- Convert the following knowledge base to conjunctive normal
form:
A AND B
B => (A OR C)
- Consider the following knowledge base:
A
B
NOT A
Does this knowledge base entail the following sentence:
B OR C
Justify your answer.
- Given a propositional-logic vocabulary with only four
symbols, A, B, C, D, how many models are there for the following
sentences? In other words, for each of those statements, determine how
many models that statement is true in. Note that each model is defined
by assigning boolean values to all four symbols A, B, C, D.
(a) (A and B) or (B and C)
(b) A or B
(c) A <=> B <=>C
- Textbook exercise 7.6 (second edition), exercise 7.8
(third edition)
- Textbook exercise 7.8 (second edition), exercise 7.10
(third edition)
- For some sentence S involving literals A, B, C, here is
the truth table:
| A |
B |
C |
Sentence |
| false |
false |
false |
true |
| false |
false |
true |
false |
| false |
true |
false |
false |
| false |
true |
true |
true |
| true |
false |
false |
false |
| true |
false |
true |
false |
| true |
true |
false |
false |
| true |
true |
true |
true |
Give a conjunctive normal form for sentence S.
- What is the negation of each of the following sentences?
1. for-every x, exists y: son(x) = y
2. for-every x, for-every y: son(x) = y <=> father(y) = x
In your answers, any "not" may only appear after the last appearance of
a universal or existential quantifier.
- Textbook exercise 8.8 (in both second and third edition).
- Consider the technique of propositionalization. For each
of the following two knowledge bases, decide if propositionalization
can be applied successfully. If not, why not?
KB 1:
for-every x: king(x) and greedy(x) => evil(x)
king(John)
greedy(John)
brother(Richard, John)
KB 2:
for-every x: king(x) and greedy(x) => evil(x)
king(John)
greedy(John)
brother(Richard, John)
king(father(John))
- Textbook exercise 9.19, parts (a), (b), (c) (second
edition), exercise 9.24, parts (a), (b), (c) (third edition).
