Expressiveness and Complexity of the Logic of Public Announcements
نویسنده
چکیده
We will use K̂iφ as an abbreviation for ¬Ki¬φ and 〈φ〉ψ as an abbreviation for ¬[φ]¬ψ. Definition 2 (Semantics). An epistemic model (or model for short) is a triple M = (S,∼n, V ) with S a non-empty set of states, ∼i an equivalence relation for i < n, and V a function assigning a subset V (p) ⊆ S with each p ∈ PL. Given a modelM = (S,∼n, V ) and an s ∈ S, we define: M, s |= p iff s ∈ V (p) M, s |= ¬φ iff M, s 6|= φ M, s |= φ ∧ ψ iff M, s |= φ and M, s |= ψ M, s |= Kiφ iff s ∼i t implies M, t |= φ, for all t ∈ S M, s |= [φ]ψ iff M, s |= φ implies M|φ, s |= ψ where M|ψ := (T,≈i, U) is defined as follows: T := {t ∈ S | M, t |= ψ} ≈i := ∼i ∩ (T × T ) U(p) := V (p) ∩ T
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