Prove the following using resolution refutation: The following story is from N.

Question

Prove the following using resolution refutation:

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

Answer

The set of expressions are as below:

In order to get the desired conclusion:

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)

Hence concluded that "I am my own grandfather."

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