Hypergraph Rewriting and the Wolfram Model


This talk will summarize some recent results obtained in connection with the Wolfram Physics Project: a systematic attempt to reduce fundamental physics to the problem of hypergraph rewriting. Specifically, we will discuss the construction of an efficient hypergraph rewriting scheme using the formalism of Wolfram model multiway systems, with a categorical semantics defined via double-pushout rewrites over selective adhesive categories, and equipped with a dagger-symmetric monoidal structure that exhibits surprising formal connections to categorical quantum mechanics. We will also demonstrate that, by equipping such a multiway system with an additional notion of causal structure (defined via the semantics of precausal categories), we are able to introduce new inference rules of selective resolution, paramodulation and factoring that generalize the standard Knuth-Bendix completion rules for term rewriting systems, and significantly improve the efficiency of automated diagrammatic reasoning algorithms over hypergraphs. Time permitting, we will discuss some near-term practical applications of these methods for quantum information theory (allowing for more efficient diagrammatic simplification of quantum circuits), as well as numerical general relativity (allowing for more explicit numerical simulation of graph-theoretic models of space and time).

Friday, April 9, 2021 15:00 Europe/Paris
GReTA seminar
Jonathan Gorard
Jonathan Gorard
Associate Director of Research

Jonathan Gorard is a researcher in applied mathematics at the University of Cambridge (where he was previously a graduate student), a consultant mathematician for Wolfram Research (leading the development of the Wolfram Language’s automated theorem proving, axiomatic mathematics, quantum computing and discrete-state quantum mechanics functionality) and one of the cofounders of the Wolfram Physics Project, where he is now associate director of research. His published research comprises novel contributions to general relativity, the foundations of quantum mechanics, quantum information theory, mathematical logic, computational complexity theory, functional analysis, combinatorics and algebraic graph theory, among many other areas. His hobbies and interests include cognitive neuroscience, psycholinguistics, analytic philosophy, abiogenesis, senescence, cryonics, hiking, running, Mediterranean food jazz piano and mixed lacrosse.