In this problem set you will work with two of the problems from the FraCaS test suite. You will extend the grammar for Cooper storage, using the amended version.
1. (FraCaS problem 017).
a. Extend the grammar so that it covers the sentences
(i) an Irishman won the Nobel prize for literature
(ii) an Irishman won a Nobel prize
(iii) an Irishman won the Nobel prize
(iv) an Irishman won a prize
You may find the following code useful, though other solutions are possible:
Possibly helpful code "the Nobel prize for literature"
PP[+FOR, SEM=[CORE=<\P x.(P(x) & for(x,?np))>, STORE=?b1]] -> P[+FOR] NP[SEM=[CORE=?np, STORE=?b1]]
N[SEM=[CORE=<?pp(?n)>, STORE=(?b1+?b2)]] -> N[PHON='Nobel prize', SEM=[CORE=?n, STORE=?b1]] PP[+FOR, SEM=[CORE=?pp, STORE=?b2]]
Det[SEM=[CORE=<\Q P.exists x.(Q(x) & P(x) & all y. (Q(y) implies (y=x)))>, STORE=(/)]] -> 'the'
NP[PHON='literature', SEM=[CORE=<literature>, STORE=(/)]] -> 'literature'
N[PHON='Nobel prize', SEM=[CORE=<\x.(prize(x) & benefactor(x,Nobel))>, STORE=(/)]] -> NP[PHON='Nobel'] N[PHON='prize']
b. Show that your grammar will now obtain readings for all of these sentences.
c. Use Prover9 to show which readings of (i) entail a reading of (ii). Do all the readings of (i) entail all the readings of (ii). If not, why not?
d. Do the same for (i) and (iv)?
e. Use Mace to show that (i) does not entail (iii). Explain why the entailment does not hold.
2. (FraCaS problem 022)
a. Extend your grammar further so that it covers the sentences:
(v) no delegate finished the report on time
(vi) no delegate finished the report
You may find the following code useful (but other solutions are possible):
Possibly useful code for "no delegate finished the report on time"
VP[SEM=[CORE=<\x.(?v(?obj)(x) & exists e.(?v_e(e)(?obj)(x) & ?pp(e)))>, STORE=(?b1+?b2+?b3)]] -> TV[SEM=[CORE=?v, EVENT=?v_e, STORE=?b1]] NP[SEM=[CORE=?obj, STORE=?b2]] PP[+ON, PHON='on time', SEM=[CORE=?pp, STORE=?b3]]
PP[+ON, PHON='on time', SEM=[CORE=<on_time>, STORE=(/)]] -> P[+ON] NP[PHON='time']
TV[SEM=[CORE=<\y x.finish(x,y)>, EVENT=<\e y x.(finish_ev(e) & finisher(e,x) & finished(e,y))>, STORE=(/)]] -> 'finished'
NP[PHON='time', SEM=[CORE=<time>, STORE=(/)]] -> 'time'
b. Show what readings your grammar obtains for both of these sentences.
c. Use Mace to show that none of the readings of (v) entail any of the readings of (vi).
d. Use Prover9 to show which readings of (vi) entail a reading of (v). Possibly there is a reading of (vi) that does not entail (v). Which is it? Explain why the entailment does not hold? Does this reading agree with our intuitions about the meaning of the sentence?
3. a. Translate FraCaS problems 017 and 022 into your native language.
b. Do the entailment relations specified in these problems hold also for your translation?
c. You do not need to implement a grammar for your translations. However, discuss any problems you foresee in adapting the grammar you have developed in exercises 1. and 2. above to cover your translations.