QUESTION

To solve this problem, you are free to use any formal method discussed in the lectures so far (including the truth table method). However, you are required to develop and to explicitly define your own logical constants; you are required to develop and to explicitly define your own logical constants;you are also required to write down, using these constants consistently, all the premises from the text that you choose to use in your proofs. Note that to answer the questions, it may not be necessary to encode all the information provided for you in the text; make sure that you do not mention in your solutions any premises that you do not use in your proofs.

For your birthday, you were given a cute chameleon (a type of lizard that can change color). You adore it, but you don’t know it well. After doinfg some research in the library, here’s what you have discovered:

Your chameleon can be in three moods: it can be happy, upset, or indignant; it can be in only one mood at any given time; in each mood, a chameleon takes on a specific color: in particular, when a chameleon is indignant or upset it turns purple;

Chameleons always become upset when they are hungry;

Chameleons always become indignant when they are busy eating and you suddenly start to pet them;

If the food bowl is empty then you can be sure your chameleon is hungry;

If the food bowl is not empty and a chameleon is hungry, it immediately engages itself in busy eating;

When a chameleon has slept enough it becomes happy.

The logical constants here are, for example, as follows:

Happy= "the chameleon is happy"

Upset="the chameleon is upset"

Indignant="the chameleon is indignant"

Purple="the chameleon is purple"

Hungry="the chameleon is hungry"

Busyeating="the chameleon is busy eating"

Pet="you are petting the chameleon"

Empty="the food bowl is empty"

We can translate some of the information from the text of the problem into the following logical sentences:

R1.happy=~upset&~indignant

R2.indignant|upset=purple

R3.hungry=upset

R4.empty=hungry

Let us prove both (a) and (b) using resolution (since we are allowed to use any legal method). By appliying INDO to the rules above, we can obtain the following clauses:

1. {~happy,~upset} From R1

2. {~happy,~indignant} From R1

3. {~indignant,purple} From R2

4. {~upset,purple} From R2

5. {~hungry,upset} From R3

6. {~empty,hungry} From R4

1. Suppose you see that the food bowl is empty: show that it follows from the data above that your chameleonnis not happy;
2. If your chameleon is not purple when you are petting it, is the food bowl empty? (show that your answer follows from the data above)

ANSWER

(a)Suppose you see that the food bowl is empty: show that it follows from the data above that your chameleon is not happy;

The additional premise here is:

7.{empty} Premise for 8a

The negated goal is:

8.{happy} Negated goal for 8a

Running resolution:

9.{hungry} Resolution:6,7

10.{upset} Resolution:5,9

11.{~happy} Resolution:1,10

12.{ }

(b)If your chameleon is not purple when you are petting it, is the food bowl empty? (show that your answer follows from the data above)

The additional premises here are:

13. {~purple} Premise for 8b

14. {pet} Premise for 8b

Let us prove that the food bowl is in this case not empty; then the negated goal is:

15.{empty} Negated goal for 8b

Running resolution:

16.{~upset} Resolution:4,13

17. {~hungry} Resolution:5,16

18. {~empty} Resolution: 6,17

19. {} Resolution: 15,18

Note that premise 14 was not used in the proof.