Duality is a phenomenon across Mathematics, Physics, and Computer Science, telling us that two different realms are structurally equivalent to each other, and thereby allowing for structural knowledge transfer between different fields. In this talk, I present a variety of categorical dualities in Logic and Computation, and their applications to Artificial Intelligence and Quantum Physics, including those to Knowledge Representation and the kernel method in Machine Learning. If time permits, I will also present my recent work on proof-theoretic semantics, in particular a general theory of Curry-Howard isomorphisms based on higher-order rules. At the end of the talk I give an outlook for the categorical integration of Symbolic AI and Statistical AI.
Yoshihiro Maruyama is a logician and computer scientist who currently holds Hakubi Assistant Professorship at Kyoto University; he obtained his DPhil in Computer Science at the University of Oxford. He works on categorical logic and its applications to computer science, artificial intelligence, and quantum physics. As his side work he sometimes publishes articles about conceptual issues in artificial intelligence and cognitive science. He was awarded a Kyoto University President's Award for his interdisciplinary research.