Proof theories (also called deductive systems) provide means of ”calculating” things about the logic. Each proof theory is a means of doing proofs in that logic.
- Proof theories are methods that perform mechanical manipulations on strings of symbols.
- Proof theories are based on pattern matching.
- For a particular proof theory, there may be multiple ways to prove a formula.
means that from we can prove using a proof theory.
- defines what is a proof
- We say that “proves”
Also see Semantics.