Chapter11

Question 1

What is Clarks Idea?

Answer 1

The idea of program completion is to turn such implications into a definition by adding the
corresponding necessary counterpart

Question 2

Every stable model of P is a model of CF(P)?

Answer 2

Yes But. not vise versa, a stable model for the completion of P is not a always a stable model of P.
Models of the completion of P are supported models.

Question 3

What causes the mismatch between supported
and stable models?

Answer 3

Answer The mismatch between supported and stable models
is caused by cyclic derivations

Question 4

Fages’ Theorem

Answer 4

Let P be a tight normal logic program and X ⊆ A(P)
Then, X is a stable model of P iff X |= CF(P)

Question 5

For L ⊆ A(P), the external supports of L for P are?

Answer 5

ESP(L) = {r ∈ P | h(r) ∈ L, B(r)+ ∩ L = ∅} External supports for L are defined as a rule that exists in P or the head of a rule that exists in the positive rule body wholse intersection with the loop is the empty set.

Question 6

what is B(r)+?

Answer 6

The positive rule body.

Question 7

What is |=?

Answer 7

The right hand side is the logical consequence of the left hand side.

Question 8

How do you read x = 3?

Answer 8

x is assigned the value 3 and not as x is 3

Question 9

If a set of atoms X is a model of a normal program P, then X is a model of the completion of P.

Answer 9

False. X would need to be a stable model to be a model of the completion. models of the completion are supported models, one of them is the stable model.

Question 10

If a set of atoms X is a stable model of a normal Program P, then X is a model of the completion of P.

Answer 10

True.

Question 11

If a set of atoms X is a model of the completion of P, then it is a model of the normal program P.

Answer 11

True

Question 12

If a set of atoms X is a model of the completion of P, then it is a stable model of the program P.

Answer 12

FALSE. It is supported.

Question 13

Given a normal program P, if the completion of P has at least one model, then P has at least one stable model.

Answer 13

False.

Question 14

Let P be a normal program and X a set of atoms such that X |= CF(P).
If X is not a stable model of P, then there is a loop L in P such that L is contained in X and X satisfies the loop formula P(L)

Answer 14

False

Question 15

Let P be a normal program and L1. L2 are elements of loop(P) if L1 intersect L2 in not the empty set then L1 union L2 are both elements of loop(P)

Answer 15

False.

Question 16

Let P be a normal program. For every partial interpretation <T,F>, Ω<T,F> = <T’.F’>, then T’ ∩ F’ = ∅

Answer 16

False. The intersection of these true and false sets may not necessarily be empty.

Question 17

Let P be a normal program and X be a st of atoms. If (A(P)\X) is an unfounded set of P wrt < X,∅>, then X is a model of P.

Answer 17

True.

Question 18

Let P be a normal program and < T,F> be a partial interpretation. if two sets. U1, and U2 ⊆ A(P) are unfounded for P wrt <T,F>, then (U1 ∩ U2) is also unfounded for P wrt <T,F>

Answer 18

False. Because it could be, it could not be.