Semantic Function as a Mathematical Model of Quantum Conceptualism

Hans Herlof Grelland

Sachi Arafat, Cornelis J. van Rijsbergen

The conceptual model and mathematical formalism of quan-tum theory are employed in creating a novel framework for modeling the computational search process addressing problematic issues that restrict information retrieval research. Mapping the mathematical formalism of search to that of quantum theory presents insightful perspectives about the na-ture of search. However, differences in operational semantics of quantum theory and search restrict the utility of the map-ping. An approach is suggested for resolving these semantic differences aiming toward a sound mathematical and concep-tual framework for search inspired by quantum theory.

Peter Bruza, Richard Cole

This article is an exploratory account of the the non-monotonic behaviour of conceptual associations in the light of context. Computational approximations of conceptual space are furnished by semantic space models which are emerging from the fields of cognition and computational linguistics. Semantic space models not only provide a cognitively motivated basis to underpin human practical reasoning, but from a mathematical perspective, they are real-valued Hilbert spaces. This introduces the highly speculative prospect of formalizing aspects of human practical reasoning via quantum mechanics. This account focuses on how to formalize context effects in relation to concepts as well as keeping an eye on operational issues.

Diederik Aerts, Massimiliano Sassoli de Bianchi, Sandro Sozzo +1 more

Bob Coecke, Eric Paquette, Duško Pavlović

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(Collaborated with ChatGPT/Gemini) This work is not a peer-reviewed paper in rigorous mathematics.It is an experimental conceptual note submitted to Zenodo.In this version, I intentionally publish a raw stream of thought as an exploratory artifact, rather than a finalized theorem-level mathematical work.The claims should therefore be read as speculative modeling, conceptual synthesis, and toy simulation, not as established mathematical proof.