### Artificial IntelligenceAIMA Exercises

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:
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 CD.)
12. Joe owns a copy of every album on which all the songs are sung by Billie Holiday.

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:
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 CD.)
12. Joe owns a copy of every album on which all the songs are sung by Billie Holiday.

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