Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 484/731
7. Modal Logic 2. Kripke Semantics
Definition 7.4 (Modal Logic with n modalities)
The language L modaln of modal logic with n
modal operators □ 1 , . . . , □ n is the smallest set
containing the propositional constants of L, and
with formulae φ, ψ also the formulae
□ i φ, ¬φ, φ ∧ ψ. We treat ∨, →, ↔, ♦ as macros
(defined as usual).
Note that the □ operators can be nested:
(□ 1 □ 2 □ 1 p) ∨ □ 3 ¬p