Multiagent Systems

of. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 418/731
6. Propositional Logic 2. Sentential Logic
Definition 6.3 (Validity of a Formula, Tautology)
1 A formula ϕ ∈ F ml L holds under the
valuation v if ¯v(ϕ) = true. We also write
¯v |= ϕ or simply v |= ϕ.
2 A theory is a set of formulae: T ⊆ F ml L . v
satisfies T if ¯v(ϕ) = true for all ϕ ⊆ T . We
write v |= T .
3 A L-formula ϕ is called L-tautology if for all
possible valuations (models) v in L v |= ϕ
holds.
From now on we suppress the language L, because it is
obvious from context. Nevertheless it needs to be carefully
defined.