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Prof. Dr. Jürgen Dix · Department of Informatics, TUC <strong>Multiagent</strong> <strong>Systems</strong>, WS 06/07 613/731<br />

9. Agents based on FOL 1. First Order Logic (FOL)<br />

Definition 9.11 (Completeness of a theory T )<br />

T is called complete, if for each formula ϕ ∈ F ml L : T |= ϕ<br />

or T |= ¬ϕ holds.<br />

Attention:<br />

Do not mix up this last condition with the property of a<br />

valuation v (or a model): each valuation is complete in the<br />

above sense.<br />

Lemma 9.12 (Ex Falso Quodlibet)<br />

T is consistent if and only if Cn(T ) ≠ F ml L .

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