Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reflective Metagraph Rewriting as a Foundation for an AGI "Language of
  Thought"   MeTTa (Meta Type Talk) is a novel programming language created for use in the
OpenCog Hyperon AGI system. It is designed as a meta-language with very basic
and general facilities for handling symbols, groundings, variables, types,
substitutions and pattern matching. Primitives exist for creating new type
systems and associated DSLs. IInformally, MeTTa is Hyperon's lowest-level
"language of thought" -- the meta-language in which algorithms for learning
more particular knowledge representations, will operate, and in which these
algorithms themselves may be represented. Here we explain how one might go
about formalizing the MeTTa language as a system of metagraph rewrite rules, an
approach that fits in naturally to the Hyperon framework given that the
latter's core component is a distributed metagraph knowledge store (the
Atomspace). The metagraph rewrite rules constituting MeTTa programs can also be
represented as metagraphs, giving a natural model for MeTTa reflection and
self-modifying code. Considering MeTTa programs that compute equivalences
between execution traces of other MeTTa programs allows us to model spaces of
MeTTa execution traces using Homotopy Type Theory. Considering the limit of
MeTTa programs mapping between execution traces of MeTTa programs that map
between execution traces of MeTTa programs that ..., we find that a given MeTTa
codebase is effectively modeled as an infinity-groupoid, and the space of all
MeTTa codebases as an (infinity,1)-topis This topos is basically the same as
the so-called "Ruliad" previously derived from rewrite rules on hypergraphs, in
a discrete physics context. The formalization of MeTTA as metagraph rewrite
rules may also provide a useful framework for structuring the implementation of
efficient methods for pattern matching and equality inference within the MeTTa
interpreter.

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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin