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Aleks Kissinger

  1. Synthesising Graphical Theories.

    Ср, 02/29/2012 - 15:01 — SomNambul
    Authors: Aleks Kissinger
    Subjects: Artificial Intelligence
    Abstract

    In recent years, diagrammatic languages have been shown to be a powerful and
    expressive tool for reasoning about physical, logical, and semantic processes
    represented as morphisms in a monoidal category. In particular, categorical
    quantum mechanics, or "Quantum Picturalism", aims to turn concrete features of
    quantum theory into abstract structural properties, expressed in the form of
    diagrammatic identities. One way we search for these properties is to start
    with a concrete model (e.g.

  2. Open Graphs and Computational Reasoning.

    Пт, 07/23/2010 - 15:01 — SomNambul
    Authors: Lucas Dixon, Ross Duncan, Aleks Kissinger
    Subjects: Logic in Computer Science
    Abstract

    We present a form of algebraic reasoning for computational objects which are
    expressed as graphs. Edges describe the flow of data between primitive
    operations which are represented by vertices. These graphs have an interface
    made of half-edges (edges which are drawn with an unconnected end) and enjoy
    rich compositional principles by connecting graphs along these half-edges. In
    particular, this allows equations and rewrite rules to be specified between
    graphs. Particular computational models can then be encoded as an axiomatic set
    of such rules.

Math-arch

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