When using infra-Bayesian logic to define a simplicity prior, it is natural to use “axiom circuits” rather than plain formulae. That is, when we write the axioms defining our hypothesis, we are allowed to introduce “shorthand” symbols for repeating terms. This doesn’t affect the expressiveness, but it does affect the description length. Indeed, eliminating all the shorthand symbols can increase the length exponentially.
When using infra-Bayesian logic to define a simplicity prior, it is natural to use “axiom circuits” rather than plain formulae. That is, when we write the axioms defining our hypothesis, we are allowed to introduce “shorthand” symbols for repeating terms. This doesn’t affect the expressiveness, but it does affect the description length. Indeed, eliminating all the shorthand symbols can increase the length exponentially.