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# The Compositional Semantics of Modification

## Summary and Keywords

Modification is a combinatorial semantic operation between a modifier and a modifiee. Take, for example, vegetarian soup: the attributive adjective vegetarian modifies the nominal modifiee soup and thus constrains the range of potential referents of the complex expression to soups that are vegetarian. Similarly, in Ben is preparing a soup in the camper, the adverbial in the camper modifies the preparation by locating it. Notably, modifiers can have fairly drastic effects; in fake stove, the attribute fake induces that the complex expression singles out objects that seem to be stoves, but are not. Intuitively, modifiers contribute additional information that is not explicitly called for by the target the modifier relates to. Speaking in terms of logic, this roughly says that modification is an endotypical operation; that is, it does not change the arity, or logical type, of the modified target constituent. Speaking in terms of syntax, this predicts that modifiers are typically adjuncts and thus do not change the syntactic distribution of their respective target; therefore, modifiers can be easily iterated (see, for instance, spicy vegetarian soup or Ben prepared a soup in the camper yesterday). This initial characterization sets modification apart from other combinatorial operations such as argument satisfaction and quantification: combining a soup with prepare satisfies an argument slot of the verbal head and thus reduces its arity (see, for instance, *prepare a soup a quiche). Quantification as, for example, in the combination of the quantifier every with the noun soup, maps a nominal property onto a quantifying expression with a different distribution (see, for instance, *a every soup). Their comparatively loose connection to their hosts renders modifiers a flexible, though certainly not random, means within combinatorial meaning constitution. The foundational question is how to work their being endotypical into a full-fledged compositional analysis. On the one hand, modifiers can be considered endotypical functors by virtue of their lexical endowment; for instance, vegetarian would be born a higher-ordered function from predicates to predicates. On the other hand, modification can be considered a rule-based operation; for instance, vegetarian would denote a simple predicate from entities to truth-values that receives its modifying endotypical function only by virtue of a separate modification rule. In order to assess this and related controversies empirically, research on modification pays particular attention to interface questions such as the following: how do structural conditions and the modifying function conspire in establishing complex interpretations? What roles do ontological information and fine-grained conceptual knowledge play in the course of concept combination?

# 1. Introduction: Defining Modification

This overview is concerned with modification as a combinatorial semantic operation between a modifier and a modifiee; the topic will be addressed primarily from a formal semantic point of view. Modification can be defined as follows (see as well Dowty, 2003; McNally, 2016):

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The key point is that the modifier’s inclusion yields a complex unit that inherits the unsaturated logical type from the modifiee. For instance, a noun such as soup in 2a is usually considered an unsaturated one-place predicate of type $〈e,t〉$ (that is, a function from entities to truth-values) and thus denotes a set of entities. The modification by the attributive adjective vegetarian in 2a does not change this: the complex unit is again a one-place predicate denoting a set of entities. The only difference is that the truth-conditions for determining the relevant set now include an additional piece of information; namely, 2a denotes the set of entities that are both vegetarian and a soup.

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The same kind of reasoning can be applied to adverbial modification. Assuming an event semantics point of view (following Davidson, 1967; Parsons, 1990), 3a denotes a two-place predicate relating agents and preparation events (the type $v$ is presumed to comprise events). Again, the modification by the adverbial locative in the camper does not change this: the complex unit still denotes a relation between agents and preparation events, here amended by the condition that the relevant events take place in the camper.

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In terms of traditional syntactic theories such as X-bar theory, modifiers correspond to adjuncts (but see Section 3.1 for a different conception; note as well that the notional distinction between modification as a semantic and adjunction as a syntactic operation is well established in research, but not consistent). Adjunction is defined as a syntactic operation that preserves the structural complexity of the head constituent and can thus be considered the natural syntactic counterpart to type-preserving modification. As a consequence, modifiers usually allow for being iterated; see 4 for illustration.

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The given characteristics allow one to distinguish modification from both argument saturation and quantification. These two operations have in common that the resulting complex constituent does not inherit the logical type of the relevant head constituent. This is most obvious for argument saturation. For instance, the combination of prepare with an object such as a soup makes for saturating one of the verbal argument slots and, thereby, for reducing the arity of the verbal head by one. This reduction is sketched in 5 (based on the assumption that prepare denotes a three-place relation between theme, agent, and event and that a soup denotes a non-quantifying indefinite object of type $e$). For quantification, the relevant type change is illustrated by 6: the quantifying determiner head every is usually considered a function from predicates to a function from predicates to truth-values; accordingly, the combination with a nominal predicate such as soup yields a quantifying determiner phrase of a different type.

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As a syntactic consequence, the complex constituents resulting from argument saturation or quantification have a different distribution than their underlying parts. More concretely, the relevant operations cannot be iterated, as shown by the examples in 7 and 8.

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It is noteworthy that, according to the definition in 1, the modifiee must bear an unsaturated logical type. Examples such as 9 raise the question of whether this additional constraint is too strict (see McNally, 2016 for analogous cases and a similar argument):

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On the one hand, the adverbial unfortunately and the appositive relative clause who is sick seem to be modifiers: the adverbial describes the fact that the head chef of the Ritz-Carlton is sick as unfortunate, while the relative clause describes the head chef as being sick. On the other hand, the respective target constituents seem to bear saturated types: as indicated in 9, the adverbial would map a full-fledged proposition of type $t$ to another full-fledged proposition; similarly, the appositive would map an entity of type $e$ to an entity. In order to cover these cases as well, one could generalize the definition in 1 by dropping the requirement that the modifiee be unsaturated. However, this would raise new questions. For instance, according to propositional logic, negation maps a truth-value to its opposite truth value and would thus count as a modifying operation. Furthermore, under the assumption that the connective and bears the relational type $〈t,〈t,t〉〉$, even the simple conjunction of two sentences yields a construal that falls under the revised definition (compare $[[Peteriscooking]tandMaryisbaking.]t$). Both consequences run counter to usual assumptions. (Admittedly, the stricter definition is potentially problematic in an analogous way; compare predicate conjunction involving unsaturated types as in $Nomealis[[tasty]〈e,t〉andhealthy]〈e,t〉$.) Alternatively, one could rethink the combinatorics of the adverbial and the relative clause in 9 in a more principled way. From a descriptive point of view, it is fairly uncontroversial that they provide secondary non-at-issue information that does not contribute to the primary at-issue assertion of the given utterances. One of several indications is that this second information cannot be easily dissented with; correspondingly, reacting to 9a by No, this is not unfortunate and to 9b by No, he is not sick would be odd. Therefore, these examples call for a special treatment at the semantics-pragmatics interface anyway; see Potts (2005), Amaral, Roberts, and Smith (2007), Morzycki (2008), Liu (2012), Schlenker (2013), and Tonhauser, Beaver, Roberts, and Simons (2013) for discussion. It is not settled whether the adverbial and the relative clause in 9 should in fact be treated as true modifiers or whether the presumptive types are correct. This overview will keep agnostic to their proper integration within a general theory of modification and proceed by focusing on cases that more easily fall under definition 1.

Given the type-logical independence of the modifiee, modifier and modifiee are connected with each other in a comparatively loose way. However, this flexibility does not render the combinatorics of modifiers random. In fact, the crucial task is to identify the factors that jointly determine a modifier’s distribution and interpretation. The present overview aims to introduce corresponding essential questions and the answers that research on modification has given to them. Section 2 is concerned with the question of how to develop the given definition into a compositional analysis. The discussion focuses on a comparison between lexicon-based and rule-based approaches to modification and their respective (dis)advantages from a descriptive point of view. Section 3 is concerned with modification at the interfaces: Section 3.1 tackles the question of how structural conditions contribute to the interpretation of modifiers and thereby limit their combinatorial options in substantial ways. Section 3.2 zooms in on the semantics-pragmatics interface by exploring the question of how conceptual knowledge resources affect the combination of concepts as put forth by modification.

