Description
-
Convert each of the following FOL sentences into CNF form.
-
x P(x) Q(x)
-
-
-
x y P(x,y) Q(x)
-
-
-
x P(x) Q(x)
-
-
-
x y P(x,y) Q(y,x)
-
-
-
x y P(x,y)
-
-
-
x y P(x,y)
-
-
-
x y z P(x,y,z)
-
-
-
x y z P(x,y,z)
-
-
-
x( y P(x,y) Q(y)) R(x)
-
-
-
x( y P(x,y) Q(y)) R(x)
-
-
We are given the following pairs of FOL sentences. For each pair of sentences, provide a substitution to unify the sentences. If no such substitution exists, please write so.
-
-
P(x)
-
-
-
P(A)
-
-
-
P(x) Q(x, A)
-
-
-
P(B) Q(x, A)
-
-
-
P(x) Q(A, x)
-
-
-
P(x) Q(A, B)
-
-
-
P(x, A) Q(A, x)
-
-
-
P(B, y) Q(y, B)
-
-
-
P(x) Q(F(x))
-
-
-
P(A) Q(F(A))
-
-
-
P(x, A) Q(F(x), x)
-
-
-
P(B, y) Q(F(B), B)
-
-
-
P(x, A) Q(F(x), x)
-
-
-
P(B, y) Q(F(A), A)
-
-
-
P(x, y) Q(x, y)
-
-
-
P(x, y) Q(F(A), A)
-
-
-
P(x, y) Q(x, y)
-
-
-
P(x, y) Q(F(x), y)
-
-
-
P(z, y) Q(z, y)
-
-
We are given the following joint distribution for variables A, B, and C. Please compute the requested probabilities. Show each probability distribution as a table/vector. Feel free to use a calculator.
-
-
P(A, C)
-
-
-
P(C)
-
-
-
P(A|C)
-
-
-
P(A, B | C)
-
-
-
P(B | A, C)
-
-
We are given random variables X2, X3, …, Xn, where n>2. (There is no X1). Please answer the following questions.
-
-
Assuming all variables are binary, how many independent parameters are needed to represent
-
-
-
-
P(X2)?
-
-
-
-
-
P(Xn)?
-
-
-
-
-
P(X2, X3, …, Xn)?
-
-
-
-
-
P(X2 | X3, …, Xn)?
-
-
-
-
-
P(X2, X3, …, Xn-1| Xn)?
-
-
-
Assuming the size of the domain of Xi is i for all i {2, 3, …, n}, how many independent parameters are needed to represent
-
-
P(X2)?
-
-
-
P(Xn)?
-
-
-
P(X2, X3, …, Xn)?
-
-
-
P(X2 | X3, …, Xn)?
-
-
-
P(X2, X3, …, Xn-1| Xn)?
-