[pure-awesome]

I'm all for using types, and pre- and post-conditions where applicable, but I don't see how they would be a useful replacement to the situations in which probabilities would apply. Could you elaborate?

To give an example where I think probabilities would be used: consider a recognition AI that should figure out who someone is. You have a phone, on which you have some photos of its owner, some voice recordings, and some text messages. For each of those, the AI can assign probabilities that e.g. my voice matches the recordings, my face matches the photos, and my writing style matches the texts. Then it could combine these into an aggregate estimate probability that the phone belongs to me.

How would you use types and pre- and post- conditions to solve this problem?

[rurban]

Some cases can be solved with probabilities, most not. These can be improved by better context.

The phone either belongs to you or not. Schrödingers cat is either dead or alive, but not 80% dead as some people assert.

[pure-awesome]

Oh, okay... are you referring to fuzzy logic where statements have a partial truth value?

I'm (mostly) referring to the case where the truth value is either true or false, but where you aren't sure, so you can say "80% probability this is your phone".

There are also cases where truth values aren't as clear cut, which I also mention, such as the question of whether or not something IS a chair. (Is a chair taped to the ceiling still a chair? Is a log I sit on out in the middle of the forest a chair? Etc.)