Artificial Intelligence - Propositional Logic

Knowledge Representation in Artificial Intelligence.

1. KNOWLEDGE REPRESENTATION
Dr.T.M.SARAVANAN
Associate Professor,
Department of Computer Applications,
Kongu Engineering College,
Perundurai –638 060.

2. Inferencerules
2

3. PROPOSITIONALLOGIC
25-08-2021

4. PROPOSITIONALLOGIC

5. PROPOSITIONALLOGIC

6. PROPOSITIONALLOGIC
Propositional Equivalences
TwostatementsXandYarelogicallyequivalentifanyofthe
followingtwoconditionshold−Thetruthtablesofeachstatement
havethesametruthvalues.
Thebi-conditionalstatementX⇔Yisatautology.

7. PROPOSITIONALLOGIC
Propositional Equivalences
TwostatementsXandYarelogicallyequivalentifanyofthe
followingtwoconditionshold−Thetruthtablesofeachstatement
havethesametruthvalues.
Thebi-conditionalstatementX⇔Yisatautology.

8. PROPOSITIONALLOGIC
Propositional Equivalences
According topropositional logicis the following atautology,
acontradictionor acontingent?
¬(A∧(¬B))↔(A→B)

9. PROPOSITIONALLOGIC
Write the following English sentences in symbolic form-
1. If it rains, then I will stay at home.
The given sentence is-“If it rains, then I will stay at home.”
This sentence is of the form-“If p then q”.
So, the symbolic form isp → qwhere-
p : It rains
q : I will stay at home
2. If I will go to Australia, then I will earn more money.
So, the symbolic form isp → qwhere-
p : I will go to Australia
q : I will earn more money

10. PROPOSITIONALLOGIC
Write the following English sentences in symbolic form-
3. He is poor but honest.
So, the symbolic form isp∧qwhere-
p : He is poor
q : He is honest
4. If a = b and b = c then a = c.
So, the symbolic form is(p∧q) → rwhere-
p : a = b
q : b = c
r : a = c
5. Neither it is hot nor cold today.
So, the symbolic form is∼p∧∼qwhere-
p : It is hot today
q : It is cold today

11. PROPOSITIONALLOGIC
Write the following English sentences in symbolic form-
6. He goes to play a match if and only if it does not rain.
So, the symbolic form isp↔ qwhere-
p : He goes to play a match
q : It does not rain
7. Birds fly if and only if sky is clear.
So, the symbolic form isp↔ qwhere-
p : Birds fly
q : Sky is clear
8. I will go only if he stays.
So, the symbolic form isp→ qwhere-
p : I will go
q : He stays

12. PROPOSITIONALLOGIC
Write the following English sentences in symbolic form-
9. I will go if he stays.
So, the symbolic form isp→ qwhere-
p : He stays
q : I will go
10. It is false that he is poor but not honest.
So, the symbolic form is∼(p∧∼q)where-
p : He is poor
q : He is honest
11.It is false that he is poor or clever but not honest.
So, the symbolic form is∼((p∨q) ∧∼r)where-
p : He is poor
q : He is clever
r : He is honest

13. PROPOSITIONALLOGIC
Write the following English sentences in symbolic form-
12. It is hot or else it is both cold and cloudy.
So, the symbolic form isp∨(q ∧r)where-
p : It is hot
q : It is cold
r : It is cloudy
13. I will not go to class unless you come.
So, the symbolic form is∼q→ pwhere-
p : I will go to class
q : You come
14. We will leave whenever he comes.
So, the symbolic form isp→ qwhere-
p : He comes
q : We will leave

14. PROPOSITIONALLOGIC
Write the following English sentences in symbolic form-
15. Either today is Sunday or Monday.
So, the symbolic form isp∨qwhere-
p : Today is Sunday
q : Today is Monday
16. You will qualify GATE only if you work hard.
So, the symbolic form isp→ qwhere-
p : You will qualify GATE
q : You work hard
17. Presence of cycle in a single instance RAG is a necessary and
sufficient condition for deadlock.
So, the symbolic form isp↔ qwhere-
p : Presence of cycle in a single instance RAG
q : Presence of deadlock

15. PROPOSITIONALLOGIC
Write the following English sentences in symbolic form-
18. Presence of cycle in a multi instance RAG is a necessary but not
sufficient condition for deadlock.
So, the symbolic form is(q → p)∧∼(p→ q)where-
p : Presence of cycle in a multi instance RAG
q : Presence of deadlock
19. I will dance only if you sing.
So, the symbolic form isp→ qwhere-
p : I will dance
q : You sing
20. Neither the red nor the green is available in size 5.
So, the symbolic form is∼p∧∼qwhere-
p : Red is available in size 5
q : Green is available in size 5

16. PROPOSITIONALLOGIC
1. Consider the statement about a party, “If it's your birthday or
there will be cake, then there will be cake.”
a)Translate the above statement into symbols. Clearly state which
statement isPand which isQ.
b)Make a truth table for the statement.
c)Assuming the statement is true, what (if anything) can you
conclude if there will be cake?
d)Assuming the statement is true, what (if anything) can you
conclude if there will not be cake?
e)Suppose you found out that the statement was a lie. What can
you conclude?

17. PROPOSITIONALLOGIC
1. Consider the statement about a party, “If it's your birthday or
there will be cake, then there will be cake.”
a)P:P:it's your birthday;Q:Q:there will be cake.(P∨Q)→Q
b)Hint: you should get three T's and one F.
c)Only that there will be cake.
d)It's NOT your birthday!
e)It's your birthday, but the cake is a lie.
2. Make a truth table for the statement(P∨Q)→(P∧Q).

18. PROPOSITIONALLOGIC
3. Make a truth table for the statement¬P∧(Q→P).What can you
conclude aboutPandQif you know the statement is true?
If the statement is true, then bothPandQ are false.
4. Make a truth table for the statement¬P→(Q∧R).
5.Determinewhetherthefollowingtwostatementsarelogically
equivalent:¬(P→Q)¬(P→Q)andP∧¬Q.P∧¬Q.Explainhowyouknow
youarecorrect.
6.ArethestatementsP→(Q∨R)and(P→Q)∨(P→R)logically
equivalent?