# 2. The Composition of Modifiers

Following the characterization from above, modification is essentially defined as an endotypical—that is, type-preserving—operation. This minimal condition leaves room for various kinds of implementations. Basically, there are two prominent strands of analysis (putting on hold both considerable variation in detail and further refinements; see the subsequent sections). According to the first type of analysis, modifiers are taken to be endotypical functors in virtue of lexical knowledge (see, for instance, Parsons, 1970; Thomason & Stalnaker, 1973; Montague, 1974). For concreteness, assume that they contribute functors from $n$-ary predicates to $n$-ary predicates; see the representations in 10 for an AP- and a PP-modifier. (Here and in the following, the contribution by the definite and the indefinite determiner is not spelled out, but glossed by def and indef respectively.) The argument vector $y→$ comprises potential argument slots of the target predicate besides the first one; accordingly, there is no additional argument slot for one-place target predicates, there is one for two-place target predicates, and so forth. As required by the definition of modification, these additional arguments are inherited by the resulting complex predicate without being affected by the modifier.

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As exemplified by 12 and 13, these meanings allow for a smooth combination with the target constituents as given in 11. Following standard assumptions, the NP-target here denotes a property of objects (see 12a) and the VP-target denotes a relation between agents and events (see 13a). Given that locatives such as in the camper are underspecified as to whether they locate objects or events, the specification of $x$ to an event variable in 13b only follows from the application to an eventive VP-target. This kind of type accommodation by an appropriate meet operation is technically not trivial; see Asher (2011) and Section 3.2 for an advanced implementation. (The representation of the verbal thematic arguments, that is, agent and theme, follows the so-called Neo-Davidsonian paradigm as proposed by Parsons, 1990.)

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In both cases, endotypicality follows from the lexical entry of the modifier’s head: in 10a, the adjective itself provides the appropriate functor type; in 10b, the preposition yields an endotypical functor after application to its internal argument (here provided by the camper). Hence, modification is a feature of the lexical endowment of certain linguistic expressions; in other words: certain expressions are considered born to project modifiers. This can be called the lexical approach to modification.

According to the second type of analysis, the modifier contributes a simple predicate, and thus is not made for modification by itself. Instead, its modifying function follows from a separate modification rule (see, for instance, Higginbotham, 1985; Partee, 1995; Heim & Kratzer, 1998; Larson, 1998; Chung & Ladusaw, 2006; Maienborn & Schäfer, 2011). One option to formulate such a rule is given by MOD in 14. If applied to a predicate as given in 15a, it yields the very same modifying meaning as assumed on the first analysis on lexical grounds; see 15b, which is identical to 10a above.

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In short, MOD involves a type-lifting and thereby makes the modifying expression a functor from $n$-ary predicates to $n$-ary predicates. Hence, endotypicality follows from the extra operation. This can be called the rule-based approach to modification.

The following sections aim at deepening the understanding of the combinatorics of modifiers from three angles. Section 2.1 will be concerned with the question of how to decide between the lexical and the rule-based approach to modification; this includes a discussion of the traditional classification of modifiers in terms of logical entailments. In Section 2.2, the role of the modified head for the complex modifier-head construction will be reconsidered. Section 2.3 calls attention to a third and, at first sight, radically different perspective on the composition of modifiers, namely, to proposals that conceive of modifiers as arguments.

## 2.1 Empirical Criteria for Deciding Between Lexical and Rule-Based Modification

The opposition between lexical and rule-based modification (although not always stated that way) has prompted many discussions over the last decades. This holds true in particular for adjectives, given that they (often) function both as predicates and modifiers; see Kamp (1975) and Siegel (1980) for early accounts and Heim and Kratzer (1998) for a textbook introduction. The following recapitulation aims at bringing out the essential ideas behind the main arguments.

Independently of empirical details, there is a trade-off between the options. On the one hand, the lexical approach allows for integrating modifiers via lexically driven standard functional application. As it spares an additional combinatorial mechanism, semantic composition can be kept uniform. On the other hand, the ruled-based approach seems to be conceptually more attractive. It better fits the intuition that in cases such as 11 both modifier and modifiee seem to do very much the same, namely, predicate a property of some entity. From this perspective, equipping the modifying expression with an additional predicative argument looks artificial. But what do empirical findings contribute to deciding between both types of analysis?

Direct predication provides one key source of evidence. The examples in 16 show that the modifying AP and PP from above can be also used for predication.

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The ruled-based approach to modification predicts this dual function without further ado: MOD takes the underlying constituents to be simple predicates and, thus, also of the appropriate type for predication proper. By contrast, the lexical approach must rely on additional assumptions, which certainly renders the lexical approach less elegant than the rule-based approach. One may assume that the relevant constituents bear flexible types: one for their predicative function, as in 17a, another one for their modifying function, as in 17b. Alternatively, one may assume that the modifying type in 17b is the only basic lexical type. Accordingly, however, direct predication must be said to license the closure of the vacuous predicate by some trivial property, for instance, by assuming application to a silent nominal meaning such as ‘entity’ in virtue of a corresponding binding by the copula, as sketched in 18. ($P$ ranges over functions of type $〈〈e,t〉,〈e,t〉〉$ here.)

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Note as well that APs and PPs can also function as arguments (see Section 2.3 for further discussion). Locative adverbials that depend on the argument structure of positional verbs are a plausible case in point; see 19 for illustration. Again, it is simpler to integrate such arguments as one-place predicates than as higher-ordered functors. Accordingly, the positional verb would be simply said to select a locative predicate that assigns the theme argument to its location, as sketched in 20.

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The second source of evidence relates to the question of whether the modification relation necessarily involves the property conveyed by the target constituent. In other words: is the target’s property compositionally relevant and thus part of the modifier’s lexical endowment, as suggested by the lexical approach to modification, or are the properties brought in by the modifier and its target compositionally independent from each other, as suggested by the rule-based approach? Corresponding discussions usually revolve around the three-way distinction between intersective, subsective, and intensional modifiers, which is based on characteristic entailment patterns (see Partee, 1995 and Kamp & Partee, 1995 for detailed introductions).

Intersective modifiers yield the intersection of the set of entities that fulfill the target’s property and the set of entities that fulfill the modifier’s property; compare the entailment schema in 21 and its exemplification in 22.

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Since the independence of modifier and modifiee is the hallmark of this type of modification, it goes very well with the rule-based approach: MOD as formulated in 14 predicts the relevant entailment pattern by its very setup. The lexical approach is not helpless either. In fact, a lexical entry such as 10a for vegetarian predicts a purely intersective behavior as well. However, the independence between the adjectival and the nominal property does not follow from the mechanism as such, but from the specific content of the adjective’s lexical entry (that is, the adjective specifies in an idiosyncratic way that the nominal target be integrated as a mere conjunct).

Subsective modifiers are characterized by their giving rise to the entailment pattern in 23. Hence, they cut out a subset of the entities described by the target constituent, which is on a par with intersective modifiers. However, in contrast to these, they do not require this subset to be also a subset of the entities described by the modifier.

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The given pattern is fulfilled by a wide range of modifiers; two typical examples are given in 24 and 25.

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These examples have in common that the truth-evaluation of the modifying property is relativized to information that is associated with the property provided by the target. The sources for this relativization are different. The modifying mild in 24 is a vague predicate (see Kamp, 1975 for an early discussion and Kennedy, 2011 for an overview). Therefore, whether some entity belongs to its extension or not, depends on a relevant comparison class; for the case at hand, this seems to be directly determined by the target’s property. Accordingly, 24 denotes the set of chilis that are mild for chilis. For 25, the subsective effect roots in the intuition that the modifier does not take its target entities as simple individuals, but relates to them under the particular role that they are assigned by the target predicate. Accordingly, 25 denotes the set of cooks that are passionate as cooks (see already Siegel, 1980 for the distinction between for and as). In addition, the example also has an intersective reading, where it denotes the set of individuals that are both passionate and a cook; under this reading, the second entailment in 25 would be valid. Subsective modifiers seem to provide good evidence for factoring the target contribution into the meaning of the modifiers and, thus, for a lexical approach to modification. The entries in 26 sketch the relevant relativization in terms of a parameter to the modifying predicate ($≈$ ‘mild for a $P$’) or the target entity ($≈$ ‘passionate as a $P$’). For passionate, the brackets around $P$ symbolize that the relativization is optional, which captures the ambiguity between subsective and intersective readings.

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Upon closer inspection, the conclusion in favor of the lexical approach to modification is less clear. On a purely theoretical level, one could argue in favor of new rules. Thus, MOD could be amended by the following variants, which, if combined with simple predicate meanings for mild and passionate, also yield representations as in 26.

