Proof Theory

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.