Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 476/731
7. Modal Logic 1. Reasoning about Knowledge
Definition 7.2 (Partition Model)
An n-agent partition model over a language L is a tuple
(W, I 1 , . . . , I n ), where
W: is a set of possible worlds, i.e. a set of
L-structures (each L sentence φ is either true
in each of w ∈ W or not).
I i : each I i is a partition of W:
I i = {W i1 , W i2 , . . . , W ir } with W ij ∩ W ik = ∅ for
j ≠ k and ⋃ 1≤j≤r W i j
= W.
We also use the notation (w ∈ W)
I i (w) := {w ′ : w ∈ W ij and w ′ ∈ W ij }
all worlds in the partition containing world w,
according to agent i’s view of the universe.