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Topic: The construction of a resolution proof using first-order log

Nkulu
posted 6/9/2012  18:43Send e-mail to userReply with quote
I have the following review question for my upcoming exam that I would like to have some help with. I have to answer the query "Mary only uses green apples to make pies" using resolution. My current knownledgebase and language is the following sentences:

Apple(a): a is a apple
Pie(π): π is a pie
Green(a): The apple a is green.
Red(a): The apple a is red.
J and M: J refers to the person John and M refers to the person Mary.
Grows(p,a): the apple a is grown by person p
Make(p,π,a): Person p makes a pie π with apple a.

Apples are either green or red:
for every(a) Apple(a) => Green(a) V Red(a)

John only grows green apples:
for every(a) Apple(a) A Grows(J,a) => Green(a)

Mary only uses apples from John to make pies:
for every(π,a) Apple(a) A Pie(π) A Make(M, π, a) => Grows(J,a)

CNF of the query:

⌐Apple(a) V ⌐Pie(π) V ⌐Make(M, π, a) V Green(a)

This are my steps in the resolution algorithm (see the picture in the link)

I don't know how to figure out how to deal with the ⌐Make(M, π, a) part of my sentence. How should I proceed?

 Picture of the resolution
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