1. 3 Logic
Translate the following four English sentences to first order logic (FOL). [4p]
1. Anyone passing his history exams and winning the lottery is happy.
2. Anyone who studies or is lucky can pass all his exams.
3. John did not study but John is lucky.
4. Anyone who is lucky wins the lottery.
(b) Convert them to conjunctive normal form (CNF). [6p]
(c) Answer the query “Is John happy?”. Use the resolution refutation algorithm. [5p]

2. 3 Logic
Translate the following four English sentences to first order logic (FOL). [4p]
1. Anyone passing his history exams and winning the lottery is happy.
2. Anyone who studies or is lucky can pass all his exams.
3. John did not study but John is lucky.
4. Anyone who is lucky wins the lottery.
(b) Convert them to conjunctive normal form (CNF). [6p]
(c) Answer the query “Is John happy?”. Use the resolution refutation algorithm. [5p]

3. 3 Logic
Translate the following four English sentences to first order logic (FOL). [4p]
1. Anyone passing his history exams and winning the lottery is happy.
2. Anyone who studies or is lucky can pass all his exams.
3. John did not study but John is lucky.
4. Anyone who is lucky wins the lottery.
(b) Convert them to conjunctive normal form (CNF). [6p]
(c) Answer the query “Is John happy?”. Use the resolution refutation algorithm. [5p]

4. 3 Logic
Translate the following four English sentences to first order logic (FOL). [4p]
1. Anyone passing his history exams and winning the lottery is happy.
2. Anyone who studies or is lucky can pass all his exams.
3. John did not study but John is lucky.
4. Anyone who is lucky wins the lottery.
(b) Convert them to conjunctive normal form (CNF). [6p]
(c) Answer the query “Is John happy?”. Use the resolution refutation algorithm. [5p]

5. 3 Logic
Translate the following four English sentences to first order logic (FOL). [4p]
1. Anyone passing his history exams and winning the lottery is happy.
2. Anyone who studies or is lucky can pass all his exams.
3. John did not study but John is lucky.
4. Anyone who is lucky wins the lottery.
(b) Convert them to conjunctive normal form (CNF). [6p]
(c) Answer the query “Is John happy?”. Use the resolution refutation algorithm. [5p]

6. CNF
First: Implication elimination

7. CNF
Then: drop the ”for all” quantifiers

8. CNF
Then: move the negation inwards

9. CNF
Then: distribute the ”ors”

10. CNF
Then: separate the ”and” sentences into individual sentences

11. Query and resolution refutation
Knowledge Base (KB)

12. Query and resolution refutation
The negation of our query

13. Query and resolution refutation
{x/John}

14. Query and resolution refutation
{x/John}

15. Query and resolution refutation
{x/John; y/HistoryExam}

16. Query and resolution refutation
{x/John; y/HistoryExam}

17. Query and resolution refutation
{x/John}

18. Query and resolution refutation
{x/John}

19. Query and resolution refutation

20. Query and resolution refutation