I need help translating these FOL sentences, I am still getting fimiliar with it
ID: 3596486 • Letter: I
Question
I need help translating these FOL sentences, I am still getting fimiliar with it.
Translate each of the following English sentences into rst-order logic, using only the following constants and predicates ...
Constants:
• Joe — a person named Joe
• McCartney — a person named Paul McCartney
• Gershwin — a person named George Gershwin
• BHoliday — a person named Billie Holiday
• EleanorRigby — a song entitled “Eleanor Rigby”
• TheManILove — a song entitled “The Man I Love”
• Revolver — the music album entitled “Revolver”
Predicates:
• CopyOf(x,y) — compact disk x is a copy of music album y
• Owns(x,y) — person x owns compact disk y
• Sings(x,y,z) — music album z contains a recording of song y sung by person x
• Wrote(x,y) — person x wrote song y
• Equal(x,y) — x and y are the same object
Exercises:
1. “Gershwin wrote ’The Man I Love’.”
2. “Gershwin did not write ’Eleanor Rigby’.”
3. “Either Gershwin or McCartney wrote ’The Man I Love’.”
4. “Joe has written at least one song.”
5. “Joe owns a copy of Revolver.”
6. “Every song that McCartney sings on Revolver was written by McCartney.”
7. “Gershwin did not write any of the songs on Revolver.”
8. “Every song that Gershwin wrote has been recorded on some album.” (Possibly different songs are recorded on different albums.)
9. “There is a single album that contains every song that Joe has written.”
10. “Joe owns a copy of an album that has Billie Holiday singing ’The Man I Love’.”
11. “Joe owns a copy of every album that has a song sung by McCartney.” (Of course, each different album is instantiated in a different physical compact disk.)
12. “Joe owns a copy of every album on which all the songs are sung by Billie Holiday.”
Explanation / Answer
Solution:
1.Wrote(Greshwin, The Man I love)
2. Not Wrote(Greshwin, Eleanor Rigby)
3.Wrote(Greshwin, The Man I love) or Wrote(McCartney, The Man I love)
4.Three exist y(Wrote(Joe,y))
5. Owns(Joe,Revolver)
6. For all y(Sings(McCartney,y,Revolver) --> Wrote(McCartney,y))
7. For all y For all x(Sings(x,y,Revolver)--> Not Wrote(Gresshwin,y))
8. For all y There exist x there exist z(Wrote(Greshwin,y)--->Sings(x,y,z))
9. For all y There exist x There exist z(Sings(x,y,z))--->Wrote(Joe,y))
10. There exist z There exist x(Owns(Joe,x) and (Copy(x,z)-->Sings(Billi Holiday,The Man I Love,z))
11. For all x For all z There exist y((Owns(Joe,x) and Copy(x,z) and Sings(McCartney,y,z))
12. For all x For all z For all y((Owns(Joe,x) and Copy(x,z) and Sings(Billi Holiday,y,z))
Please, please upvote and ask your doubts in the comments.
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