Multiagent Systems

of. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 448/731
6. Propositional Logic 4. Calculi for SL
Definition 6.11 (Axiom, Inference Rule)
Axioms in SL are the following formulae:
1 φ → ⊤, □ → φ, ¬⊤ → □, □ → ¬⊤,
2 (φ ∧ ψ) → φ, (φ ∧ ψ) → ψ,
3 φ → (φ ∨ ψ), ψ → (φ ∨ ψ),
4 ¬¬φ → φ, (φ → ψ) → ((φ → ¬ψ) → ¬φ),
5 φ → (ψ → φ), φ → (ψ → (φ ∧ ψ)).
Note that φ, ψ stand for arbitrarily complex
formulae (not just constants).