Question

First-Order Logic Knowledge Representation Exercise Set #3 Translate each of the following English sentences into first-order logic, using only the following constants and predicates... Constants: Joe- a person named Joe McCartney-a person named Paul McCartn 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" ey Predicates: CopyOffx,y) compact disk x is a copy of music album y ·Owns(x,y) . . personx 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(xy)-x and y are the same object

Answer 1

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))