Commit 14fbf4e8 by jfschaefer

### modal semantics

parent d659b15d
 ... ... @@ -21,6 +21,8 @@ theory TruthValues : krmt:?Meta = // switch : ℬ ⟶ ℬ ❘ = [b] if b ≐ T then F else T ❙ // switch F to T and T to F ❙ switch : ℬ ⟶ ℬ ❘ = [b] if_then_else ℬ (b ≐ T) F T ❙ max : ℬ ⟶ ℬ ⟶ ℬ ❘ = [a,b] if_then_else ℬ (a ≐ T) b F ❙ // maximum element (T > F) ❙ impl = [a, b] switch (max (switch a) b) ❙ ❚ view proplogSemantics : ?proplog -> ?TruthValues = ... ... @@ -60,6 +62,28 @@ theory MLO : ur:?LF = diamond : o ⟶ o ❘ # ◇ 1 prec 20 ❘ = [x] ¬ □ ¬ x ❙ ❚ theory KripkeModel : krmt:?Meta = include ☞http://mathhub.info/Teaching/KRMT?TypedSets ❙ include ?TruthValues ❙ world_type : type ❘ # 𝒲 ❙ accessibility_relation : 𝒲 ⟶ 𝒲 ⟶ ℬ ❘ # 1 ℛ 2 ❙ ❚ view modalSemantics : ?MLO -> ?KripkeModel = include ?proplogSemantics ❙ prop = 𝒲 ⟶ ℬ ❙ conjunction = [A : 𝒲 ⟶ ℬ, B : 𝒲 ⟶ ℬ] [w : 𝒲] max (A w) (B w) ❙ negation = [A : 𝒲 ⟶ ℬ, w : 𝒲] switch (A w) ❙ // box = [A : 𝒲 ⟶ ℬ, w : 𝒲] ∀ ([v : 𝒲] (w ℛ v) ⇒ (A v)) ❙ box = [A : 𝒲 ⟶ ℬ, w : 𝒲] ([P : 𝒲 ⟶ ℬ] if_then_else ℬ (in ℬ F (im P (fullset 𝒲))) F T) ([v : 𝒲] impl (w ℛ v) (A v)) ❙ ❚ // theory KripkeFrames : ur:?LF = include ?TruthValues ❙ worlds : type ❘ # 𝒲 ❙ ... ...
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!