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Chapter 5
Composition Relations
In the discussion of natural reasoning in Chapter 4, we have noticed that natural lan- guage quantifiers do not realize the full set of combinatorial possibilities for scope depen- dencies predicted by their semantic type assignment as sets of properties. As a result, certain monotonicity inference substitutions that would be logically valid are not avail- able in natural reasoning. Furthermore, we have seen that the syntactic distribution of certain expressions depends on the semantic properties of other expressions in their syntactic environment, which act as licensors. In this part of the thesis, we investigate these phenomena in more detail switching the focus from natural reasoning inferences to the study of grammatical composition relations.
Linguistic composition is affected by several aspects of the constituents involved. In Chapter 6, we investigate logico-semantic properties of quantifier phrases, and how they influence their different scope behavior. In Chapter 7, we focus attention on the composition relations based on the sensitivity of an item with respect to a certain se- mantic property shared by other expressions called ‘triggers’. Following [Gia97], we consider the relation between a sensitive item and the trigger to be either a licensing or an antilicensing relation. From this it follows that a structure can be ungrammatical either because the sensitive item is not provided with the required property, or because it occurs in a context supplying the property the item is allergic to. Categorial Type Logic (CTL) helps us clarify these differences among composition relations and the ways scope elements interact.
The behavior both of quantifier phrases and sensitive items provides the informa- tion required to reach a classification of such expressions. These classifications can be thought of as reflecting distinctions within the domains of interpretation of the linguistic signs. By means of CTL we spell out the link between the subset relations holding at the semantic level and the way the interpreted items behave syntactically. Using our extended vocabulary of type-forming operators, the subset relations within semantic domains are captured by syntactic derivability relations between types. As a result, we gain a proof theoretical understanding of the syntactic licensing/antilicensing relations.
86 Chapter 5. Composition Relations
5.1 Two Sorts of Deviations
In her discussion of scopal possibilities [Sza97], Szabolcsi makes an important distinction between coherent and incoherent deviations, illustrated by the two examples below.
(1) a. Three referees read few abstracts. [Three > Few, *Few > Three].
b. Few referees read three abstracts. [Three > Few, Few > Three].
(2) a. *How didn’t Fido behave?
b. Who didn’t Fido see?
The difference between (1-a) and (1-b) shows that no incoherence results when few n takes scope over three N. This reading, though blocked in (1-a), is available in (1-b). The reason for this contrast is to be found on the syntax-semantic interface and has been described by saying that ‘counting’ quantifier phrases take scope locally [BS97], or in other words that they cannot have scope wider than where they occur overtly.
The sentences in (2) form a different case of deviation. The inability of the wh- phrase how to take scope over didn’t (2-a) is traditionally thought of as the effect of a syntactic constraint: the so-called weak island constraint of Ross [Ros67]. Recently, weak islands have been explained in terms of algebraic semantic characterizations of scope interaction [SZ97], which would explain the incoherence of the interpretation needed in (2-a) and the availability of it in (2-b).
Szabolcsi and Zwarts [SZ97] consider wh-phrases as items sensitive to weak islands, or more specifically, sensitive to the property of the scope elements which form the island. For instance, how is said to be sensitive to the weak island formed by didn’t and the extraction from it is blocked (2-a). Moreover, Szabolcsi and Zwarts show that different wh-phrases are sensitive to weak-islands of different strength.
In the Szabolcsi and Zwarts’ account, for a wh-phrase to take wide scope over some scope element (SE) the definition/verification of the answer involves specific operations associated with the SE. For instance, not corresponds to taking the complement of a set (¬), universal quantifiers are associated with intersection (∩), and existential quantifiers with union (∪). If the wh-phrase ranges over a semantic domain corresponding to an algebraic structure which is not closed under such an operator, it is unable to have scope over the SE. One could say that a wh-phrase is allergic to a property particular to the SE or more generally that it is sensitive to the weak-island formed by the SE. Briefly, the different distributional behavior of wh-phrases receives a semantic explanation: A classification of weak-islands and hence of the extractees can be given based on the properties of their domains of interpretation.
Let us illustrate this theory by looking at an example. From the fact that how ranges over manner adverbial which denote on an algebraic structure closed under ∪, namely semilattices (SL), it follows that how is sensitive to weak islands created by SEs involving ∩ and ¬ (e.g. it cannot have scope over universal quantifier and negation). Similarly, since how many ranges over numbers —lattices (LA) which are closed under ∪ and ∩— and who over individuals —boolean structures (BO) which are closed under ∪, ∩ and ¬ — it follows that how many is sensitive to SEs associated with ¬ (2-a), and who can extract from all weak islands (2-b). Note that since a set inclusion relation
88 Chapter 5. Composition Relations
In [Wou94], it is shown that a classification of both Dutch positive and negative polarity items can be given in terms of their sensitivity to (downward) monotonicity properties. The following examples illustrate their different relations with such functions. The monotone functions are emphasized, whereas the polarity items are underlined. We take weinig (tr. few), niemand (tr. nobody) and niet (tr. not) as representative of the sets DM, AA and AM, respectively; the determiner ook maar (tr. any) and the idiomatic mals (tr. tender) are examples of negative polarity items (NPIs) whereas allerminst (tr. not-at-all) and een beetje (tr. a bit) exemplify their positive counterparts. We indicate with % mildly ungrammatical sentences.
(4) a. %Weinig Few
monniken monks
zullen will
ook maar iets anything
bereiken. achieve.
[%DM > ook maar].
tr. Few monks will achieve something. b. Niemand Noboy
zal will
ook maar iets anything
bereiken. achieve.
[AA > ook maar].
tr. Nobody will achieve anything. c. Ik I
denk think
niet not
dat er that
ook maar iemand anybody
zal will
komen. come.
[AM > ook maar].
tr. I don’t think that anybody will come d. *Van Of
weinig few
monniken monks
was was
de the
kritiek criticism
mals. tender.
[*DM > mals].
tr. The criticism of few monks was tender. e. *De The
kritiek criticism
van of
vader father
abt abbot
was was
nooit never
mals. tender.
[*AA > mals].
tr. The criticism of father abbot was never tender. f. De The
kritiek criticism
zal will
niet not
mals tender
zijn. be.
[AM > mals].
tr. The criticism will be harsh.
(5) a. *Weinig Few
monniken monks
zijn are
allerminst not-at-all
gelukkig. happy.
[*DM > allerminst].
tr. Few monks are not-at-all happy. b. Weinig Few
monniken monks
zijn are
een beetje a bit
gelukkig. happy.
[DM > een beetje].
tr. Few monks are a bit happy. c. %Niemand Nobdy
is is
een beetje a bit
gelukkig. happy.
[%AA > een beetje].
tr. Nobody is a bit happy. d. Niemand Nobody
wil wants
nog still
Donne Donne
lezen. read.
[AA > nog].
tr. Nobody wants to read Donne anymore. e. *Jan Jan
wil wants
niet not
nog still
Donne Donne
lezen. read.
[*AM > nog].
5.3. Calibrating Grammatical Composition Relations 89
tr. Jan does not want to read Donne anymore.
From a comparison of the sentences in (4) and (5), it follows that positive polarity items (PPIs) mirror the behavior of their negative relatives. The whole picture is sum- marized in Table 5.2 taken from [Wou94]. The + and – indicate grammaticality and ungrammaticality, respectively.
Negation NPIs PPIs
Minimal (DM) Regular (AA) Classical (AM)
strong medium weak
mals ook maar hoeven (tender) (anything) (need)
strong medium weak
- – +
- – – allerminst een beetje nog (not-at-all) (a bit) (still)
Table 5.2: Polarity items distribution in Dutch.
Table 5.2 can be read as saying that NPIs are licensed, where PPIs are antilicensed by a certain property among the ones characterizing downward monotone functions. From this it follows that a NPI licensed by the property of a function in DM will be grammatical also when composed with any functions belonging to a stronger set. On the other hand, if a PPI is ‘allergic’ to one specific property shared by the functions of a certain set, it will be ungrammatical when composed with them, but compatible with any other function in a weaker set which does not have this property. In the next section we introduce the general method we will work out in detail in the next chapters to reach a CTL analysis of licensing and antilicensing relations.
5.3 Calibrating Grammatical Composition Relations
Our aim in the next chapters is to obtain a deductive account of the linguistic clas- sifications discussed above. In particular, we account for the scope deviations among quantifier phrases, and the licensing/antilicensing relations using modalities as ‘logical features’ controlling composition relations. We claim that a type logical approach sheds light on the distinction between (a) an element sensitive to the function which can taken it as argument, and (b) a functional expression sensitive to its argument, e.g. NPIs. Thus, in a function-argument structure the function can be either (a) the trigger or (b) the sensitive item. Moreover, in each case the sensitive item and the trigger can be either in a licensing or in an antilicensing relation. These distinctions call for a general definition of the ways in which linguistic expressions containing sensitive items are composed. Recall from Section 1.3 that linguistic signs are structured objects and their com- position is driven by the way their components interact. In particular, we can think of an expression as a pair consisting of a form component α, and a meaning component α′, represented as [αA : α′ a], where A and a are the syntactic and semantic types, re- spectively. Expressions with the same semantic type take their denotation in the same
5.3. Calibrating Grammatical Composition Relations 91
iii. A sign [α : α′] is in a incompatiblity relation with a sign [β : β′], if the relation below holds:
If [[β′]] ∈ P, then¬∃[γ : γ′] s.t. C([γ : γ′], [α : α′], [β : β′]).
iv. A sign [α : α′] is in an antilicensing relation with a sign [β : β′], if
[[β′]] ∈ P iff ¬∃[γ : γ′] s.t. C([γ : γ′], [α : α′], [β 1 : β 1 ′]).
We will alternatively say that a sign is licensed by the property which is licensor must have. Finally, as commented above in a function-argument structure, we can distinguish two cases:
(a) [α : α′] is an element sensitive to the property of a function, then in the points above M is such that β′^ has immediate scope over α′^ in γ′;
(b) [α : α′] is a function sensitive to the property of its argument, then in the points above M is such that α′^ has immediate scope over β′^ in γ′^2.
Remark 5.3. Some logical consequences derive from the definition above. In particular, if a sign [α : α′] is licensed by a sign [β : β′] that has a property P , it will be compatible (resp. incompatible) with any sign [β 1 : β′ 1 ] that has a property equal to or stronger (resp. weaker) than P. Similarly, if a sign [α : α′] is antilicensed by a sign [β : β′] that has a property P , it will be incompatible (compatible) with any sign [β 1 : β′ 1 ] that has a property equal to or stronger (resp. weaker) than P.
Intuitively, one could think of the composition of a sensitive item with a trigger as a relation which ‘must’ or ‘must not’ hold, and the grammatical and ungrammatical construction which follows as relations which ‘can’ or ‘cannot’ hold. Based on this definition we can identify the sensitive items and their triggers as below.
Definition 5.4. [Sensitive Items and their Triggers]
i. An expression A := [α : α′] is a sensitive item if it is in a licensing or antilicensing relation. ii. A sign B := [β : β′] is a direct trigger of A sensitive to P , if [[β′]] ∈ P and for any other stronger property P ′^ [[β′]] 6 ∈ P ′. iii. A sign B 1 := [β 1 : β′ 1 ] is an indirect trigger of A if [[β 1 ′]] ∈ P and also [[β′ 1 ]] ∈ P ′^ for P ′^ ⊆ P.
Let us now check how these definitions apply to the linguistic phenomena we have introduced in the previous section. In the case of Dutch negative polarity items, the relevant sets of licensors are identified by the properties of ‘antimorphic’, ‘antiadditive’
(^2) Note that the definition of antilicensing relation we propose differs from the definition given
in [Gia97] where it is seen as the negation of a licensing relation. Her definition of antilicensing relation correponds to what we refer to as incompatiblity relation: it is a negative information from which no positive relation can be derived.
92 Chapter 5. Composition Relations
and ‘downward monotone’, which we have represented as the sets AM, AA, and DM. A negative polarity item, licensed by a certain property, will have as direct triggers the expressions displayed in Table 5.1 as representative of the corresponding set.
Consider the weak negative polarity item ook maar (tr. any) which is licensed by ‘antiadditivity’. Let ook maar be represented by A := [α : α′]. For any function B := [β : β′] which belongs to a set stronger than or equal to AA ∃C := [γ : γ′] C(C, A, B); whereas for any function B 1 which does not belong to AA such C does not exist. For instance, niemand (tr. nobody) and niet (tr. not) are in AA and ook maar is grammatical when in construction with them, whereas weinig n (tr. few n) does not belong to AA and ook maar is not grammatical in its (immediate) scope. Moreover, niemand is a direct trigger whereas niet is an indirect one.
The definition of antilicensing relation can be illustrated by looking at (a) Dutch pos- itive polarity items and their relation with respect to monotone functions, and (b) the behavior of wh-phrases with respect to the scope elements forming weak-islands. The first case exemplifies Definition 5.2-(iva), whereas the second instantiates Definition 5.2- (ivb). A weak positive polarity item like nog (tr. still) is antilicensed by ‘antimorphicity’: it is incompatible with the characteristic function identifying the set AM, and is compat- ible with all the other functions building bigger sets. In other words, it is ungrammatical in construction with its triggers, but it is grammatical with the functions belonging to bigger sets and which are not in AM.
Similarly, in English the wh-phrase how many is antilicensed by the property of ‘having the complement operation’. Consequently, its application to scope elements which take their denotation over domains of elements having this property is undefined. Again, how many is compatible with the characteristic function identifying bigger sets, i.e. it can be in construction with elements belonging to bigger sets^3.
Finally, an example of an expression in a compatibility relation with a semantic property is given by the adverb almost which can modify universal quantifiers (8-a), but not the existential ones (8-b).
(8) a. Almost every student came. b. *Almost some student came. c. He almost missed the train.
Almost is compatible with the property ‘being universal’ and it is incompatible with the one of ‘being existential’. Note that the compatibility relation is weaker than the licens- ing one, since it does not require the item to be incompatible with all the expressions which do not have the property it is compatible with (8-c). Similarly, the incompatibil- ity relation differs from the antilicensing one, since it does not say anything about how the item behaves with respect to other weaker properties^4.
(^3) Note that, the subset relation holding among the algebraic structures is reversed when considering
the sets of the expressions which denote over them. For example, the set of the expressions with the property of ‘having the complement’ (which denote over BO) is smaller than the set of the expressions with the property of ‘having the intersection’ (which denote over LA). (^4) In [Gia99] the English negative polarity item any is claimed to be incompatible (accordingly to our
terminology) with veridicality. Therefore, it may be grammatical with nonveridical functions, but not necessarily with all of them.
