10 Syntactic Structure and Semantic Scope 10.1 Object Quantifiers and Quantifier Raising 10.1.1 Object Quantifiers and Scope Ambiguity So far we were concerned with sentences that contain just one quantifier, a quantifier that also oc- curs in just one position, the subject position. But quantified NPs may occur in a variety of other positions, e.g. the object position, and we may have more than one quantified NP in one clause: (1) a. Some girl liked every book. b. No girl liked every book. A problem with the derivation of (1) is that we have analyzed quantifiers as being of type D(et)t, and transitive verbs as being of type Deet. Obviously, these two meanings don’t go together — we can- not use functional application here. Another issue that appears when we consider sentences with more than one quantifiers is that such sentences often are ambiguous. For example, (1.a) has one reading in which it is stated that there is some girl x such that x read every book, and another reading that says that for every book y it holds that some girl read y. The latter reading is perhaps not very prominent, but it clearly exists for examples like the following: (2) Some girl or other liked every book. When we translate (1.a) into predicate logic, we can express the two readings as follows: (3) a. $x[G(x) Ù " y[B(y) ® L(x, y)]] b. " y[B(y) ® $x[G(x) Ù L(x, y)]] That is, the subject quantifier can have scope over the object quantifier, or the object quantifier can have scope over the subject quantifier. Often the reading with the subject quantifier having wide scope (over the object quantifier) is more natural, but there are many cases in which only the other interpretation makes sense: (4) a. A nanny brought most kids to the kindergarten. b. An American flag stood in front of every building. c. A member of the Expose the Right group attended every public event held in Iowa or New Jersey. (The New Republic, Feb. 19, 1996). We find such scope ambiguities with other operators as well. The following sentence can either mean that nothing that glitters is gold (wide-scope interpretation of all), or that it is not the case that everything is gold (wide-scope interpretation of negation). Of course, the idiom wants to express the second reading. (5) All that glitters isn’t gold. a. " x[Gl(x) ® ØGo(x)] b. Ø" x[Gl(x) ® Go(x)] © Manfred Krifka, Institut für deutsche Sprache und Linguistik, HU Berlin, WS 2000/200 Object Quantifiers by Quantifier Raising 160 Let us see how we can deal with object quantifiers and how we can express such scope ambi- guities. 10.1.2 Object Quantifiers by Quantifier Raising In section (8) we were concerned with the phenomenon that a quantifier can bind a pronoun, and we have proposed to deal with this phenomenon by a movement operation for quantifiers. To be spe- cific, we have assumed the following rule: (6) If [S...a NP,i...] is a sentence that contains an NP a with index i, then we can form the structure [Sa NP l i[S...ei...]] as input for semantic interpretation. And we called the resulting structure Logical Form (LF) and distinguished it from Surface Structure (S-Structure). Recall the interpretation rule for structures like l i[S...ei...]: (7) [l i[Sa ]] = l gáiÎ DOM(g), gÎ DOM([a ])ñl xÎ De[[a ](g[i/x])] This means that any trace or pronoun with the index i in a will be interpreted as x, which in turn creates a lambda term. Now, the rule for quantifier raising works for subject quantifiers as well as for object quantifi- ers. This allows us to treat cases with object quantifiers, as follows: S NP every book l 1 S S S NP VP NP VP NP VP Mary Mary Mary V NP V NP V NP 1 1 read every book read every book read e S-Structure Indexation Quantifier Raising (LF) The Logical Form then can be interpreted in the following way: (8) a. LF: [S [NP [Det every] [N book]] l 1[S [NP Molly] [VP read [NP e]1]]] b. [[NP [Det every] [N book]]] = l gl PÎ Det [l x[x is a book] Í P], = • c. [l 1[S [NP Molly] [VP read [NP e]1]]] = l gá1Î DOM(g)ñl x[Molly read g[1/x](1)], = l gá1Î DOM(g)ñl x[Molly read x], = ‚ d. [[S [NP [Det every] [N book]] l 1[S [NP Molly] [VP read [NP e]1]]]] e. = l gágÎ DOM(•), gÎ DOM(‚)ñ[•(g)(‚(g))] f. = l gá1Î