I read the book "Introduction modern cryptography". It gives the notion of computational security of private-key encryption at first which comes from perfect security and statistical security.
Let $(E,D)$ be an encryption scheme that uses $n$-bits keys to encrypt $l(n)$-length messages. $(E,D)$ is computationally secure if $$E_{U_{n}}(x_{0}) \approx E_{U_{n}}(x_1)$$
And then it introduces the secure game (e.g. CPA, CCA)? I think it is a part of provable security.
"Unconditional security" (or "information-theoretic security" or "perfectly secrecy") and "computational security" are two opposite classes of security. But I do not think "computational security" and "provable security" are two independent classes of security. I know that computational security emphasizes the power of attacker is bounded (polynomial-time algorithm). And the provable emphasizes the mathematical assumptions or cryptography primitives. But it also related to the computational power.