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I think you are right to be impressed with the Curry-Howard correspondence. It is a detailed and extensive rule-by-rule and feature-by-feature isomorphism. This strongly suggests that proof and ...

It is neither. A proof that an algorithm solves the problem (it claims to solve) is typically deductive in computer science, but in AI it's more likely to be inductive, i.e. based on benchmarks/...

Algorithms are time-bound sets of instructions. Logic is an atemporal transfer of properties among classes and their instances. A logical proof (in principle) takes no time and makes no changes. The ...

Algorithms are more closely related to deductive reasoning, but it's not quite as straightforward as that. Suppose for simplicity that by deductive reasoning, you roughly mean a proof given in a logic ...