MathZero, The Classification Problem, and Set-Theoretic Type Theory


Cited 0|Views9
No score
AlphaZero learns to play go, chess and shogi at a superhuman level through self play given only the rules of the game. This raises the question of whether a similar thing could be done for mathematics -- a MathZero. MathZero would require a formal foundation and an objective. We propose the foundation of set-theoretic dependent type theory and an objective defined in terms of the classification problem -- the problem of classifying concept instances up to isomorphism. The natural numbers arise as the solution to the classification problem for finite sets. Here we generalize classical Bourbaki set-theoretic isomorphism to set-theoretic dependent type theory. To our knowledge we give the first isomorphism inference rules for set-theoretic dependent type theory with propositional set-theoretic equality. The presentation is intended to be accessible to mathematicians with no prior exposure to type theory.
Translated text
Key words
classification problem,type,theory,set-theoretic
AI Read Science
Must-Reading Tree
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined