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Introduction – Basic Notions

  • A proof system is collection of inference rules of the form:

    P 1 … P n



    where C is a conclusion sequent, and P i ‘s are premises sequents .

    • If an infererence rule does not have any premises that are taken to be true (called an axiom ), its conclusion automatically holds.
    • Example:
      Modus Ponens: From P, P → Q infer Q,
      Universal instantiation: From (∀x)p(x) infer p(A)
  • Theorems:
    • Expressions that can be derived from the axioms and the rules of inference.

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