| 1. | Analyze the sentences below in as much detail as possible. For the most practice using existentials, avoid using universals in your analyses. | |
| a. | Someone is missing. | |
| b. | No one found the loot. | |
| c. | There is a tavern in the town. | |
| d. | Some winner of the lottery has not come forward. | |
| e. | Tod watched a dance troop from India. | |
| f. | The search turned up no car fitting the description. | |
| g. | There is a button behind you that will open the door. | |
| h. | If Tom doesn’t find anything, he’ll be disappointed. | |
| i. | Al went to a restaurant no one he knew had heard of. | |
| 2. | Synthesize idiomatic English sentences that express the propositions associated with the logical forms below by the intensional interpretations that follow them. | ||
| a. | ∃x Bx | [B: λx (x is burning)] | |
| b. | (∃x: Px) Axd | [A: λxy (x is at y); P: λx (x is a person); d: the door] | |
| c. | (∃x: Fx) Rtx | [F: λx (x is a fire); R: λxy (x reported y); t: Tamara] | |
| d. | ¬ (∃x: Px ∧ Nxr) Kxs | [K: λxy (x knew y); N: λxy (x was in y); r: the room; s: Sam] | |
| e. | (∃x: Vx) (Tvx ∧ Sx) | [S: λx (x shattered); T: λxy (x touched y); V: λx (x is a vase); v: Vic] | |
| f. | ∃x (Hx ∧ Ljx) | [H: λx (x had happened); L: λxy (x left to deal with y); j: Jane] | |
| g. | ∃x (Fax ∧ Rbx) | [F: λxy (x forgot y); R: λxy (x remembered y); a: Ann; b: Bill] | |
| h. | (∃x: Fx ∧ Hx) Dix | [D: λxy (x detected y); F: λx (x was fast); H: λx (x was heavy); i: the instrument] | |