Consider a first-order logical knowledge base that describes worlds
containing people, songs, albums (e.g., “Meet the Beatles”) and disks
(i.e., particular physical instances of CDs). The vocabulary contains
the following symbols:
${CopyOf}(d,a)$ : Predicate. Disk$d$ is a copy of album$a$ .
${Owns}(p,d)$ : Predicate. Person$p$ owns disk$d$ .
${Sings}(p,s,a)$ : Album$a$ includes a recording of song$s$ sung by person$p$ .
${Wrote}(p,s)$ : Person$p$ wrote song$s$ .
${McCartney}$ ,${Gershwin}$ ,${BHoliday}$ ,${Joe}$ ,${EleanorRigby}$ ,${TheManILove}$ ,${Revolver}$ : Constants with the obvious meanings.
Express the following statements in first-order logic:
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Gershwin wrote “The Man I Love.”
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Gershwin did not write “Eleanor Rigby.”
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Either Gershwin or McCartney wrote “The Man I Love.”
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Joe has written at least one song.
-
Joe owns a copy of Revolver.
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Every song that McCartney sings on Revolver was written by McCartney.
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Gershwin did not write any of the songs on Revolver.
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Every song that Gershwin wrote has been recorded on some album. (Possibly different songs are recorded on different albums.)
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There is a single album that contains every song that Joe has written.
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Joe owns a copy of an album that has Billie Holiday singing “The Man I Love.”
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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 CD.)
-
Joe owns a copy of every album on which all the songs are sung by Billie Holiday.