11.7 Øvingseksamen 2 — temablokk-format (formell tyngde)

Sist du var her — de sju tingene fasitene bygger på, ferdig oppfrisket:

- Kvantorene parres fast: $\forall$ med $\rightarrow$, $\exists$ med $\land$. Parringen skifter aldri, heller ikke under negasjon.
- Nøkkelen skal stå der, med argumentplassene markert: «$E(x,y)$: $x$ sendte e-post til $y$».
- Ordnede par er ordnede. Skriv paret ned i riktig rekkefølge før du slår opp.
- Antall rader i en sannhetstabell er $2^n$, og hovedkonnektivet er det som blir stående når du dekker over parentesene.
- En nedovergående posisjon er en der slutningen går fra overmengde til delmengde, og forklaringen skal gis i mengdespråk.
- Et konseptuelt tre er komplett eller galt: GO krever et [Path], BE og STAY krever et [Place], og CAUSE krever et helt innfelt [Event].
- Situasjonstype avgjøres på hele verbfrasen, og klassen skrives etter trekkene.

Symbolene som brukes, står samlet i symbol- og formellisten nederst.

Exam paper — LING1100 practice set 2

Nyskrevet øvingseksamen — skrevet av oss for denne boka etter mønster fra materialet. Ingen oppgave er gjengitt fra et virkelig sett.

> Instructions. The paper consists of five Topics. Each Topic contains three questions. Answer exactly two questions in each Topic, so that you submit ten answers in total. Answering all three questions in a Topic gives you no extra credit.
>
> Time: four hours. No aids are permitted. Digital hand drawing is available for questions that ask for a diagram.
>
> You may answer in English or in Norwegian.

Symbol list

¬   negation                 ∧   conjunction              ∨   inclusive disjunction
⊻   exclusive disjunction    →   material implication     ↔   biconditional
⊨   entailment               ∀   universal quantifier     ∃   existential quantifier
{ } set                      ⟨ ⟩ ordered pair             ∈   set membership
⟦ ⟧ denotation               ∩   intersection             ∪   union       ⊆   subset

Topic 1 — Predicate logic and model theory

1.1 Translate each sentence into predicate logic. State your key first, marking the argument positions of every predicate.

(1) a.  Every curator emailed Mira.
    b.  Mira emailed some curator.
    c.  Someone emailed everyone.
    d.  No curator emailed themselves.

1.2 Consider the model $M = \langle D, F\rangle$ below, where C(x) means «x is a curator» and E(x,y) means «x emailed y». Determine the truth value of each formula in $M$. Show every lookup, and identify the individual or the ordered pair that settles the matter.

D      = { Iver, Jonas, Kaja }
F(C)   = { Iver, Kaja }
F(E)   = { <Iver, Kaja>, <Kaja, Iver>, <Jonas, Kaja> }

(i) $\forall x\,(C(x) \rightarrow \exists y\, E(x,y))$ (ii) $\exists x\, E(x,x)$ (iii) $\forall x \forall y\,(E(x,y) \rightarrow E(y,x))$

1.3 The sentence below is scope-ambiguous. Give both readings in predicate logic, give a paraphrase of each, and explain briefly what Quantifier Raising is supposed to do.

(2)  Every reviewer read a manuscript.

Topic 2 — Truth, entailment and inference direction

2.1 Set up the truth table for $(p \rightarrow q) \land (q \rightarrow p)$. Show that it has the same truth values as $p \leftrightarrow q$, state the truth conditions of the biconditional in words, and explain why the two expressions are equivalent.

2.2 For each pair below, decide whether the first sentence entails the second. Justify each answer with a test, and state what the inference is instead where it is not an entailment.

(5) a.  The council approved every application.
        >  The council approved some application.
    b.  Ida managed to submit the form.
        >  Submitting the form was difficult.
    c.  Yusuf is a bachelor.
        >  Yusuf is unmarried.
    d.  Three of the lamps were replaced.
        >  Not all of the lamps were replaced.

2.3 Show with a Venn diagram that the position after none of is downward entailing. Draw the diagram, state the subset relation explicitly, and explain the direction of the inference in set-theoretic terms. Digital hand drawing is available.

Topic 3 — Conceptual structure and compositionality

3.1 Explain the Principle of Compositionality, stating both of its parts. Give one example pair of your own in which the words are identical and only the grouping differs, and explain what the pair shows.

3.2 Draw a conceptual (Jackendoff) tree diagram for the sentence below. State the main function and the root category, explain what each node stands for, and say what a wrong alternative would have looked like. Digital hand drawing is available.

(7)  The waiter carried the tray from the kitchen.

3.3 Explain Jackendoff's two-tier analysis, and account for why the same conceptual functions are used for domains that have nothing to do with physical space. Give one example of your own from a non-spatial domain.

Topic 4 — Situation types, aspect and tense

4.1 Classify each of the sentences below for the features ±stative, ±durative and ±telic. Apply at least two diagnostic tests per sentence, state the Vendler/Dowty class, and state the tense.

(9) a.  Hedda knew the answer.
    b.  The climbers reached the summit.
    c.  Ola was assembling the shelf.
    d.  The tenants complained for weeks.

4.2 Explain the difference between tense and aspect, and use Reichenbach's three points to analyse the tense of (9c) and of the sentence Hedda had known the answer.

4.3 Show, with two example pairs of your own, how the verb phrase rather than the verb alone determines telicity. Explain in each case what changes the feature.

Topic 5 — Implicature, properties and Horn's principles

5.1 Explain the difference between conventional and conversational implicature. Give one example of your own for each, and state the test that separates them.

5.2 Name four of Huang's seven properties of conversational implicature, and explain each of them. Illustrate at least two with your own examples.

5.3 Explain Horn's Q-principle and R-principle, and account for how a Horn scale gives rise to a scalar implicature. Give one example of your own of a scalar implicature and set out the inference.

Etter settet

— naturlig pausepunkt —

Ta pause før du går videre til kap. 11.8. Det siste settet har et helt annet format, og det er verdt å møte med hvilt hode.

Slik bruker du settet best etter at du har skrevet det:

- Sammenlign tidsbruken med sett 1. Gikk de formelle blokkene raskere denne gangen? Da virker prosedyrene, og det er den eneste målingen som betyr noe.
- Se på tegneoppgavene. Fikk treet alle nodene, og fikk Venn-diagrammet en etikett på det fargede området? To små ting, og de er begge forskjellen på en figur og et svar.
- Tell hvor mange oppslag du faktisk skrev ut i modelloppgaven. Et svar som bare oppgir sannhetsverdiene, er halvt — også når verdiene er riktige.
- Legg merke til hvilken blokk du valgte bort mest i. Var det den samme som i sett 1, har du funnet ditt eget hull, og du vet hva du skal lese neste uke.