Solutions - Semantics

  1. For each of the following sentences, state whether it is ambiguous or not, and why. In particular, you should indicate what sort of ambiguity (if any) is present - word sense, syntactic structure, or a combination of the two. (Sentences c-f are supposed to have been actual newspaper headlines.)

    a. We saw her duck. Ambiguous - word sense and structural. duck could be a verb meaning to bob down, e.g. to avoid being hit, or a noun meaning an aquatic bird or a zero score in cricket or a kind of cloth, etc. Since the lexical categories of the two senses differ, structural as well as word sense ambiguity is present. The first version is:

    sees1(s1, agent[pro(w1, we1)], theme[duck1(agent[pro(h1, female1)])])

    and the second is something like

    sees1(s1, agent[pro(w1, we1)], theme[the<d1, &({duck1 duck2 duck3}(d1), owner(d1, pro(h1, her1)))>])

    It is also ambiguous as to whether "we" all saw her duck on a single occasion, or whether different ones of "us" saw her duck on a range of occasions. I'd call this a kind of scoping ambiguity, similar to what you'd get with Every person saw her duck.

    There is further ambiguity in the word saw which could be the past tense form of see, or the present tense of the verb meaning to use the cutting tool called a saw.

    b. A man stopped at every truck stop. Ambiguous - was it the same man that stopped at every truck stop, or different men at at least some of the truck stops?

    a(m1 : man1(m1), every(t1 : truckstop1(t1), stopsat1(m1, t1)))
    every(t1 : truckstop1(t1), a(m1 : man1(m1), stopsat1(m1, t1)))

    c. Killer sentenced to die for second time in 10 years. Ambiguous - structural - relating to attachment of the PP for the second time in 10 years. In one reading (the non-comical one) the PP attaches to sentenced - in the other reading the PP attaches to die.

    d. Teacher strikes idle kids. Ambiguous - the structure of the sentence depends on whether strikes is a plural noun meaning e.g. industrial action where the workers refuse to work (and the verb is idle) or strikes is a verb meaning "hit" (and idle is an adjective meaning something similar to "lazy").

    e. Prostitutes appeal to Pope. Ambiguous - word-sense only. Appeal to can mean to seek assistance from or seem attractive to.

    f. Squad helps dog bite victim. Ambiguous - like (d) but slightly more complicated. In one reading, dog bite victim is an embedded sentence, in which the verb is bite, and this embedded sentence is the complement of the verb helps. In the other reading, dog bite victim is a compound noun phrase, with dog and bite functioning as qualifiers of victim, and the NP is the object/theme of helps.

  2. Expand out the follwing ambiguous logical forms, giving a complete list of the full logical forms allowed by the ambiguous logical form:

  3. Simplify the following formulae using lambda reduction:

    lambda(X, p(X)) a reduces to p(a).

    lambda(X, X a) lambda(Y, q(Y)) reduces first to lambda(Y, q(Y)) a and then to q(a).

    lambda(X, (lambda(Y, p(Y)) X)) a reduces first to lambda(X, p(X)) a and then to p(a).

  4. Using the interpretation rules defined in Chapter 9 of Allen and shown in lectures, and defining any others that you need, give a detailed trace of the interpretation of the sentence The man gave the apple to Bert. In particular, give the analysis of each constituent and show its sem feature.

    Begin by listing the lexical entries for the words: apple, Bert, gave, man, the, to:

    n(sem(apple1), agr(3s))
    name(agr(3s), sem('Bert'))
    v(sem(give1), vform(past), subcat(np_pp:to), agr({3s, 3p}))
    n(sem(man1), agr(3s))
    v(sem(man2), vform(base), subcat(np), agr(3s))
    art(sem(the), agr({3s 3p}))
    p(pform(poss), sem(to-poss1))

    We will also be using some of the semantically augmented grammar rules from Grammar 9.3 in Allen (reproduced in the lecture notes), and extra ones for np → name, pp → p np, and vp → np pp:to:

    1. PP(pred(–), pform(?pf), sem(?semnp)) → P(pform(?pf) NP(sem(?semnp))
    2. VP(var(?v), sem(lambda(A4, ?semv(?v, A4, ?semnp, ?sempp)))) →
      V[_np_pp:to](sem(?semv)) NP(sem(?semnp)) PP(sem(?sempp))

    In this rule, A4 is a variable holding a place for the subject, and the ?semnp is the direct object while the ?sempp is the pp for the indirect object.

    The word the is parsed as an article using the lexical lookup. Similarly man is parsed as a noun (and also as a verb, but this version leads nowhere, so we shall ignore it). Both words have var features generated for them, but that for the is never used. Let the var feature for man be m1.

    Grammar rule 7 then interprets the noun as a cnp (common noun phrase) and inherits the var feature of the noun. At this point we have det(sem(the)) , n(sem(man1), var(m1)) and cnp(sem(man1), var(m1)).

    Grammar rule 6 combines the sems of the det and the cnp and the var of the cnp to build an np: np(sem(the<m1, man1(m1)>, var(m1)).

    Next the verb gave is looked up and gives rise to v(sem(past(give1)), var(ev1)).

    Then the words the and apple are in turn looked up, as were the and apple and give rise to (another) det(sem(the)), an n(sem(apple1), var(a1)), a cnp(sem(apple1)), var(a1)), and an np(sem(the(a1, apple1(a1)), var(a1)).

    The word to is looked up, giving a constituent p(sem(to-poss1)) (with an unused var feature).

    The word Bert is looked up, giving a constituent name(sem('Bert'), var(b1)).

    Rule 5 then interprets the name as an np, producing: np(sem(name(b1, 'Bert')), var(b1)).

    Rule 14 then combines this np with p(sem(to-poss1), pform(poss)) to produce
    pp(pred(–), pform(poss), sem(name(b1, 'Bert'))).

    Then rule 15 combines the V, the np(sem(the(a1, apple1(a1)), var(a1)). and the PP to produce vp(var(ev1), sem(lambda(A4, past(give1)(ev1, A4, the(a1, apple1(a1)), name(b1>, 'Bert'))))).

    Finally, rule 1 combines the np(sem(the<m1, man1(m1)>, var(m1)). with the VP to produce:

    s(sem(lambda(A4, past(give1)(ev1, A4, the(a1, apple1(a1)), name(b1, 'Bert')))  the(m1, man1(m1)) ))

    and the sem simplifies to

    past(give1)(ev1, the(m1, man1(m1)), the(a1, apple1(a1)), name(b1, 'Bert'))

CRICOS Provider Code No. 00098G