Quantum Grammar and Symbolic AI: From Linguistic Recursion to SU(2)ₖ Algebra

This work is part of the project Typology of the Word, developed at Ca’ Foscari University of Venice, as the outcome of a teaching-research pathway conducted with the students of the Italian Literature course. The research is grounded in a question–answer methodology, where the hypotheses were directly inspired by the questions raised by the students: 1. How to analyze the linguistic mechanisms and rhetorical-metrical calculations in Dante’s Divine Comedy. 2. Why the Fibonacci sequence emerges in the structure of Dante’s verses, and what its formal-linguistic significance may be. 3. Why to privilege a linguistic environment (NooJ) instead of a purely algorithmic one (Python), or how grammars and computational models can be integrated. From these questions, a collaborative research trajectory was shaped, where students actively contributed with analyses, experiments, and digital tools. This dialogue has led to the definition of a rigorous scientific model, grounded in the work of Michel Planat, who reduces all languages—poetic, musical, biological—into fixed and homologous categories, thereby making them computable. The model proceeds in three steps: - Graph coverings and Isoc (X; d) reduce linguistic sequences into numerical classes (Planat, 2020). - These classes are then synthesized into topological nodes, where each word becomes a node and rhetorical relations are mapped onto operators (S, F, R). - Finally, the structure SU (2)ₖ and its braid generators (σ₁ = R, σ₂ = FRF⁻¹) introduce the dynamics of fusion and braiding, which connect linguistic formalization with topological computation and large language models (Planat, 2024). This trajectory builds on Michel Planat’s exploration of topological quantum computation, from graph coverings to the anyon hypothesis (Graph Coverings and Conjugacy Classes, 2020; What ChatGPT Has to Say About Its Topological Structure: The Anyon Hypothesis, 2024). It also resonates with Giuseppe Longo’s epistemological reflections on the role of mathematics in shaping biological and linguistic structures. By reducing human language to numerical invariants, topological nodes, and braided operators, this study opens a bridge between rhetorical recursion, quantum mathematics, and symbolic artificial intelligence.