Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 617/731
9. Agents based on FOL 1. First Order Logic (FOL)
We have already defined a complete and correct calculus
for propositional logic L P L . Such calculi exist also for first
order logic L F OL .
Theorem 9.14 (Completeness of first order logic)
A formula follows semantically from a theory T if it can be
derived:
T ⊢ ϕ if and only if T |= ϕ
Theorem 9.15 (Compactness of first order logic)
A formula can be derived from a theory T if it can be derived
from a finite subset of T :
Cn(T ) = ⋃ {Cn(T ′ ) : T ′ ⊆ T, T ′ finite}.