The new OpenAI Decisions API calls it "predicate". Also calling the API "decisions" rather than "system one". Usually I don't like inventing new standards but I hope the OpenAI schema takes over. We don't need this hype terminology.

My guess is if you pronouce this "nool" it sounds similar to "bool", and it's a slice of the name "Bernoulli" because the models generate Bernoulli distributions

The same reason why they’re calling this System One thinking. Everyone wants to be seen doing different things and smart ones.

Claude generated it and it stuck.

It's from Bernoulli.