Question: I need help translating these FOL sentences, especially with 5 & 8-12.

Question

Question: I need help translating these FOL sentences, especially with 5 & 8-12.

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

1. “Gershwin wrote ’The Man I Love’.
Ans: Wrote(Greshwin, The Man I love)

2. “Gershwin did not write ’Eleanor Rigby’.”
Ans: Not Wrote(Greshwin, Eleanor Rigby)

3. “Either Gershwin or McCartney wrote ’The Man I Love’.”
Ans: Wrote(Greshwin, The Man I love) or Wrote(McCartney, The Man I love)

4. “Joe has written at least one song.”
Ans: Three exist y(Wrote(Joe,y))

5. “Joe owns a copy of Revolver.”
Ans: Owns(Joe,Revolver)

6. “Every song that McCartney sings on Revolver was written by McCartney.”
Ans: For all y(Sings(McCartney,y,Revolver) --> Wrote(McCartney,y))

7. “Gershwin did not write any of the songs on Revolver.”
Ans: For all y For all x(Sings(x,y,Revolver)--> Not Wrote(Gresshwin,y))

8. “Every song that Gershwin wrote has been recorded on some album.” (Possibly different songs are recorded on different albums.)
Ans:For all y There exist x there exist z(Wrote(Greshwin,y)--->Sings(x,y,z))

9. “There is a single album that contains every song that Joe has written.”
Ans:For all y There exist x There exist z(Sings(x,y,z))--->Wrote(Joe,y))

10. “Joe owns a copy of an album that has Billie Holiday singing ’The Man I Love’.”
Ans:There exist z There exist x(Owns(Joe,x) and (Copy(x,z)-->Sings(Billi Holiday,The Man I Love,z))

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.)
Ans:For all x For all z There exist y((Owns(Joe,x) and Copy(x,z) and Sings(McCartney,y,z))

12. “Joe owns a copy of every album on which all the songs are sung by Billie Holiday.”
Ans: For all x For all z For all y((Owns(Joe,x) and Copy(x,z) and Sings(Billi Holiday,y,z))

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