I'm starting to review a ~300-page document produced by Topos Research UK for the UK's Safeguarded AI program. It's called simply "the thesis", and it's a general approach to cyberphysical systems.
The idea is to not merely be able to handle many specific models of physical systems, but many *kinds* of models - you could call such a kind a "system for modeling". A modeling system is a "meta-model", one step up in abstraction from a specific model. However, modeling systems also come in different well-known kinds. A kind of modeling system, as opposed to a specific modeling system, is a "meta-meta-model".
A crucial part near the beginning of the thesis, which I paraphrase:
"How can we find a mathematical semantics which can handle not only the variety of particular models used in practice, but their organization into a variety of meta-models and the translations and relations between them? How can we find a mathematical meta-meta-model?
The only mathematical formalism up to the task of providing a formal semantics and guide to declarative higher modelling is higher category theory. Category level roughly corresponds to meta level:
A 0-category is a set, a 1-category has objects which are generally sets with structure, a 2-category has objects which are generally categories-with-structure.
Models are sets-with-structure (0-categories); meta-models are categories of these sets-with-structure; meta-meta-models are the 2-categories of meta-models."
The main authors of the thesis are David Jaz Myers, Jason Brown, Sophie Libkind and Matteo Capucci (Matteo Capucci (npub1lez…3yeq)). Reading it is quite a challenge. I will try to explain bits of it here.
John Carlos Baez
npub1nf…3nqe4
2026-08-20 16:33:39 UTC
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2026-08-20 16:33:39 UTCEvent JSON
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"content": "I'm starting to review a ~300-page document produced by Topos Research UK for the UK's Safeguarded AI program. It's called simply \"the thesis\", and it's a general approach to cyberphysical systems. \n\nThe idea is to not merely be able to handle many specific models of physical systems, but many *kinds* of models - you could call such a kind a \"system for modeling\". A modeling system is a \"meta-model\", one step up in abstraction from a specific model. However, modeling systems also come in different well-known kinds. A kind of modeling system, as opposed to a specific modeling system, is a \"meta-meta-model\".\n\nA crucial part near the beginning of the thesis, which I paraphrase:\n\n\"How can we find a mathematical semantics which can handle not only the variety of particular models used in practice, but their organization into a variety of meta-models and the translations and relations between them? How can we find a mathematical meta-meta-model?\n\nThe only mathematical formalism up to the task of providing a formal semantics and guide to declarative higher modelling is higher category theory. Category level roughly corresponds to meta level:\n\nA 0-category is a set, a 1-category has objects which are generally sets with structure, a 2-category has objects which are generally categories-with-structure.\n\nModels are sets-with-structure (0-categories); meta-models are categories of these sets-with-structure; meta-meta-models are the 2-categories of meta-models.\"\n\nThe main authors of the thesis are David Jaz Myers, Jason Brown, Sophie Libkind and Matteo Capucci (nostr:npub1lezrwa7qdjfwnfqhyumqr47nyrs2c7vw24p8ddq8uuzn7r7uk9uqkv3yeq). Reading it is quite a challenge. I will try to explain bits of it here.",
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