DOM(g)ñ[[l PÎ Det [l x[x is a book] Í P](l x[Molly read x])] g. = l gá1Î DOM(g)ñ[l x[x is a book] Í l x[Molly read x]] This is the right result; it maps every assignment g (with 1 in its domain) to 1 if the set of books is a subset of what Molly read, and else to 0. © Manfred Krifka, Institut für deutsche Sprache und Linguistik, HU Berlin, WS 2000/200 161 Syntactic Structure and Semantic Scope We see that quantifier raising leads to a structure in which the object argument is a trace, of type e. If transitive verbs are of type eet, then expressions like [VP read [NPe]1] can be interpreted without any problem, by functional application: (9) [[VP read [NPe]1]] = l g[[read](g)([e1](g))] 10.1.3 Quantifier Raising and Scope Ambiguity Quantifier raising also allows us to treat scope ambiguities in case of sentences with two quantifi- ers. Notice that the raising rule (6) can be applied more than once if necessary. It does not say anything about the order in which different applications of the rule should be executed. This allows for the expression of scope ambiguities: (10) Indexed S-Structure: S NP1 VP somegirl V NP2 read every book Subsequent raising of first quantifier (two options): S S NP NP somegirl everybook l 1 S l 2 S NP VP 1 NP1 VP e somegirl V NP2 V NP2 read every book read e Raising of second quantifier: S S NP NP | | everybook somegirl l 2 S l 1 S NP NP somegirl everybook l 1 S l 2 S NP1 VP NP1 VP e e V NP2 V NP2 read e read e © Manfred Krifka, Institut für deutsche Sprache und Linguistik, HU Berlin, WS 2000/2009 VP-Ellipsis and Antecedent-Contained Deletion 162 Consider the way how the left-hand structure is interpreted: (11)a. [[S [NPe]1 [VP [V read] [NPe]2]]] = l gá1,2Î DOM(g)ñ[g(1) read g(2)], = • b. [l 1[S [NPe]1 [VP [V read] [NPe]2]]] = l gá1Î DOM(•), gÎ DOM(•)ñl x[•(g[1/x])], = l gá1,2Î DOM(g)ñl x[x read g(2)], = ‚ c. [[S [NP some girl] l 1[S [NPe]1 [VP [V read] [NPe]2]]]] = l gágÎ DOM(•), gÎDOM( ‚)ñ([[some girl](g)(•(g))], = l gá1,2Î DOM(g)ñ[l x[x is a girl] Ç l x[x read g(2)] ¹ Æ], = ƒ d. [l 2[S [NP some girl] l 1[S [NPe]1 [VP [V read] [NPe]2]]]] = l gá2Î DOM(g), gÎ DOM(ƒ)ñl y[ƒ(g[1/y])], = l gá1,2Î DOM(g)ñl y[l x[x is a girl] Ç l x[x read y] ¹ Æ], = „ e. [[S [NP every book] l 2[S [NP some girl] l 1[S [NPe]1 [VP [V read] [NPe]2]]]]] = l gÎ DOM(„)[[every book](g)(„(g))] = l gá1,2Î DOM(g)ñ [l y[y is a book] Í l y[l x[x is a girl] Ç l x[x read y] ¹ Æ]] We get the right result, a function from assignments g that maps g to 1 if the books are a sub- set of the things that were read by a girl, and false otherwise. 10.2 Evidence for Quantifier Raising In this section we will discuss some additional evidence for the idea that quantifiers undergo raising on a syntactic level of logical form. 10.2.1 VP-Ellipsis and Antecedent-Contained Deletion In section (8) we have discussed the phenomenon of VP-ellipsis, illustrated by the following exam- ples: (12)a. Leopold read the letter, and Molly did, too. b. Leopold read the letter before Molly did. Now, consider the following case, which exhibits what is known as antecedent-contained deletion: (13)Leopold read [NP every letter [CP that Molly did]]. What is remarkable here is that VP ellipsis occurs inside the object NP, which is every letter that Molly did. It has to be spelled out, of course, as ‘every letter that Molly read’. But notice that there is no antecedent VP that just consists of the verb read here; what we have is an antecedent read every letter that Molly did. But this certainly is not the proper antecedent; if we spell out did in (13) by read every letter that Molly did we get before Molly read every letter that Molly did. This cannot be the right result, of course, not the least because it again contains a VP ellipsis. But see what happens is we allow the object NP to undergo Quantifier Raising: © Manfred Krifka, Institut für deutsche Sprache und Linguistik, HU Berlin, WS 2000/200 163 Syntactic Structure and Semantic Scope (14) IP NP IP l 2 Det | N DP every | I' letter CP Leopold I 0 | VP3 C 0 2 read 1–PAST V NP | IP 1 2 | | that e e NP | I' Molly I0 | VP3 do–PAST V1 NP2 | | e e Here, the NP every letter that Molly did has undergone Quantifier Raising.