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This shows that rule-based approaches are not as such incompatible with target-sensitive modification. However, one would have to assume a multitude of rules and, moreover, ensure that rules and simple predicates are paired in a correct way. In other words, the predicates themselves should be sensitive to what kind of MOD they combine with, which again tips the balance towards a lexical encoding of a modifier’s (non-)sensitivity to its target. While this line of attack is thus not very promising, there are more principled ways to question the lexical approach to subsective modifiers.

One can start with vague predicates. The argument above builds on the assumption that the comparison class is always determined by the modifiee; only this is a justification for factoring the modifiee’s contribution into the invariant semantics of the modifier. However, examples such as 28 show that this assumption is wrong (see Kennedy, 2007, (16), for an analogous example). The same chili can be said to be a spicy chili and not spicy for a chili without contradiction. The reason is that the modifying spicy in the first occurrence is not relativized to chilis, but to dishes in general.

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One can conclude that the comparison class for vague predicates is determined by contextual knowledge, the target property merely being the most obvious candidate. Hence, the relevant relativization can be captured by a contextual parameter $C$, which is compatible with both a simple predicate meaning for vague predicates and their integration as modifiers by intersective modification, as sketched in 29. The subsective effect follows from pragmatically identifying $C$ with whatever property comes in for $P$. (As $C$ in the given form is unrestricted, the approach begs the question of how to adequately restrict the range of specification options. For spicy chili in 28, for instance, $C$ is neither identified with the explicit target property nor specified randomly; in lieu thereof, the specification resorts to a superordinate category of the target.)

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For examples such as 25, repeated in 30, the strategy for reconciling the subsective behavior with an intersective analysis is different. The most prominent idea is to not intersect the modifying predicate with the target predicate itself, but with some mediating event predicate. This nicely captures the intuition that the modifier in 30 relates to the way the cook is cooking.

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In order to spell this idea out, one may act on the assumption that the nominal target involves an additional event predicate, as proposed by Larson (1998). A corresponding entry is given in 31 (building on standard representations for characterizing sentences as discussed, for instance, by Krifka et al., 1995; Mari, Beyssade, & Prete, 2013). This says that a cook is someone who cooks in all normal situations $s$ that are suitable for him cooking. Based on a simple predicate meaning as in 32 and MOD, passionate may now be said to relate either to the event or to the individual itself (glossing over the difficult question of how to compositionally implement this variance; see Larson, 1998 for a syntactic and Egg, 2005 for a semantic solution). The first option yields the subsective reading, as in 33a; the second option yields the intersective reading, as in 33b.

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So far, the rule-based approach via MOD promises a parsimonious and uniform analysis to modification. This interim conclusion can be strengthened by the observation that the relevant modifiers can be also used predicatively, including those with a subsective effect, as shown by 34.

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One may be puzzled by noting a preference for the intersective reading in 34b; that is, the cook is said to be passionate in general. This might suggest a principled distinction between the predicative and the modifying attributive use of passionate and thereby putting again the lexical approach to modification on the table. However, the more restricted interpretation of direct predication can be traced back to a compositional difference that is independent of the present discussion und roots in the key difference between direct predication and modification: in 34b, the predicate passionate takes the cook of the Ritz-Carlton as an argument of type $e$ in order to thereby saturate its bearer argument; therefore, direct predication amounts to argument saturation instead of modification (recall the discussion in Section 1). Correspondingly, passionate does not apply to the nominal predicate cook of type $〈e,t〉$ and its internal event component; plausibly, then, the event cannot be accessed directly and is, thus, compositionally opaque for the main predication.

Let us now turn to intensional modifiers. They map the set of entities picked up by the target predicate to a set of entities for which it is not entailed that they fulfill the original target predicate; compare the entailment schema in 35 and its exemplification in 36.

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Intuitively, the entailment does not go through because the modifiers make the truth-evaluation of the target predicate dependent on alternative worlds or times. In other words, the composition is not blind to the way the target predicate picks out a set of entities, but sensitive to its informational content, that is, its intension. The lexical approach to modification can easily capture this interference by an appropriate lexical entry; see 37, according to which the target predicate is said to hold in those worlds that comply with the allegations of some world, irrespectively of whether these allegations are correct or not. (In the spirit of modal logic, see Portner, 2009 for an introduction, $Rallegations$ is short for an accessibility relation that relates a world $w$ to those worlds $w′$ that are compatible with the allegations in $w$.) The combination with the intensionalized contribution by cook in 38a yields 38b, that is, the set of entity-world pairs $〈x,w〉$ such that $x$ is a cook in all those worlds that are compatible with the allegations of $w$. Notably, according to the given format, the intensional modifiers do not change the logical type of their target and thus comply with the general definition of modification as given in the introduction above: an expression of type $〈e,〈s,t〉〉$ is mapped to an expression of type $〈e,〈s,t〉〉$ (with $s$ as the type for worlds).

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The rule-based approach faces a serious challenge here. MOD as given in 14 unequivocally yields an intersective analysis and thus certainly fails to work. One may resort to an alternative rule; compare, for instance, $MODintens$ in 39, which gives us the right representation if combined with a simple predicative lexical entry such as 40 for alleged.

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However, this workaround is not without problems. First, and similarly to the discussion of introducing $MODvague/role$ as in 27 above, it runs the risk of proliferating adequate (intensional) MODs; for instance, former would need a relation to alternative times instead of worlds, and possible introduces rather existential than universal quantification. It therefore seems to be more parsimonious to tie this information to the lexical entries themselves than to extra rules. Second, evidence for simple entries such as 40 are (widely) missing. As it stands, it is an intensionalized predicate of worlds. This is conceptually feasible, as shown by 41a; however, the corresponding direct predication in 41b is odd.

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In fact, intensional modifiers such as alleged or former are generally considered ungrammatical in predicative position, irrespectively of the type of entity they apply to (but see below); compare 42.

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The most obvious conclusion is that these modifiers forbid the predicative use exactly because they bear a higher-ordered type that selects an intensional predicate, but not an individual. In other words, there would be an elegant type-based distinction between adjectives that allow for predicative uses and those that do not.

The upshot of the present section is threefold. On the one hand, the majority of cases can be handled within a rule-based approach to modification, which nicely reflects the idea that modification is a combinatorial process in its own right and, moreover, a process that largely builds on a lexical independence between modifier and modifiee. On the other hand, intensional modifiers, while being in line with the endocentricity requirement for modification, cannot be easily reconciled with a rule-based approach. This leads to the conclusion that modification cannot be reduced to a rule such as MOD. Finally, the type-logical distinction between simple predicates and higher-ordered functors that emerges from the converging evidence as provided by predicative uses and logical entailment patterns looks very promising. However, it is probably too simple, and this section concludes by briefly considering two prominent problems.

First, the question of whether role-based subsective readings should in fact be captured in terms of intersective modification highly depends on whether the relevant compositional details can be worked out properly and motivated on independent grounds. To assume that nouns may provide for compositionally accessible additional argument slots is clearly a severe encroachment upon their semantic setup; see McNally (2005) for a more general discussion of argument slots within modifiees. Furthermore, as will be discussed in Section 3.2, modifiers can induce meaning adaptations regarding their targets and thereby also question the putative compositional independence between modifier and modifiee.

Second, there are several adjective classes that question the correlation between the (non-)intensionality of adjectives and their use potential. Adjectives such as awake allow for predicative uses, as shown by 43a. The predicative use suggests that the adjective bear the type $〈e,t〉$; moreover, this simple assumption fully complies with the intuition that awake does not open an intensional context, but merely predicates of an individual the property of being awake. Then, however, there is no type-theoretical reason why MOD cannot apply and thereby render awake a fine prenominal attributive modifier; see (43b). Note as well that postnominal uses are again feasible, as in (43c). Given that this pattern is regular for formations with the prefix a-, a morpho-syntactic explanation instead of a semantic one seems likely; see Larson and Marušič (2004) for some remarks.

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So-called privative adjectives such as fake give rise to the entailment pattern in 44. As this pattern is a stronger variant of the condition given in 35, privative adjectives should be intensional modifiers that do not allow for predicative uses. However, they do, as shown by examples such as 45b (which, moreover, leads to the puzzling situation that the object under consideration should be simultaneously a stove and not a stove; see Partee, 2010 and Section 3.2 for discussion). Even for putatively indisputable intensional modifiers such as alleged, the data are more controversial than one might think; see the famous predicative example in 46 from Higginbotham (1985). Furthermore, on so-called sententialist accounts of intensionality (see, for instance, Larson, 2002), intensional adjectives such as alleged are not treated as true attributive modifiers, but as predicates taking a (partly silent) sentential complement; see the sketch in 47.

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The opposite situation seems to hold for (some) so-called relational adjectives such as technical, as shown by 48 (building on McNally & Boleda, 2004, (1)). They obey the inference pattern for subsective adjectives, but their predicative use is restricted; see Demonte (1999b) and McNally and Boleda (2004) for further discussion.

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In sum, once fine-grained differences among adjectives are taken into account, the regularities that shape their distribution and interpretation become fairly complex. So, despite the promising initial observations, the overall question of whether the dual function of adjectives actually supports the assumption of a rule-based approach to modification is still not settled.

## 2.2 Refining Intersective Modification: The Primacy of the Head

Intersective modification as defined in the previous section yields a conjunction of two predications of the same variable (irrespectively of whether lexicon-based or rule-based modification is used). Since conjunction is a commutative operation, the order of both predications does not play a role, as shown by 49.

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Hence the resulting logical form does not distinguish between the modifying predicate and the target predicate, which predicts them to have the same status. However, several observations question this symmetry and argue for keeping track of whether a property is contributed by the modifier or the target. For a start, reconsider the given example. At first sight, it looks fairly inconspicuous: the modifier-head construction denotes the set of $x$ that are both red and a fish, or, equivalently, both a fish and red. However, these paraphrases conceal the fact that both predicates play different roles here: fish provides the relevant referential anchor, while red predicates an additional property of these potential referents; in other words, the complex structure does not denote a set of colors, but a set of fishes. This suggests that modifier-head constructions inherit the referential force from the head by rendering the head property accessible for further computation.

The following contrast from Kamp and Partee (1995) points in the same direction from the angle of vague predicates.

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Combining the predicates giant and midget by intersective modification (as motivated in Section 2.1) invariably yields the conjoined predication in 51. However, intuitions clearly diverge from this equivalence. Most plausibly, in 50a, Sam is said to be a midget who is exceptionally large for a midget, whereas in 50b, Sam is said to be a giant who is exceptionally small for a giant. Following Kamp and Partee (1995) (see as well Keenan, 1974 or Chung & Ladusaw, 2006), the target head predicate provides the domain of potential referents relative to which the modifying predicate is interpreted. In other words, what falls under the head property depends on the global context ($C$ may contribute a fairy tale about midgets and giants, a scenario with tall basketball players, and so forth), and what falls under the modifying property depends on the local context that is provided by the explicit head (recall the identification of $C$ with the target property as discussed in Section 2.1). Notably, this asymmetry is specific to modification here. If, by contrast, both predicates contribute separate predications in a symmetric fashion, as in 52, the resulting sentence is not well-formed: under normal circumstances, both predicates are evaluated relative to the very same global context and thus yield a contradiction.

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A third illustrative case in point is provided by the quantificational contrast in 53. (The argument builds on a similar example and reasoning in Chung & Ladusaw, 2006, 340f. who attribute it to personal communication from Jim McCloskey.)

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According to standard assumptions (see, for instance, Heim & Kratzer, 1998), restrictive relative clauses and their nominal heads are combined via intersective modification, which yields for both 53a and 53b the representation in 54. However, the sentences are truth-conditionally distinct. For instance, let the scenario be that there are altogether 500 people, with equal numbers of men and women; out of these people, 15 are male cooks and 5 are female cooks. In this scenario, 53a is judged true, while 53b is judged false. Again, the reason seems to be that the head projects the property that provides the relevant domain for quantification; the modifying property, by contrast, is kept local and therefore does not contribute to the set of referents the quantifier pertains to. Thus, the partition relates to the men of the given scenario in 53a and to the cooks in 53b.

Informally, the illustrated asymmetry of modifier-head constructions may be captured in terms of the following Head Primacy Principle from Kamp and Partee (1995, p. 161) (designed, in particular, for cases such as giant midget).

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One may strengthen it by the following reformulation: the modifying predicate does not render its contribution compositionally accessible for operations above the modifier-head construction and is thus kept local; instead, the head predicate projects its constribution to the complex constituent and thereby makes it accessible for further compositional operations such as referential anchoring and quantification. This, in turn, also ensures that the global context determines the interpretation of the head itself.

It is not a trivial task to account for the primacy of the head in a formally precise way. A promising first step consists in distinguishing between referential and thematic arguments of predicates. (The referential argument represents what a predicate refers to, while thematic arguments are related to this referential argument by a specific semantic role; see Williams, 1981; Wunderlich, 1996; and Bierwisch, 1997 for a more general discussion.) Let us illustrate this line of thought by a refined analysis of the simple example in 56, repeated from 49 above.

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There are two crucial assumptions. First, the modifying predicate red is not considered a simple predicate anymore, but a relation between a bearer and a color, as indicated by 57. That is, adjectives are taken to both involve a referential argument for the property itself and a thematic argument for the bearer of the property. The assumption that adjectives introduce referential slots for properties is analogous to the Davidsonian assumption that verbs introduce referential slots for events; a corresponding ‘externalization’ is shown by nominalizations such as 58 (see Bücking, 2012b; Moltmann, 2013; Maienborn, 2015; McNally & de Swart, 2015 for discussion).

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Second, the referential argument of adjectives is closed at the phrasal boundary, which renders the bearer argument the compositionally active one; see 59. (This echoes the traditionally more or less tacit assumption that modifying predicates such as red are equipped only with an argument slot for the bearer of a certain property, not with one for the property itself; see Wunderlich, 1996; Baker, 2003.) In turn, the head constituent fish contributes a referential argument for a sort of animal. Intersective modification then yields a set of entities that are both a bearer of a certain color and a fish, as in 60. As desired, the resulting representation makes the distinction between colors and fishes transparent.

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In order to adapt this strategy to the other cases, one has to assume that giant, etc., contribute different kinds of meaning, depending on whether they function as heads or modifiers. Accordingly, giant, for instance, contributes a predicate of giants when used in head position, while it contributes a predicate of bearers of a certain size when used as a modifier. Similarly, cook in head position denotes a set of cooks, whereas the corresponding relative clause denotes a set of bearers that exemplify the property of being a cook. The general idea would be that the referential arguments that predicates such as giant or cook are endowed with get locally bound once the predicates are part of modifiers and therefore are not targeted by functional elements such as determiners. Admittedly, the underlying distinctions are less obvious in these examples than in the simple case red fish above and thus in need for clarification. However, the distinction between referential arguments on the one hand and the ascription of properties on the other seems to be intuitively on the right track (see, however, Chung & Ladusaw, 2006, Sect. 5 for a different perspective on the overall problem).

## 2.3 Reconsidering the Combinatorics: Modifiers as Arguments?

The endocentricity requirement of modification is primarily based on the intuition that modifiers are not called for by their modifiees and thus do not contribute to a modifiee’s argument structure. However, there are also proposals that, by contrast, conceive of (certain) modifiers as arguments and thus seem to fundamentally oppose conventional wisdom. The most prominent representative of such an approach is probably McConnell-Ginet (1982). (See as well Pollard & Sag, 1987; Landman, 2000; Dowty, 2003; Beaver & Condoravdi, 2007; or Asher, 2011; however, their motivations and implementations partly differ considerably from McConnell-Ginet’s proposal.) Her argument-based approach aims at covering a wide range of adverbial examples. For the present purpose, the focus will be on examples such as 61 (which build on McConnell-Ginet, 1982, (41a)/(37b)).

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Her basic idea and its motivation can be recapped as follows (see as well Schäfer, 2013, ch. 6.2; Morzycki, 2016, ch. 5.4.1 for summaries).

First, McConnell-Ginet points out that verbs may obligatorily select for adverbials; see the examples in 62 (building on McConnell-Ginet, 1982, (43)/(45)). The examples are either ungrammatical without an adverbial (see 62a), or, the lack of an adverbial yields a specialized meaning of the verb that is different from the intended general one (see 62b). Moreover, according to standard assumptions, location verbs such as stand in 63 (= 19 in Section 2.1) select for their locative adverbials.

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There is, therefore, nothing conceptually wrong with assuming argument slots for adverbials. This suggests that adverbials could be treated as verbal arguments more generally, whether they are obligatory as in 62 or optional as in 61.

Second, modifiers such as quickly and arguments block entailments in a parallel way (see McConnell-Ginet, 1982, 162f. for the following scenarios; see as well Larson, 1998, 2002). Let a world be such that everyone who is walking is also talking and vice versa, so that runners and talkers comprise the same entities in a given situation; see 64a-i (where $〚iswalking〛w={x:xiswalkinginw}$, etc.). Nevertheless, 64b is not entailed by 64a-ii in this situation.

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The intuitive reason is that quickly in 64a-ii specifies some internal aspect of the scullion’s walking, namely, the speed, and that this specification does not automatically carry over to other kinds of action such as the talking in 64b, irrespectively of whether the agents of both types of actions are the same in a given situation. Crucially, an analogous explanation holds true for arguments. Let a world be such that cooks and eaters are the same in a given situation, as indicated by 65a-i. Again, 65b does not follow from 65a-ii, because the specification of some internal aspect of the scullion’s cooking, here, the specification of the theme argument, does not carry over to his eating.

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Notably, the given explanation opposes an intensional solution to the puzzling lack of entailment: the reason for the patterns in 64 and 65 is not that, in other situations, talkers and walkers, or cooks and eaters, can refer to distinct entities. Instead, the relevant entailments do not go through because internal aspects of the relevant events can differ from each other, even if the events as such coincide in a given situation. This is further corroborated by the observation that adverbials such as quickly do not give rise to opacity effects, which would be surpring under an intensional analysis. For instance, given the premises in 66a, 66b is entailed; that is, co-extensional expressions can be substituted for each other salva veritate.

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In order to implement her idea that certain modifiers contribute a special kind of verbal argument, McConnell-Ginet proposes that verbal meanings provide for inactive argument slots for internal specifications that are activated when an appropriate modifying adverbial is encountered. This activation is achieved by an augmentation function that increases the verbal meaning by an additional argument slot for the adverbial. Let us make this implementation concrete within a Davidsonian event semantics; see Morzycki (2016, ch. 5.4.1) for a similar perspective. (Notably, an event semantics treatment runs counter to McConnell-Ginet’s original proposal; however, it facilitates a comparison with the standard Davidsonian perspective on adverbial modification by abstracting away from ontological differences and focusing on the combinatorial contrast.) Corresponding standard entries for the verb and the adverbial are given in 67; the adverbial is taken to denote a simple predicate (as in the rule-based approach to modification).

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The combination of both meanings then licenses an augmention function such as that sketched in 68. It transforms an $n$-ary verbal meaning into an $n+Qmanner$-ary verbal meaning, that is, it augments the verbal event predicate by an additional argument slot for a predicate of a manner of the event, as exemplified by 69 (see Piñón, 2008; Schäfer, 2013 for a general discussion of manners). This can be smoothly combined with the adverbial meaning, yielding 70, which, as desired, denotes the set of talking events by $x$ that unfold in a quick manner.

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The proposal captures the intuition that adverbials such as quickly in 61a specify some internal aspect of the target event, namely, the way it unfolds. Furthermore, since the argument slot for the manner predicate is only created in the course of combining the meanings of the verb and the adverbial, the proposal also keeps track of a distinction between ordinary ‘given’ arguments and ‘silent’ ones that must be activated during composition. Therefore, the solution even complies with the endocentricity requirement for modification: the integration of the adverbial both creates and cashes the relevant argument slot, so that the resulting complex phrase is of the same arity as the original verb; see the representations in 67a and 70, which are both of type $〈e,〈v,t〉〉$. In this sense, the given implementation is not fundamentally different from the lexical and rule-based approaches to modification. In fact, one may conceive of AUG as a special kind of MOD. It does not lift the modifier but the modifiee; moreover, instead of merely conjoining two predicates, it introduces an additional relating component between the predicates. More specifically, the modifiee must be a predicate of events that have manners as part of their internal structure, and the modifying adverbial must contribute a property that may reasonably specify such manners. This raises the follow-up question of what kind of grammatical, lexical, and conceptual information licenses functions such as AUG and constrains their application in a systematic way. A full-fledged answer to this question is beyond the scope of this introduction to modification. However, the challenges to modification at the interfaces as addressed in Section 3 relate to corresponding issues in crucial ways, irrespectively of whether the discussion is explicitly linked to McConnell-Ginet’s point of view or not.

# 3. Modification at the Interfaces

## 3.1 Modification at the Interface Between Semantics and Structure

Numerous findings suggest that structural conditions affect the interpretation and distribution of modifiers in crucial ways. Of particular interest are correlations between a modifier’s position or structural integration and its interpretation, as illustrated by the adverbial examples in 71–73, which are adapted from prominent examples from the literature (namely, Jackendoff, 1972, (3.1), (3.3); Jackendoff, 1972, (3.6)–(3.8), (3.11)–(3.13); Maienborn, 2003, (9a)). 71 shows that the epistemic modifier certainly is fine in initial position, but excluded from the clause-final position, whereas the degree modifier completely behaves the opposite way. Moreover, if both are projected in an intermediate position between the auxiliary and the main verb, their order is fixed. The examples in 72/73 are particularly revealing, because they show that the same (kind of) adverbial receives different interpretations, depending on its integration site: cleverly in 72 yields a manner reading in the clause-final position and a subject-oriented (or a manner) reading in the intermediate position. The verb-adjacent locative in the steamer in the German clause 73a yields an event-internal interpretation and thus locates the chili, not the whole event, whereas the locative in the camper, which precedes the whole verbal phrase, yields an event-external interpretation and thus locates the preparation holistically. (Correspondingly, 73b is odd because preparations usually do not take place in a steamer.) Overviews of adverb classifications are given in, for instance, Bonami, Godard, and Kampers-Manhe (2004) and Maienborn and Schäfer (2011).

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Notably, structure-related observations are ubiquitous. For instance, not only simple adverbials but also full adverbial clauses are subject to structure-sensitive effects: the initial, prosodically separate dependent while-clause in 74 suggests an adversative reading, whereas its occupying a final, prosodically integrated position suggests a temporal reading (see Haegeman, 2004). The examples in 75 and 76 are indicative of structural constraints in the nominal domain (see Alexiadou, Haegeman, & Stavrou, 2007, Part III, ch. 1 for an overview): according to 75, the epistemic attributive modifier must precede the completive one, which is on a par with the restriction on corresponding adverbials above; according to 76, attributive modifiers are ordered along a scale such as ‘evaluation $>$ size $>$ color $>$ origin $>$ material.’

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Another much-discussed topic is the opposition between prenominal and postnominal uses of adjectives and its role for interpretation. This is particularly true for the Romance languages; see, for instance, Bouchard (2002) and the contrasts in 77 and 78. The first contrast is reminiscent of the distinction between intersective and subsective interpretation as discussed in Section 2.1, while the second contrast can be captured in terms of a distinction between restrictive and non-restrictive modification; recall the remarks on non-restrictive appositive relative clauses in Section 1. It is also noteworthy that there are language-specific case studies on the relation between adjectives and adverbs, including a discussion of their structure-dependent range of interpretations; see, for instance, Torner (2007) on qualitative adjectives and their adverb counterparts in -mente in Spanish.

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Finally, the interpretation of a modifier can also be module-dependent, that is, hinge on whether the modifier is integrated by morphological or syntactical means. For instance, the phrasal modification in 79 yields an ordinary descriptive interpretation, whereas its lexical counterpart has a naming function and thereby contributes to a complex concept that apparently deviates from the descriptive interpretation (see Olsen, 2012 for an overview; the interaction between adjectival order and concept formation is discussed by, for instance, Bouchard, 2005).

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There are two major theoretical angles from which this structure-sensitivity can be approached. According to the first angle, modifiers are integrated as specifiers to rigidly ordered functional heads and thus conceived of as integral parts of ‘cartographic’ structural hierarchies (see Alexiadou, 1997; Laenzlinger, 1998; Cinque, 1999, 2010 for prominent representatives and Hole, 2015 for a general overview). Given a right-branching structure, the ordering restriction as observed for the example in 71b follows from the assumption that the epistemic head projects in a hierarchically higher position than the completive aspectual head; compare the sketch in 80.

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According to the second angle, modifiers are adjuncts and thus not bound to ordered heads (see Ernst, 2002; Haider, 2000, 2004; Frey, 2003). Their distribution is derived from (the interaction of) other factors, whether compositional principles at the syntax-semantics interface, lexical or phonological information, or processing effects. More specifically, the ordering restriction for 71b could be explained as follows: completely modifies the degree to which the ignoring holds and, thus, must relate to an internal component of the verbal event such as its intensity scale. By contrast, certainly modifies the degree to which the speaker commits to the truth of the given proposition and thus must relate to the proposition as a whole. The ordering *completely certainly is, then, ruled out because the integration of the epistemic certainly enforces the raising to a proposition, which is the wrong type for the event-sensitive completive adverbial. This reasoning, of course, acts on the assumption that one cannot easily go back from a proposition to its underlying event description. More generally, one may assume a hierarchy of semantic types such as in 81, amended by an incrementality principle that forbids access to lower type domains once their composition is completed; compare for variants of such a system Haider (2000) and Ernst (2002).

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The adjunct approaches differ in the question of how (and of how rigidly and fine-grainedly) domains and structural conditions are mapped onto each other. For instance, Frey (2003) is known for promoting genuinely syntactic factors. He argues for relating adverbial classes (in German and English) to syntactic base positions that are determined by structural conditions holding between adverbials and (the position of) other parts of a sentence such as the verb or arguments. The rule in 82 for event-internal adverbials (such as manner adverbials, event-internal locatives, or degree adverbials) exemplifies the approach. It, for instance, correctly predicts the verb adjacent position of the internal locative in the German middle field as in 73a and the clause-final position of both manner and degree adverbial in English as in 71a/72a. The structural sketches in 83 show that either the main predicate itself or its trace ensure the compliance with the given rule.

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Remarkably, the adjunct-based perspective and, in particular, syntactic regularities such as 82 have stimulated a general structure-sensitive approach to modification as a semantic operation. Based on Maienborn (2001, 2003), Bücking (2012a), and Schäfer (2013), the modification rule from 14 for intersective modification can be refined to the rule MOD* in 84. Crucially, MOD* introduces a free variable $v$ that mediates between modifier and modifiee. The mediation proceeds via a relation variable $R$ that is either the identity function or a relation that pairs an entity with one of its internal components.

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According to the given interface constraint, syntax guides the interpretation in the following way: if a modifier targets a projection at the head-level, it relates to internal components of the corresponding lexically introduced entity and thereby affects its internal make-up; if, by contrast, the modifier targets the complete projection, it relates to the target entity as a whole. Applied to, for instance, 83a, the refined rule yields the semantic representation in 85.

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That is, compositional semantics correctly predicts the VP-related adverbial im Wohnmobil (‘in the camper’) to locate the preparation as a whole, while it predicts the V-related adverbial im Dampfgarer (‘in the steamer’) to relate to a semantically underspecified integral component of the preparation. The corresponding specification of the free variable $v$ depends on pragmatic resources such as context information and conceptual knowledge. Put in simplified terms, the locative does not plausibly locate a manner or a degree of the preparation, but its participant. This allows for identifying $v$ with the chili $h$ and, thereby, correctly captures the intuitive reading according to which the chili is localized in the steamer (see Maienborn, 2003 for a detailed pragmatic account). Based on an analogous semantic derivation via MOD*, cleverly in 83b yields the representation in 86. However, in this case the most plausible modifiee is the manner of the ignoring event (see Schäfer, 2013 for details). (The subject-oriented reading of cleverly correlates with a higher adjunction site, which nicely reflects the fact that it contributes a relation between the subject referent and the explicitly given event as a whole. However, making this relation more precise is beyond the scope of MOD* alone; see McConnell-Ginet, 1982; Geuder, 2000; and Wyner, 2008 for a controversial discussion.)

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This approach to modification proceeds from a parsimonious syntactic structure, while it complicates the semantics-pragmatics interface by crucially involving ontological commitments and conceptual knowledge. However, these resources seem to be independently needed for adequately capturing the potentially fairly fine-grained semantic effects modifiers can have on interpretation; one of the corresponding challenges is adressed in Section 3.2. Moreover, the proposed constraint is fairly general and therefore applicable beyond the verbal domain. Bücking (2012a) shows how MOD* can be adapted to the interpretation of adnominal locatives; based on Haider (2004), the proposal argues that modification is sensitive not only to the hierarchical organization of phrases, but also to the incremental linear order. (The sensitivity of modification relations to linear order is also tackled in Morzycki, 2008; however, he focuses on the distinction between at-issue and non-at-issue content, as briefly discussed in Section 1.) The application of MOD* to compounds as opposed to phrases is discussed in Bücking (2009) and Olsen (2012); see Dowty (1979) for a prominent predecessor. Accordingly, the contrast in 79 can be traced back to a difference between target entities: given a phrasal structure such as $[NP[APblauer][NPTee]]$, MOD* predicts blau to apply to the nominal target entity as a whole, which invariably says that the tea itself is blue. Given a compound structure such as $[N[ABlau][Ntee]]$, MOD* predicts blau to apply to some integral component of the target entity, which leaves open whether the tea itself is blue. Based on variants of causal modifiers to adjectival projections such as (German counterparts to) tired from the trip and grey from the dust, Maienborn and Herdtfelder (2017) consider a constraint similar to the one in 84 for the adjectival domain.

## 3.2 Modification at the Interface Between Semantics and Pragmatics

Many modifiers provide lexical content and relate to the lexical core of their targets, which explains why their combinatorics is often intuitively conceived of as the amalgamation of concepts. For instance, the concepts that the properties red and chair contribute become jointly manifest in entities that are red chairs. Correspondingly, the interaction between rigid semantic knowledge on the one hand and context-sensitive conceptual knowledge on the other furnishes a foundational aspect of the semantics-pragmatics interface for modifiers. A particularly challenging task arises where the contributions of modifier and modifiee do not match at first sight and thus call for adaptive processes. (The distinction between at-issue and non-at-issue content gives rise to a second key issue of the semantics-pragmatics interface of modifiers; this is not discussed here, but see the references in Section 1.)

A wide range of phenomena are illustrative of how the lexical contents of modifier and modifiee may interact and of how this interaction relates to semantic composition in crucial ways. For instance, the fact that (certain) verbal meanings can be modified by temporals or locatives is usually taken to substantiate the event semantics claim that (certain) verbs introduce worldly events having a time and a place. Moreover, a more fine-grained differentiation such as the one between unbounded activities and bounded accomplishments is justified by their being (in)compatible with duration and frame-setting temporal adverbials; compare 87 for illustration. The classical references include Davidson (1967) and Vendler (1967); see Maienborn (2011) for an overview.

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So, modifiers may serve as a vital diagnostic for ontological distinctions. Notably, however, the relation between a modifier and its target is not always straightforward; examples such as 88 point to adaptive potentials upon an impending conflict. The punctual verb here receives an iterative reading if combined with a duration adverbial that it would otherwise not be compatible with; see Moens and Steedman (1988) for a first systematic treatment of such instances of so-called aspectual coercion, Bott (2010) for a comprehensive, psycholinguistically informed account, and de Swart (2011) for an overview.

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As mentioned in Section 2.1, conceptual distinctions may also have a bearing on the logically inspired partition into intersective, subsective, and intensional modifiers. Recall that, following the tradition initiated by Larson (1998), the subsective reading of examples such as passionate cook can be analyzed as intersective modification if the adjective is taken to apply not to the predicate of cooks itself but to some mediating eventive predicate. Such a conceptual adaptation builds on a sortal differentiation that goes beyond a view where predicates simply contribute functions from entities (of whatever sort) to truth-values. Similar considerations hold for candidates for privative modifiers such as fake or plastic in 89 (building on examples in Partee, 2010).

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Partee (2010) (see as well Asher, 2011) argues that these modifiers are in fact not privative. Instead, they involve the coercive potential of amending the target denotation by adding to it a set of entities that comprises in some sense unreal representatives of the given property. In other words, what counts as stove or carrot is conceptually adapted; correspondingly, the privative entailment goes through just because the bare noun is usually understood as if it were modified by something like real. Evidence for this proposal stems from otherwise puzzling locutions such as 90. Del Pinal (2015) argues for an alternative account, according to which privative adjectives interact with a so-called non-extension-determining layer of meaning within nouns (which builds on qualia roles as proposed by Pustejovsky, 1995). Although he thereby objects to Partee’s meaning shift account, he still corroborates the overarching idea that compositional semantics should be sensitive not only to the usual extension-determining content of lexical items but also to their lexical conceptual core.

