Ontologies and toposes

The slides of the double talk given by Laurent Lafforgue and myself at the recent Huawei workshop on semantics are now available:

Our talk is based on an expository article written by AI theorists on the general theme of “ontology” and “knowledge representation”. We explain that the theory of Grothendieck toposes, of their geometric presentations by sites and of their linguistic descriptions in terms of first-order theories provides the means to incarnate in mathematical objects amenable to computations what could have seemed at first sight loose philosophical views. We present a number of important basic ideas about Grothendieck toposes and motivations for beginning to study them, and give an idea of the possibilities of the theory of “toposes as bridges” and its significance for the problem of “knowledge representation”.

3 thoughts on “Ontologies and toposes

  1. Hi Ivan, thanks for your message. Yes, I have had a look at the book “The Topos of Music”, but was disappointed in not really finding any serious topos theory there. All the best, Olivia

  2. This idea blew my mind.
    I have been interested and working in Semantics, Logic, Foundations of Mathematics, and Computational Linguistics, and I had no idea there could be a topic straight in the intersection of all of those areas!

    Will you be doing more about this idea of using toposes and ontologies?

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