Operational Noncommutativity in Sequential Metacognitive Judgments

Computer Science > Artificial Intelligence [Submitted on 15 Feb 2026] Operational Noncommutativity in Sequential Metacognitive Judgments Enso O. Torres Alegre, Diana E. Mora Jimenez Metacognition, understood as the monitoring and regulation of one's own cognitive processes, is inherently sequential: an agent evaluates an internal state, updates it, and may then re-evaluate under modified criteria. Order effects in cognition are well documented, yet it remains unclear whether such effects reflect classical state changes or reveal a deeper structural non-commutativity. We develop an operational framework that makes this distinction explicit. In our formulation, metacognitive evaluations are modeled as state-transforming operations acting on an internal state space with probabilistic readouts, thereby separating evaluation back-action from observable output. We show that order dependence prevents any faithful Boolean-commutative representation. We then address a stronger question: can observed order effects always be explained by enlarging the state space with classical latent variables? To formalize this issue, we introduce two assumptions, counterfactual definiteness and evaluation non-invasiveness, under which the existence of a joint distribution over all sequential readouts implies a family of testable constraints on pairwise sequential correlations. Violation of these constraints rules out any classical non-invasive account and certifies what we call genuine non-commutativity. We provide an explicit three-dimensional rotation model with fully worked numerical examples that exhibits such violations. We also outline a behavioral paradigm involving sequential confidence, error-likelihood, and feeling-of-knowing judgments following a perceptual decision, together with the corresponding empirical test. No claim is made regarding quantum physical substrates; the framework is purely operational and algebraic. Comments: 15 pages, 1 figure Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2604.04938 [cs.AI]   (or arXiv:2604.04938v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.04938 Focus to learn more Submission history From: Enso Onill Torres Alegre [view email] [v1] Sun, 15 Feb 2026 08:15:48 UTC (16 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)