I am asking if there are some good or standard references for proof complexity theory? I didn't find references when I search in internet. Thanks!
These are three books that I know:
- Logical Foundations of Proof Complexity
- Bounded Arithmetic, Propositional Logic and Complexity Theory
- Logical Foundations of Mathematics and Computational Complexity, Proof complexity chapter
Also, I suggest you read the following papers:
Update. Jan Krajíček wrote a new book on this topic recently. You can find the final manuscript of it here.