Quantum Theory in Knowledge Representation: A Novel Approach to Reasoning with a Quantum Model of Concepts

This thesis explores novel approaches to compositional reasoning in AI leveraging the mathematics of quantum theory as a general probabilistic theory. Starting from the quantum picturialism paradigm, offering a diagrammatic category-theoretic language, I show that quantum theory provides practical modelling and computational benefits for AI. A literature survey connect various applications, from quantum game theory and satisfiability to ML, NLP and cognition. How to formally represent and reason with concepts is a longstanding challenge in cognitive science and AI. My thesis studies the Quantum Model of Concepts (QMC), which provides conceptual space theory with quantum theoretical semantics. The diagrammatic language serves as a compositional framework for both, exposing common structures and facilitating insights between domains. I implement the model as a hybrid quantum-classical architecture on real quantum hardware to explore how QMCs can form practical intermediate, compositional representations for artificial agents combining symbolic and subsymbolic reasoning. Addressing the symbol grounding problem, I show that QMC representations can be learned from raw data in a (self-)supervised subsymbolic way, but that composite concepts can also be grounded in simpler ones to be interpretable and data-efficient. By transforming quantum concepts into probabilistic generative processes, the QMC can solve visual relational Blackbird puzzles involving abstraction and perceptual uncertainty, similar to Raven’s Progressive Matrices.