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Axiom schemata

  • The implication introduction schema ( II ), together with Modus Ponens, allows us to infer implications

    φ → (ψ → φ)

  • The implication distribution schema ( ID ) allows us to distribute one implication over another

    (φ → (ψ → c)) → ((φ → ψ) → (φ → c))

  • The contradiction realization schemata ( CR ) permit us to infer a sentence if the negation of that sentence implies some sentence and its negation

      (ψ → ¬ φ) → ((ψ → φ) → ¬ ψ)

      (¬ ψ → ¬ φ) → ((¬ ψ → φ) → ψ)


Speaker notes:

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