The general question emerging from these brief illustrations is how to reconcile the intrusion of conceptual knowledge with compositional semantics; see Maienborn (2017) for a survey of representative theories on conceptual semantics and their opposing views on compositionality. One obvious option consists in giving up compositionality as the one and only crucial combinatorial principle for natural language interpretation and instead allowing for manifold mappings between structural units and conceptual representations; typically, this option goes with conflating linguistic semantic and world-dependent conceptual knowledge resources (a prominent spokesperson of such a perspective is Ray Jackendoff; see the overview in Jackendoff, 2011). Among the approaches that adhere more closely to a rigid mapping between structure and semantic interpretation and maintain a distinction between semantic and conceptual information, two strands of thought can be distinguished. According to so-called underspecification, the linguistically determined meaning composition yields a rather sparse semantic representation that by and large abstracts away from conceptual information. Instead, this meaning skeleton leaves considerable room for secondary conceptual specifications; for instance, it is endowed prophylactically—that is, irrespectively of a particular compositional environment—with free relation variables that must be filled by conceptual information (a corresponding inclination can be attributed to Blutner, 1998; Dölling, 2003; and Egg, 2005). According to so-called coercion, the composition process builds in fine-grained conceptual distinctions more directly. Upon a conceptual conflict, the composition process resorts to an alternative coerced interpretation that circumvents the impending conflict; for instance, it licenses the interpolation of an additional mediating variable (a corresponding inclination can be attributed to Pustejovsky, 1995, 2011 and Asher, 2011). Notably, however, details can vary considerably and integrate facets of both perspectives. Furthermore, which road to take may heavily depend on the phenomenon under consideration; see, for instance, Bücking (2012a) for a formal semantics comparison between underspecification and coercion with regard to the modifying function of adnominal genitives, or Lukassek, Prysłopska, Hörnig, and Maienborn (2016) for an experimental approach to the opposition between underspecification and coercion, using the modification of motion verbs as exemplification. Pylkkänen and McElree (2006) provide a general overview of adaptive mechanisms from a psycholinguistic angle. Recall as well the dual content approach to the interaction between semantic composition and lexical concepts defended by Del Pinal (2015). Finally, optimality theoretic treatments of the interaction between semantic and conceptual knowledge such as Hogeweg (2012) are noteworthy.

In order to make the debate between coercion and underspecification accounts concrete, a more detailed look at the simple case in point in 91 is worthwhile (see Pustejovsky, 1994, Lascarides & Copestake, 1998, Asher, 2011 for similar examples; the following outline draws mainly on the elaborate discussion in Bücking & Maienborn, 2016).

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The key observations to be addressed are the following. First of all, the modifying quick contributes a predication of spatio-temporal entities such as events and is thus incompatible with the object-denoting modifiee mushroom soup. Intuitively, however, the interpretation does not crash, but integrates a mediating event the content of which is underspecified. As a result, 91 receives the interpretation ‘mushroom soup that is prepared quickly’ or ‘mushroom soup that is consumed quickly,’ or, under extraordinary circumstances, ‘mushroom soup that falls quickly to the ground.’ Second, the event-sensitive adaptation operates on the local predication between modifier and modifiee without changing the referential properties of the resulting complex constituent; in other words, 91 denotes a set of physical objects, not a set of events. This locality is made evident by examples such as 92/93: the main predication taste is compatible with the extended projection of an object-denoting noun, irrespectively of whether it is accompanied by an event-sensitive modifier or not; a corresponding event-denoting noun, however, yields an infelicitous sentence.

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The given locality effect is clearly reminiscent of the Head Primacy Principle discussed in Section 2.2. This renders a principled compositional solution all the more desirable. (The attentive reader will notice that the privative modifiers discussed above pose the opposite challenge, since the requirements of the modifier seem to be passed on to the complex constituent. Correspondingly, they are the most prominent candidate for a violation of the Head Primacy Principle; see, however, the discussion in Del Pinal, 2015.) Third, the adaptation does not operate randomly. For instance, the adjective nimble, which is semantically similar to quick, is odd in combination with mushroom soup, as in 94a. This is puzzling, given that the adjective is compatible with a corresponding explicit eventive target, as in 94b. This suggests a specific restriction for the conflict-based interpretation: nimble only allows for mapping non-eventive targets to small fast movements. Since mushroom soups do not move, 94a is deviant; notably, the restriction to movements prohibits the mediation by a preparation event as employed for the interpretation of quick in 91. By contrast, 95 allows for an adaptation because needles may very well move in a nimble way.

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As a consequence, the interpretation process should be able to integrate fine-grained conceptual differences among modifiers; moreover, it must be sensitive to whether the composition proceeds directly, as in 94b, or resorts to some adaptive mechanism, as in 94a/95.

Let us first turn to a potential coercion account. Glossing over differences in detail, the exemplification will adopt the approach to coercion in terms of type composition logic by Asher (2011). The basic ingredients are as follows. Semantic terms involve not only the usual intensional semantics, but also a layer of information about potentially fine-grained types (which are conceived of as concepts). This information includes typing presuppositions that are encoded within contextual parameters $π$ and must be met in the course of building full-fledged meaning representations. Upon a type conflict, the composition may resort to a mediation via so-called polymorphic types. Notably, it is part of the lexical semantics of individual lexical items whether this option exists and what kind of constraints it involves. 96 provides a corresponding lexical entry for quick; $*$ symbolizes the link between the contextual parameter of a particular predication and its relevant type presuppositions.

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The key aspects of this entry are the following. First, quick presupposes its first argument to be of type event (= ev). However, this type requirement may be met in one of two ways: either directly by the event as introduced by the compositional target or indirectly by the polymorphic eventive type $ε({[a1,…]TY(P)+})$ that mediates between the modifier and the compositionally given target type. The constraints on this mediating event are rather lax. The typing just says that this event must be related to the fine-grained proferred type of the compositionally given target ($TY+$ is a function from a predicate to its fine-grained proferred type) and that it might optionally involve further argument types besides the compositionally given one (see $[a1,…]$; the curly brackets indicate that the thematic hierarchy of the argument types is not predetermined). Second, the entry maps the typing presupposition of the modifiee, that is $TY(P)ps$, on the local context parameter for the modifying adjectival predicate. This assumption ensures that any conflict between the presuppositions of modifier and modifiee will be resolved locally within the adjectival predication and not pertain to the predication of the nominal target. A plausible entry for the nominal target is given in 97; its states that mushroom soup presupposes its first argument to be food. Standard composition then yields the representation in 98.

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As a result, $x$ should be both of type food and of type event, which is clearly impossible. However, the polymorphic type licenses a conceptual adaption. Glossing over details (see Asher, 2011 and Bücking & Maienborn, 2016 for spelling out corresponding derivations), the basic idea is that a coercive functor transforms the problematic predicate of events into a predicate of entities that are participants of an existentially bound event; see the sketch in 99 ($ϕ$ stands for the underspecified event predicate on the level of logical form). The corresponding revised logical form yields a smooth justification of the relevant types, which is reflected in the simplified representation in 100.

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In prose: 100 denotes the set of $x$ so that $x$ is a mushroom soup; additionally, there must be an event $e$, which is quick and in which $x$ (and, potentially, further arguments) participate. This reading is intuitively on the right track. Its more specific merits are as follows. First, it opens up an underspecified event slot, the content of which can be determined by appropriate context-sensitive knowledge; this allows for identifiying $e$ with, for instance, a preparation or a consumption. Second, the repair complies with the primacy of the head and, thus, makes sure that the resulting noun phrase denotes a set of physical objects instead of events. Finally, since the repair is based on a lexically given polymorphic type, potential constraints can be arbitrarily fine-grained. For instance, according to the brief illustrations above, nimble only allows for assigning a non-eventive target to an event that involves a particular kind of movement. This can be captured by endowing the corresponding lexical entry with a polymorphic type such as $εsmallfastmovements(TY+(P)[a2,…])$. Accordingly, only events involving small fast movements can be interpolated; moreover, the compositionally given target $P$ always provides their first thematic argument. Therefore, the repair invariably maps a non-eventive target to its moving nimbly; this is conceptually compatible with needle, but not with mushroom soup.

