Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 687/731
9. Agents based on FOL 5. (Concurrent-) MetaTeM
The semantics of FML is given by the |= relation that
assigns the truth value of a formula in a model M at a
particular moment in time i and with respect to a variable
assignment.
〈M, i, h v 〉 |= ⊤
〈M, i, h v 〉 ̸|= ⊥
〈M, i, h v 〉 |= p(x 1 , ..., x n ) iff h p (i, p)(τ vh (x 1 ), ..., τ vh (x n )) = true
〈M, i, h v 〉 |= ¬φ iff 〈M, i, h v 〉 ̸|= φ
〈M, i, h v 〉 |= φ ∨ ψ iff 〈M, i, h v 〉 |= φ or 〈M, i, h v 〉 |= ψ
〈M, i, h v 〉 |= φ Uψ iff for some k s.t. i < k, 〈M, k, h v 〉 |= ψ
for all j, if i < j < k then 〈M, j, h v 〉 |= φ
〈M, i, h v 〉 |= φ Sψ iff for some k s.t. 0 ≤ k < i, 〈M, k, h v 〉 |= ψ
for all j, if k < j < i then 〈M, j, h v 〉 |= φ
〈M, i, h v 〉 |= ∀x.φ iff for all d ∈ D, 〈M, i, h v [d/x]〉 |= φ
〈M, i, h v 〉 |= ∃x.φ iff there exists d ∈ D s.t. 〈M, i, h v [d/x]〉 |= φ