Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 421/731
6. Propositional Logic 2. Sentential Logic
Definition 6.7 (MOD(T), Cn(U))
If T ⊆ F ml L then we denote with MOD(T ) the set of all
L-structures A which are models of T :
MOD(T ) = def {A : A |= T }.
If U is a set of models, we consider all those sentences,
which are valid in all models of U. We call this set Cn(U):
Cn(U) = def {ϕ ∈ F ml L : ∀v ∈ U : ¯v(ϕ) = true}.
MOD is obviously dual to Cn:
Cn(MOD(T )) = Cn(T ), MOD(Cn(T )) = MOD(T ).