Assignment of Default Reasoning in AI

1. Which of the following is/are true about default reasoning?

It is non monotonic: It allows us to draw conclusions from limited data, which may be withdrawn later if we get more information.

It is monotonic: If some statement is entailed by a KB, it is also entailed by any superset of the KB.

It allows us to make reasonable inferences in the absence of complete information.

Once a conclusion has been drawn, it remains valid thereafter.

Accepted Answers:

It is non monotonic: It allows us to draw conclusions from limited data, which may be withdrawn later if we get more information.

It allows us to make reasonable inferences in the absence of complete information.

2. What is closed-world assumption?

Unless an atomic sentence is known to be true, it is assumed to be false.

Unless an atomic sentence is known to be false, it is assumed to be true.

The KB is fixed and cannot be expanded by entailments.

None of the above.

Accepted Answers:

Unless an atomic sentence is known to be true, it is assumed to be false.

3. Given a consistent knowledge base KB = { p ∨ q } and the augmented knowledge base (KB+),
mark all the correct options.

Under GCWA, KB+ is always consistent.

Under CWA, KB+ is always consistent.

Under CWA, KB+ is { p ∨ q,  ¬p,  ¬q }.

GCWA is a stronger version of the CWA.

GCWA agrees with CWA in the absence of disjunctions.

Accepted Answers:

Under GCWA, KB+ is always consistent.

Under CWA, KB+ is { p ∨ q,  ¬p,  ¬q }.

GCWA agrees with CWA in the absence of disjunctions.

4. Given the knowledge base KB = { p ∨ q ∨ r,   q,  ¬q ∨ r },
mark all the entailments of the KB when we use Generalized Closed World Assumption.

Neither q nor ¬q

Both q and ¬q

Neither p nor ¬p

Both p and ¬p

p

¬p

¬q

q

r

¬r

Accepted Answers:

¬p

q

r

5. Consider a KB containing atomic sentences of the form Edge(x,y) which states that node x is connected to node y.
Suppose there is a node called 'p' which is not connected to any other node.
Which properties of KB would necessarily entail ¬∃x Edge(x,p)?

Circumscription and Closed World Assumption.

Closed World Assumption only.

Domain closure and Closed World Assumption.

Circumscription only.

Accepted Answers:

Domain closure and Closed World Assumption.

6. For the given KB, identify the set of statements that define the minimal model for circumscription.

KB = {
∀x [ ( Student(x) ∧ ¬Ab(x) ) ⊃ Studies(x) ],
Student(jack),   Student(tim),   Student(kim),
jack ≠ tim,   jack ≠ kim,   tim ≠ kim,
¬Studies(jack),   ¬Studies(kim)
}

{ ¬Ab(kim), ¬Ab(tim), ¬Ab(jack) }

{ Ab(kim), ¬Ab(tim), ¬Ab(jack) }

{ Ab(jack), ¬Ab(kim), Ab(tim) }

{ Ab(tim), ¬Ab(kim), Ab(jack) }

{ Ab(kim), Ab(jack), ¬Ab(tim) }

{ Ab(kim), Ab(tim), ¬Ab(jack) }

{ Ab(tim), Ab(jack), ¬Ab(kim) }

{ Ab(kim), Ab(tim), Ab(jack) }

Accepted Answers:

{ Ab(kim), Ab(jack), ¬Ab(tim) }

7. Which of the following sets of statements are true in some model of the KB in question 6.

{ Studies(kim), Studies(tim), Studies(jack) }

{ ¬Studies(kim), Studies(tim), Studies(jack) }

{ ¬Studies(jack), Studies(kim), Studies(tim) }

{ ¬Studies(tim), Studies(kim), Studies(jack) }

{ ¬Studies(kim), ¬Studies(jack), Studies(tim) }

{ ¬Studies(kim), ¬Studies(tim), Studies(jack) }

{ ¬Studies(tim), ¬Studies(jack), Studies(kim) }

{ ¬Studies(kim), ¬Studies(tim), ¬Studies(jack) }

Accepted Answers:

{ ¬Studies(kim), ¬Studies(jack), Studies(tim) }

{ ¬Studies(kim), ¬Studies(tim), ¬Studies(jack) }

8. Which of the following sets of statements are true under Circumscription in the KB from question 6?

{ Studies(kim), Studies(tim), Studies(jack) }

{ ¬Studies(kim), Studies(tim), Studies(jack) }

{ ¬Studies(jack), Studies(kim), Studies(tim) }

{ ¬Studies(tim), Studies(kim), Studies(jack) }

{ ¬Studies(kim), ¬Studies(jack), Studies(tim) }

{ ¬Studies(kim), ¬Studies(tim), Studies(jack) }

{ ¬Studies(tim), ¬Studies(jack), Studies(kim) }

{ ¬Studies(kim), ¬Studies(tim), ¬Studies(jack) }

Accepted Answers:

{ ¬Studies(kim), ¬Studies(jack), Studies(tim) }

9. What is the Frame Problem in the context of Event Calculus?

The problem of deciding which fluents remain true or become true at future time instances.

The problem of determining the effects of stochastic actions.

The problem of determining which actions are needed to make a fluent true.

All of the above.

Accepted Answers:

The problem of deciding which fluents remain true or become true at future time instances.

10. Circumscribing a Simple Event Calculus KB with respect to the Happens predicate means

saying that effects of actions are only the ones stated in the narrative.

saying that the only events that happened are the ones stated in the narrative.

saying that some random effects of stochastic actions (like Spin) may happen.

saying that no action that is unstated in the narrative has happened.

saying that once an event has happened it cannot happen again.

none of the above.

Accepted Answers:

saying that the only events that happened are the ones stated in the narrative.

saying that no action that is unstated in the narrative has happened.