Translate each of the following English sentences into first-order logic, using

Question

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 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 objec

1) “Every song that Gershwin wrote has been recorded on some album.” (Possibly different songs are recorded on different albums.)

2) “There is a single album that contains every song that Joe has written.”

3) “Joe owns a copy of an album that has Billie Holiday singing ’The Man I Love’.”

4) “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.)

5) “Joe owns a copy of every album on which all the songs are sung by Billie Holiday.

Explanation / Answer

For all y There exist x there exist z(Wrote(Greshwin,y)--->Sings(x,y,z)) For all y There exist x There exist z(Sings(x,y,z))--->Wrote(Joe,y)) There exist z There exist x(Owns(Joe,x) and (Copy(x,z)-->Sings(Billi Holiday,The Man I Love,z)) For all x For all z There exist y((Owns(Joe,x) and Copy(x,z) and Sings(McCartney,y,z)) 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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