Contextual semantics in quantum mechanics from a categorical point of view

Claudio Garola

Ali Nabi Duman

Categorical quantum mechanics, which examines quantum theory via dagger-compact closed categories, gives satisfying high-level explanations to the quantum information procedures such as Bell-type entanglement or complementary observables (\cite{AC}, \cite{Co}, \cite{Co2}). Inspired by the fact that Quantum Game Theory can be seen as branch of quantum information, we express Quantum Game Theory procedures using the topological semantics provided by Categorical Quantum Mechanics. We also investigate Bayesian Games with correlation from this novel point of view while considering the connection between Bayesian game theory and Bell non-locality investigated recently by Brunner and Linden \cite{BL}.

Claudio Garola

François-Igor Pris

A realist interpretation of quantum mechanics is proposed - Contextual Quantum Realism (CQR) - according to which there exists a categorical distinction between the ideal (theory, observation instrument) and the real (quantum physical systems, properties), and, consequently, quantum ontology is context-sensitive. CQR is compared with QBism and Relational Quantum Mechanics (RQM), both of which also claim to offer realist interpretations. However, both approaches conflate the ideal and the real, thereby introducing an anti-realist dimension. RQM is an objectivist (physicalist) interpretation that naturalizes epistemic concepts, whereas QBism is subjectivist (phenomenological). RQM and QBism share a common presupposition of (post-)Modern philosophy - namely, the reduction of reality to objectivity - which CQR explicitly rejects.

Samson Abramsky, Bob Coecke

Pranay M. Mahendrakar

Life of Research AbstractThis paper introduces a novel theoretical framework for understanding semantic processing in Large LanguageModels through the lens of sheaf theory and quantum contextuality. We propose that the semantic structure ofLLM-generated text can be rigorously modeled as a sheaf over the topological space of prompt contexts, wherelocal semantic sections may fail to glue into globally consistent interpretations. This mathematical formalizationreveals a deep structural parallel between LLM behavior and quantum mechanical systems exhibitingcontextuality, as characterized by the Kochen-Specker theorem. Our central thesis posits that hallucinationphenomena in LLMs arise fundamentally from cohomological obstructions to the existence of global semanticsections, analogous to how quantum systems exhibit measurement outcomes that cannot be explained by preexisting hidden variables. We develop a complete categorical framework using topos-theoretic methods, introduceformal definitions of semantic presheaves and their associated Grothendieck topologies, and demonstrate howCech cohomology groups can quantify the degree of semantic inconsistency in model outputs. This work bridgesabstract mathematics with practical AI interpretability, offering new diagnostic tools for understanding when andwhy language models produce incoherent or factually inconsistent outputs.