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Axiom schemata (cont’)

  • The equivalence schemata ( EQ ) captures the meaning of the operator

      ψ) → (φ → ψ)

      ψ) → (ψ → φ)

      (φ → ψ) → ((ψ → φ) → (ψ φ))

  • The meaning of the other operators in propositional logic is captured in the following axiom schemata

      (φ ← ψ) (ψ → φ)

      (φ ∨ ψ) (¬φ → ψ)

      (φ ∧ ψ) ¬(¬φ ∨ ¬ψ)

  • The above axiom schemata are jointly called the standard axiom schemata for Propositional Logic

    • They all are valid

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