Prove the following using Modus Ponens: The following story is from N. Wirth\'s

Question

Prove the following using Modus Ponens:

The following story is from N. Wirth's (1976) Algorithms + data structures = programs. I married a widow (let's call her W) who has a grown-up daughter (call her D). My father (F), who visited us quite often, fell in love with my step-daughter and married her. Hence my father became my son-in-law and my step-daughter became my mother. Some months later, my wife gave birth to a son (S_1), who became the brother-in-law of my father, as well as my uncle. The wife of my father, that is, my step-daughter, also had a son (S_2). Using predicate calculus, create a set of expressions that represent the situation in the above story. Add expressions defining basic family relationships such as the definition of father-in-law and use modus ponens on this system to prove the conclusion that "I am my own grandfather."

Explanation / Answer

Solution: 1. father (X,Y) ^ father (Y,Z) grandfather (X,Z)

2. father (X,Y) ^ married (Y,Z) father-in-law (X,Z)

3. father (X,Y) ^ mother (Y,Z) grandfather (X,Z)

4. father (X,Y) ^ father (X,Z) brother (Y,Z)

5. brother (X,Y) ^ grandfather (Z,Y) grandfather (Z,X)

6. married (I,W)

7. married (F,D)

8. father (I,S1)

9. father (I,D)

10.father (F,S2)

11.father (F,I)

12.mother (D,S2)

13.grandfather(I,S2)

USING 3:

9 ^ 12 grandfather (I, S2) (RESULT 1)

USING 4: 10 ^ 11 brother (S2,I) (RESULT 2)

USING 5: brother (X,Y) ^ grandfather (Z,Y) grandfather (Z,X) Result2 ^ Result1 brother (I , S2) ^ grandfather (I, S2) grandfather (I,I).

Therefore, I am my own grandfather.

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