Could you explain that? Here’s my guess at what you mean: “If ⊢B and the shortest proof of B in classical logic contains the statement A, or if A⊢B but not ⊢B, then A → B in ‘compressed logic’.”
It’s really just simplifying the logical expression. Like (A and not A) = True. I think that’s what you’re getting at, although I’m not familiar with your notation, and don’t want to think too hard.
“Logical compression” would take care of these examples. I remember reducing logic circuits way back in some introductory computer engineering class.
Could you explain that? Here’s my guess at what you mean: “If ⊢B and the shortest proof of B in classical logic contains the statement A, or if A⊢B but not ⊢B, then A → B in ‘compressed logic’.”
It’s really just simplifying the logical expression. Like (A and not A) = True. I think that’s what you’re getting at, although I’m not familiar with your notation, and don’t want to think too hard.