Let us now turn to a potential underspecification account (which, significant differences notwithstanding, is inspired by the underspecification analyses for other domains in Dölling, 2003 and Bücking, 2012a). The general idea is that the relation between modifier and modifiee is not direct, but is mediated prophylactically by an underspecified relation variable $ϕ$; the general format for modification then is 101. (Obviously, this is reminiscent of MOD* in Section 3.1; however, 101 does not make use of a specific structure-sensitive interface constraint, but suggests underspecification across the board.)

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More specifically, the implementation may factor presuppositional types into the underspecification. So a corresponding entry for quick could be 102, which yields the compositional representation in 103a for the combination with the head noun. Most notably, the presuppositions of both predicates relate to different variables so that, trivially, no conflict may arise; this allows smoothly for the simplification in 103b.

(102)

(103)

The result is essentially the same as for the coercion-based computation, and so are the merits: like the coercion account, 103b complies with the primacy of the head by projecting the head noun variable as the relevant one for the complex constituent. Furthermore, the relation variable $ϕ$ allows for identifying the relevant mediating event $e$ with some conceptually appropriate candidate such as a preparation or a consumption. A procedural difference to the coercion account arises in those cases where the target itself provides an event. On the coercion account, the composition proceeds directly without involving the polymorphic type. On the underspecification account, the prophylactical relation variable $ϕ$ is fixed; in order to handle cases where it is not needed, $ϕ$ is resolved as the identity function and thereby rendered ineffective.

It is often argued that underspecification accounts cannot deal properly with constraints, given their prophylactical freedom between modifier and modifiee. However, this does not hold for the present implementation. The lexicalist perspective enriched by typing information allows for factoring arbitrarily fine-grained constraints into the lexical entries for modifiers. For instance, nimble could constrain the relation variable $ϕ$ by only allowing it to resolve to identity or to events that involve a particular kind of movement. A constraint such as $ϕ(e,x[v1,…],π*ARG1ϕ:EVsmallfastmovements)$ would then mirror the suggested polymorphic type of the coercion account.

Wrapping up: once underspecification and coercion accounts are made comparable by using implementations that use the same kind of tools (here, fine-grained typing information), they make very much the same descriptive predictions. The main difference relates to the way the composition proceeds. The coercion account builds on a fairly complicated and computationally costly repair mechanism. However, it makes a natural distinction between direct and conflict-based composition and thereby also nicely reflects the intuition that, for instance, quick introduces primarily a predicate of events. By contrast, the underspecification account allows for a fairly simple semantic composition; however, it does not capture naturally the distinction between cases that enforce a mediation between modifier and modifiee and cases that do not. It is noteworthy that the interaction between semantic and conceptual knowledge as envisaged here has a fairly intriguing bearing on the more general question of how modifiers should be composed; recall the discussion in Section 2. Neither the given coercion account nor the given underspecification account builds on a rule-based approach to modification; in fact, only the assumption that the modifier has direct lexical access to its modifiee allows the modifier to directly impose fine-grained conceptual restrictions on its modifiee. In other words, once conceptual information is factored into the semantic composition, the foundational question of whether modifiers should be integrated by an extra rule or by functional application with higher-ordered types is back on the agenda, even for seemingly easy intersective modification.

# Acknowledgments

I thank an anonymous reviewer and Wilhelm Geuder for their having carefully reviewed the present paper; it has benefitted considerably from their instructive suggestions. I am also indebted to Antonio Machicao y Priemer and Martin Schäfer for their helpful comments on the first draft of the paper. Finally, I thank Holger Gauza, Claudia Maienborn, Britta Stolterfoht, Sophie von Wietersheim, and Sarah Zobel for the discussion of several questions of detail that came up in the course of writing this overview.

## General overviews of modification as a semantic operation:

Bücking, S. (2015). Modification. In M. Aronoff (Ed.), Oxford bibliographies in linguistics. New York: Oxford University Press.Find this resource:

Heim, I., & Kratzer, A. (1998). Semantics in generative grammar. Malden, MA: Blackwell.Find this resource:

McNally, L. (2016). Modification. In M. Aloni & P. Dekker (Eds.), The Cambridge handbook of formal semantics (pp. 442–465). Cambridge, U.K.: Cambridge University Press.Find this resource:

Morzycki, M. (2016). Modification. Cambridge, U.K.: Cambridge University Press.Find this resource:

## Foundational questions of what modifiers are and how they are combined:

Chung, S., & Ladusaw, W. A. (2006). Chamorro evidence for compositional asymmetry. Natural Language Semantics, 14, 325–357.Find this resource:

Dowty, D. R. (2003). The dual analysis of adjuncts/complements in categorial grammar. In E. Lang, C. Maienborn, & C. Fabricius-Hansen (Eds.), Modifying adjuncts (pp. 33–66). Berlin: de Gruyter.Find this resource:

Higginbotham, J. (1985). On semantics. Linguistic Inquiry, 16, 547–593.Find this resource:

Kamp, H., & Partee, B. H. (1995). Prototype theory and compositionality. Cognition, 57, 121–191.Find this resource:

Bonami, O., Godard, D., & Kampers-Manhe, B. (2004). Adverb classification. In F. Corblin & H. de Swart (Eds.), Handbook of French semantics (pp. 143–184). Stanford, CA: CSLI Publications.Find this resource:

Demonte, V. (2011). Adjectives. In K. von Heusinger, C. Maienborn, & P. Portner (Eds.), Semantics: An international handbook of natural language meaning (Vol. 2, pp. 1314–1340). Berlin: de Gruyter.Find this resource:

Maienborn, C., & Schäfer, M. (2011). Adverbs and adverbials. In K. von Heusinger, C. Maienborn, & P. Portner (Eds.), Semantics: An international handbook of natural language meaning (Vol. 2, pp. 1390–1420). Berlin: de Gruyter.Find this resource:

Kennedy, C., & McNally, L. (2005). Scale structure, degree modification, and the semantics of gradable predicates. Language, 81, 345–381.Find this resource:

## Syntax-semantics interface:

Alexiadou, A., Haegeman, L., & Stavrou, M. (2007). Noun phrase in the generative perspective. Berlin: de Gruyter.Find this resource:

Cinque, G. (1999). Adverbs and functional heads: A cross-linguistic perspective. Oxford: Oxford University Press.Find this resource:

Ernst, T. (2002). The syntax of adjuncts. Cambridge, U.K.: Cambridge University Press.Find this resource:

Frey, W. (2003). Syntactic conditions on adjunct classes. In E. Lang, C. Maienborn, & C. Fabricius-Hansen (Eds.), Modifying adjuncts (pp. 163–209). Berlin: de Gruyter.Find this resource:

Hole, D. (2015). Arguments and adjuncts. In T. Kiss & A. Alexiadou (Eds.), Syntax—theory and analysis: An international handbook (Vol. 2, pp. 1284–1320). Berlin: De Gruyter.Find this resource:

## Semantics-pragmatics interface:

Asher, N. (2011). Lexical meaning in context: A web of words. New York: Cambridge University Press.Find this resource:

Dölling, J. (2003). Flexibility in adverbal modification: Reinterpretation as contextual enrichment. In E. Lang, C. Maienborn, & C. Fabricius-Hansen (Eds.), Modifying adjuncts (pp. 511–552). Berlin: de Gruyter.Find this resource:

Morzycki, M. (2008). Nonrestrictive modifiers in nonparenthetical positions. In L. McNally & C. Kennedy (Eds.), Adjectives and adverbs: Syntax, semantics, and discourse (pp. 101–122). Oxford: Oxford University Press.Find this resource:

Pustejovsky, J. (1995). The generative lexicon. Cambridge, MA: MIT Press.Find this resource:

## Psycholinguistics:

Bott, O. (2010). The processing of events. Amsterdam: John Benjamins.Find this resource:

Frazier, L., & Clifton, C., Jr. (1997). Construal: Overview, motivation and some new evidence. Journal of Psycholinguistic Research, 26, 277–295.Find this resource:

Pylkkänen, L., & McElree, B. (2006). The syntax-semantics interface: On-line composition of sentence meaning. In M. A. Gernsbacher & M. J. Traxler (Eds.), Handbook of psycholinguistics (2d ed., pp. 539–579). Boston: Elsevier Academic.Find this resource:

Syrett, K., & Lidz, J. (2010). 30-month-olds use the distribution and meaning of adverbs to interpret novel adjectives. Language Learning and Development, 6, 258–282.Find this resource:

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