Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 452/731
6. Propositional Logic 4. Calculi for SL
Theorem 6.13 (Completeness)
A formula follows semantically from a theory T if
and only if it can be derived:
T |= ϕ if and only if T ⊢ ϕ
Theorem 6.14 (Compactness)
A formula semantically follows from a theory T if
and only if it already follows from a finite subset
of T :
Cn(T ) = ⋃ {Cn(T ′ ) : T ′ ⊆ T, T ′ finite}.