Please post your solutions to the Nov 2 In-Class Exercise to this thread.

Best,

Chris

Universe = Domain: a, b, c, d Knows(a,a) Knows(b,b) Knows(c,c) Knows(d,d) Knows(a,b) Knows(b,c) Knows(a,d)

x -> a, y-> d, z->b For_All(x) Knows(x,x) AND Exists(y)not Knows(z,y)

Let universe U = {"PersonA", "PersonB", "PersonC", "PersonD"} Knows := {("PersonA", "PersonA"), ("PersonB", "PersonB"), ("PersonC", "PersonC"}, ("PersonD","PersonD")} F := (x)Knows(x,x)(y)Knows(z,y)[z -> "PersonB"] T Knows(z,y)[z -> "PersonB", y -> "PersonA"] F T

Consider the model M with universe {Tyrell's Secret, Jim's Secret}

Knows := {(Tyrell's Secret,Tyrell's Secret),(Jim's Secret,Jim's Secret)}

M |= (x)Knows(x,x)(y)Knows(z,y) [z->Jim's Secret]

M |= (x)Knows(x,x)(y)Knows(z,y) [y->Tyrell's Secret, z->Jim's Secret]

Knows(x,y)

U = {A, B}

(x)Knows(x,x)[x = (A, A), (B, B)] <=> True

(y)Knows(z,y)[z = A, y = B] <=> True

(x)Knows(x,x)(y)Knows(z,y) <=> True

(x)Knows(x,x) (y)Knows(z,y) Domain: (Alice, Bob, Cali) Knows: (Alice, Alice), (Bob, Bob), (Cali, Cali) Right side evaluates to true if we set it's variables to (Bob, Alice) or (Alice, Bob) or (Bob, Cali) or (Alice, Cali) or (Cali, Bob) or (Cali, Alice)

Predicate: Knows(X, Y)

Model: M = {Alice, Bob, Dave} Knows(Alice, Alice) Knows(Bob, Bob) Knows(Dave, Dave)

Formula: (x)Knows(x,x)(y)Knows(z,y)

Variable Assignment: x -> Dave, Y -> Alice, Z -> Bob

(x)Knows(x,x) (y)Knows(z,y) Universe = ["John", "Peter", "Bob"] (x)Knows(x,x) := {["John", "John"], ["Peter", "Peter"], ["Bob", "Bob"]} = T (y)Knows(z,y) := [z = "John", y = "Peter"] = T (x)Knows(x,x) (y)Knows(z,y) = T