Dear Editors, I would like to submit my paper "THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture" as a full paper to the Special Issue on Explainable Neurosymbolic AI (X-NeSy). The paper is about how a neural network can handle "Unknown" values. Kleene's three-valued logic (K3) has clear rules for this, but earlier neural models put these rules into the network by hand, or they give the logic part to a symbolic solver. In my model THEIA, there are four small engines (arithmetic, order, set and logic) and no K3 rules are built in. The model still learns all 39 K3 rules with more than 99% accuracy on every rule, on 5 seeds. I think the paper fits X-NeSy for one main reason. Because each engine in THEIA gets a known set of inputs, I can calculate from the logic of the task how much information each engine output can have, and then check the trained network against this number. The "Unknown" signal is close to this limit at every engine, and the final answer only appears at the logic engine. I also compare with a Transformer. It learns the same rules, but its layers cannot be checked in this way. In a long-chain test with 500 steps, THEIA was also the most stable model among the ones I tested. An earlier version of this work is on arXiv (arXiv:2604.11284), and a short version was shown as a poster at an ICML 2026 workshop, which has no archival proceedings. The paper is not published anywhere else and is not under review at any other venue. The code is public at https://github.com/xxx12e/theia-k3. I am the only author, and I have no conflicts of interest. Thank you very much for your time and for considering my paper. Sincerely, Augustus Haoyang Li Irvine Valley College, Irvine, CA, USA hli132@ivc.edu