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Multiagent Systems

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Prof. Dr. Jürgen Dix · Department of Informatics, TUC <strong>Multiagent</strong> <strong>Systems</strong>, WS 06/07 612/731<br />

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

Definition 9.10 (MOD(T ), Cn(U))<br />

If T ⊆ F ml L , then we denote by MOD(T ) the set<br />

of all L-structures A which are models of T :<br />

MOD(T ) = def {A : A |= T }.<br />

If U is a set of structures then we can consider all<br />

sentences, which are true in all structures. We<br />

call this set also Cn(U):<br />

Cn(U) = def {ϕ ∈ F ml L : ∀A ∈ U : A |= ϕ}.<br />

MOD is obviously dual to Cn:<br />

Cn(MOD(T )) = Cn(T ), MOD(Cn(T )) = MOD(T ).

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