Monthly Assignment 3
LINC12 Fall 2024
November 25, 2024
Assignment due: Wednesday December 4, 23:59 on Quercus
Total points: 40
The following exercises must be completed by uploading a PDF document onto Quercus. This assign- ment covers material through the Thursday, November 21 lecture.
This assignment is worth 45 points altogether. It contains a variety of questions ranging from simple to difficult. It also includes problems that were presented as practice exercises. Refer to your notes from lecture for information on how to complete those problems.
If you work with anyone else, or discuss answers with your classmates, please indicate their names some- where on your returned answer document. This is so we know to expect similar answers. However, you should hand in your own unique work!
1 Quantificational Phrases (12 points)
1.1 Quantifiers in Set Relations (6 points)
The underlined phrases in the following sentences below can be analysed as quantifiers. For each of these sentences, write the truth conditions as a translation of the sentence in set notation.
(1) More than fifteen hundred transit workers are on strike.
(2) Vending machines have killed between 30 and 40 people.
(3) Twice as many people have been injured by subway turnstiles as have been injured by sharks.
1.2 Restricted Quantifier Notation (6 points)
The following sentences below contain phrases with quantifiers. For each of these sentences, write the truth conditions as a translation of the sentence using restricted quantifier notation.
(4) Several of the crows that Mei feeds bring her gifts.
(5) Most sailors from Glasgow sing.
(6) None of the anthropologists Chigozie knows like Chomsky.
2 Modal Flavour (10 points)
For each of the sentences below, describe two contexts: one where the modal verb most likely has an epistemic flavour, and one where it most likely has a deontic interpretation.
(7) The director must not see me.
(8) Jerome ought to be home by now.
(9) Bridgitte may vote on this motion.
(10) The marketing team should be working in the office on Friday.
(11) You have to know how to use Photoshop.
3 Truth Conditions for Modals (8 points)
Below you will find sentences that contain an underlined modal expression, as well as a context in italics that clarifies the flavour of the modal. For each sentence, write the verbose truth conditions of the sentence using our most recent analysis of modals.
(12) Sahar must finish the paperwork by Monday.
Context: Sahar has a new job and is required by HR tofill out paperwork about her address, payroll information etc.
(13) The HDMI cable might be somewhere in my desk.
Context: I am looking for a cable to connect my computer to a television, and I am trying to remember where it is.
(14) You should leave now to catch the last subway.
Context: I am at a party in apart of town I’m unfamiliar with, and I asked how I should get home and when.
(15) Piotr may have taken the bus to Montreal.
Context: Piotr is missing, and I am writing a description of events prior to his disappearance.
4 Translating Sentences with Modals into Predicate Logic (10 points)
Translate the following sentences containing modals into logical form (i.e. Predicate Logic). Remember our analysis of modals.
(16) All the mice might have escaped.
(17) If Sally is absent, then Lily should write a report.
(18) Chigozie may not submit her files to Ife.
(19) Henry might not find a job.
(20) If someone is sick or contagious, they should stay at home. (Treat “stay at home” as an intransitive predicate.)