding and building more reliable AI agents.
This could lead to a new generation of AI systems with provable properties regarding knowledge and belief revision, critical for high-stakes decisions.
These advancements might contribute to the development of AI that can autonomously learn and adapt in complex, uncertain environments with guaranteed logical consistency.
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Read at arXiv cs.CL