Midterm Short Answer Portion
LINC12 Fall 2024
October 24, 2024
1 Implicatures (20 points)
1.1 Calculating Implicatures (10 points)
Below you will find two short dialogues, followed by an implicature that could be generated by each dialogue. Your job is to calculate how the implicature arises using Gricean reasoning. Formulate your calculations from the perspective of speaker (a).
1.1.1 Dialogue 1
(1) Context: Speaker A is friends with both speaker B, and their sibling, Sam. The two siblings are both students. Speaker A is asking about their semester.
a. Which courses are you and Sam taking this term?
b. I’m taking several psychology and linguistics courses. Sam has at least three courses.
Implicature: (B) does not know which courses Sam is taking.
1.1.2 Dialogue 2
(2) Context: Speaker B is tired, and walking home from work. They pass through a busy intersection, where an energetic public salesperson (speaker A) with a clipboard begins to follow them and ask questions.
a. Nice sweater! You seem like a fashionable person. Have you heard about the new store opening up a few blocks from here? I have coupons for 20% off on shoes! Where do you live?
b. I live in Antarctica.
Implicature: B wants the salesperson to leave them alone.
1.2 Implicature or not? (10 points)
Below are five sentences, followed by an inference. Determine whether or not this inference is an implicature of the sentence by performing a test and evaluating the results. Clearly state what test you are performing, and what the conclusion is.
(3) a. Some of my friends are vegetarian.
b. Inference: not all of my friends are vegetarian.
(4) a. Brìghde started teaching Gaelic this year.
b. Inference: Brìghde didn’t teach Gaelic before.
(5) a. Dalton called his mother and drive back to the reservation.
b. Inference: Dalton called his mother first, and then drove back, in that order.
(6) a. I know Chim came home some time late – must have been after midnight.
b. Inference: The speaker does not know exactly when Chim returned.
(7) a. My mother drove my car to the airport because hers broke down.
b. Inference:My mother drove to the airport.
2 Entailments and Presuppositions (12 points)
For the following pairs of sentences, decide whether the second sentence is an entailment of the first, or is a presupposition, or whether there is no relation. Support your answer by performing test(s), evaluating the results, and describing the conclusions. When there is no logical relation between two sentences, make sure you demonstrate this with entailment tests from both directions. When you can demonstrate entailment or presupposition, focus on showing the the second sentence is an entailment or presupposition of the first sentence.
(8) a. Virginia was unable to find my favourite restaurant again. b. Virginia had found my favourite restaurant before.
(9) a. Sandra and her aunt adore wildflower honey. b. Sandra’s aunt adores wildflower honey.
(10) a. Winter is especially harsh in the Maritimes. b. Winters are cold in the Maritimes.
(11) a. The texture of this dessert is oddly pleasing. b. The texture of the dessert is odd.
(12) a. It’s odd that Regina didn’t come into work today. b. Regina didn’t come to work today.
(13) a. Bjorn rushed home after work to practice accordion. b. Bjorn went home after work.
3 Speech Acts (5 points)
Below you are presented with a number of sentences. Your job is to identify, descriptively, the illocutionary force of these sentences if uttered in the real world, and then to classify this illocutionary force under one of Searle’s classes of illocutionary acts.
(14) Do you have any hot sauce?
(15) I’ll be home by 10pm.
(16) I’m so glad you could visit.
(17) Meeting adjourned.
(18) Let passengers exit the train first.
4 Truth Tables (18 points)
4.1 Filling in Truth Tables (4pts)
In the following truth table, there are missing values, represented by __. Fill these in to complete the truth table.
Note: in this presentation, the value of an expression (e.g. (p → r) ) appears under the connective, (e.g. → ). You can consider this to be a column containing that whole expression. For negation of a proposition (e.g. →r), the value appears under the connective (e.g. →) as well. As these columns are sub-parts of the larger expression, they will appear next to or inside of larger expressions, with the truth value of the entire formula being represented under the highest-level connective, in the centre of the table. Below, this is the biconditional.
4.2 Identifying Errors in Truth Tables (4 points)
In the following truth table, there are several errors. Identify these errors, and state what the correct value should be. This can be done by circling or crossing out the incorrect value and writing the correct one near it, or on the side connected by an arrow. Rows have also been numbered, so alternatively, you can answer descriptively in text in the following way, for example: “In row 4, the value for (p Λ r) should be F”
Note: in this presentation, the value of an expression (e.g. (p → r) ) appears under the connective, (e.g. → ). You can consider this to be a column containing that whole expression. For negation of a proposition (e.g. ¬r), the value appears under the connective (e.g. ¬) as well. As these columns are sub-parts of the larger expression, they will appear next to or inside of larger expressions, with the truth value of the entire formula being represented under the highest-level connective, in the centre of the table.
4.3 Using Truth Tables to identify Equivalence (10 points)
Are the following two formulas equivalent?
(19) a. (pΛr)∨¬(rΛq)
b. (¬p∨¬q)∨(¬p∨¬r)
To answer this question, first fill in the final two columns of the truth table below. (The beginning of the truth table with some relevant sub-formulas has been provided for you.) Then, state clearly in written form. whether or not the two formulas in (19) are equivalent, and identify any / which valuation rows in the table that lead you to this conclusion.
5 Predicate Logic and Models (20 points)
The questions in this section are about the following model, M1
• U = {Bjorn, Sam, Regina, Lemon, Basil, Laura, April}
[ b ]
M1 = Bjorn; [ s ]
M1 = Sam;
[
r ]
M1 = Regina; [ e ]
M1 = Lemon;
[
i ]
M1 = Basil; [ l ]
M1 = Laura;
[
a ]
M1 = April
• [ CAT IM1 = {Lemon, Basil}
• [ PERSON IM1 = {Bjorn, Sam, Regina, Laura, April}
• [ CHILD IM1 = {Sam, Regina, April}
• [ INTRODUCE IM1 = {〈Laura, Sam, Bjorn〉,〈Regina, Bjorn, Lemon〉,〈Regina, Basil, Lemon〉}
• [ LIKE IM1 = {〈Bjorn, Lemon〉,〈Bjorn, Basil〉,〈Regina, Lemon〉,〈Regina, Basil〉,〈Laura, Lemon〉}
• [ BITE IM1 = {〈Basil, Lemon〉,〈Basil, April〉,〈Basil, Laura〉}
• [ SLEEPY IM1 = {Sam, Regina, Lemon, Basil, April}
5.1 Evaluating Truth of statements relative to M1 (14 points)
Below are several statements, written in either plain English, or in the syntax of Predicate Logic. You should determine whether these statement are true in the given model, and say very briefly (one or two sentences) how you know, or where you looked to determine this.
1. |{x :〈[ i IM1 , x〉∈ [ BITE IM1}| ≤ 3
2. Laura likes every cat.
3. {x : (x ∈ [ CHILD IM1) V (x ∈ [ CAT IM1)} ∈ [ SLEEPY ]M1
4. Basil bit a child.
5. {x :〈[ i IM1 , x〉∈ [ BITE IM1 } C {x :〈x , [ i IM1〉∈ [ LIKE IM1}
6. INTRODUCE(r,s,e)
7. Only one childlikes a cat.
5.2 More work with M1 (6 points)
5.2.1
Write a new definition for a “know” relation in M1 that reflects those individuals that have been introduced to eachother.
5.2.2
Rewrite the definition of the LIKE relation in M1 so that Lemon likes all the children (everything else in the LIKE relation remains the same).
5.2.3
Lemon has started scratching people. Write a definition for a “scratch” relation where Lemon scratches at least three other individuals.