"But well is semantically complex. It combines the features of 'approval' and 'fulfillment' in ways that defy separation of the two." —D. Bolinger (1972:29)

1 The Puzzle

In Kennedy and McNally (hereafter, K&M) 1999, we observed that well allows both a degree reading and a "quality" reading in examples like (1a), but only a quality reading in (1b).

(1)	a.	a well-loaded truck (high degree of loadedness or loaded in a skilled/neat etc. way)
	b.	well-loaded hay (loaded in an organized/skilled/neat etc. way)

In that paper we accounted for this constrast by treating well as ambiguous between a degree reading and a "quality" reading and by placing constraints on its use as a degree modifier which excluded that use in cases like (1b). However, positing a lexically ambiguous well is not only ad hoc; it is also computationally undesirable. Multiple lexical entries are more costly in computational terms; therefore, when some relationship exists between the different senses of a word, as Bolinger rightly observes is the case with well, it is worth trying to derive the observed polysemy from information available in the linguistic or conversational context. In this squib, we suggest how a simple and completely standard representation of participles in the Generative Lexicon framework (Pustejovsky 1995; hereafter, GL), together with a unified analysis of well modeled on current GL analyses of adjectival modification (e.g. Pustejovksy 1995, Bouillon 1999, Badia and Saurí 1999), actually predicts the attested readings.

Section 2 reviews the constraints on degree uses of well which will concern us here. We sketch our analysis in Section 3.

2 The constraints on degree well

Since our analysis of well will ultimately depend on our being able to derive its polysemy from the interaction of its lexical semantics with the lexical semantics of its arguments, it is necessary first to describe briefly exactly when a degree reading of well is found. It is found only with participles that meet two semantic requirements: 1) they are associated with scales which are closed on both ends,² and 2) their standard value (that is, the value on the adjective's scale which determines whether or not its denotation truthfully holds of an entity) cannot be the maximum value on that scale (see Kennedy 1999 and K&M 1999 for a thorough introduction to our assumptions concerning the scalar semantics of adjectives). In K&M 1999 we argue that closed-scale adjectives can be distinguished from open-scale adjectives in that only the former permit modification by endpoint-oriented modifiers such as partially or fully:

(2)	a.	The truck was partially/fully loaded.
	b.	The hay was half/completely loaded.

Open-scale adjectives such as worried do not permit modification by partially, etc. Nor do they permit modification by well:

(3)	a.	??	Marge was completely worried when she saw the flying pig.
	b.	??	Marge is still well-worried.

The condition on the standard value is what distinguishes the possible interpretations of well in (1a) vs. (1b) and is motivated as follows. Among the semantic effects of well is to "boost" the standard value for the attribute with which it combines. For example, holding all potentially variable factors constant, the standard of loadedness which must be reached for a vehicle to be considered well-loaded in any given situation is considerably higher than that required for the vehicle to qualify as simply loaded. It is possible for well to boost the standard value associated with loaded as applied to vehicles because this standard value is demonstrably the minimum degree on the "loaded" scale. In contrast, well cannot boost the standard value associated with loaded as applied to contents, because the standard value in this case turns out to correspond to the maximum value on the "loaded" scale—a value which cannot be meaningfully boosted. Thus, we correctly expect the degree reading of well to be effectively blocked in the latter case, and indeed any time the standard value is a maximum. Now, how do we know when a standard value is a minimum or a maximum value on a scale?

K&M 1999 argue that the scale structures associated with participles can be homomorphically related to (and, ultimately, derived from) aspects of their event structures, and that a given participle may be associated with more than one scale. Continuing with the "loading" example, a (maximal) loading event involving a vehicle x and contents y can be divided into temporally and incrementally ordered subevents of loading x with subamounts amounts of y. The temporal endpoints of each of these subevents can be mapped onto a degree on a scale associated with loaded. The endpoint of the first subeventof loading of the smallest amount of x onto y corresponds to the minimum on a "loaded" scale for both x and y. However, what constitutes the maximum value on the scale depends on the participle's argument structure, since argument structure arguably affects the nature of the event described by the participle; see e.g. Dowty 1991, Levin and Rappaport-Hovav 1999. The endpoint of the last subevent of loading of the last bit of x onto y corresponds to the maximum on a scale for x. In contrast, the endpoint of the subevent of loading the last bit of x that fits onto y corresponds to the maximum on a scale for y.³

Now that we have briefly described how the minimum and maximum values on a scale are determined, we turn to the question of the standard value. Interestingly, the standard value for application of a participle also depends on the thematic role borne by the participle's argument in the event related to that participle. If the argument is a classic incremental theme (see Dowty 1991), the sort that Ramchand 1997 calls "Pat₌", as is the case of hay in loaded hay, the standard will be the maximal value on the scale. This is so because the conditions for truthful application of the participle will not be met unless all of the incremental theme has undergone the event in question: (4a) is not true of the individual x we refer to as the hay unless 100% of x has undergone loading. Further evidence that the standard for the scale is the maximum value can be derived from considering sentences like (2b), whose truth is evaluated by mapping the hay onto the scale associated with loaded and then computing the distance of the value assigned to the hay from the standard-the upper endpoint of the scale. Note that even though the truth of (2b) depends on the hay having some value on the "loaded" scale, (2b) crucially does not entail (4a): note that (4b) is a contradiction.

(4)	a.		The hay is loaded.
	b.	??	The hay may be only half-loaded, but it's loaded (so I'm going home).

In contrast to what happens with a classic incremental theme, if the "measuring out" of the event related to a participle is achieved in terms not of the argument itself but rather some property it has as an entirety (as is the case with arguments bearing Ramchand's incremental theme-like role "Pat_+/–"), then the standard will correspond to the minimum value on the scale. This is what happens in the case of the loaded vehicle, where the vehicle as a whole is involved in each subevent of loading, but where one of its properties, namely the degree to which its volume is occupied, changes incrementally. (5a) can be true as soon as the truck has undergone a minimal loading event; it is not necessary for its entire volume to be occupied, as seen in the fact that (5b) is not a contradiction:

(3)	a.	The truck is loaded.
	b.	The truck may be only half-loaded, but it's loaded (so I'm going home).

Generalizing, the standard for a closed-scale participle will be a maximum value when that participle applies to a Pat₌ argument, and a minimum when it applies to a Pat_+/– arguments.

We now sketch an analysis of well+participle expressions in GL which captures the observations made in this section.

3 A GL analysis

GL representations are typed-feature structures which encode fine-grained lexical semantic information. Exactly what information one chooses to encode constitutes a claim concerning what semantic information is linguistically significant. GL representations are compatible with various syntactic theories; we combine them here with a version of Head-Driven Phrase Structure Grammar (HPSG, see e.g. Pollard and Sag 1994; we follow Badia and Saurí 2000 in making sets of qualia the values of the HPSG REST(RICTION) feature, though we diverge from them on other details). Pustejovsky's 1995 GL representations contain three basic structures. Argument structure (ARGSTR) specifies the number and nature of the participants in the situation described by a predicate. Event structure (EVSTR) contains information about the nature of the situation described, including possible subevents and relations between them. Finally, qualia structure (QSTR) provides information about four essential aspects of the entity or situation described by a predicate: its distinguishing characteristics (the value of the formal quale); its constituent parts (the constitutive quale); how it came into existence (the agentive quale); and its stereotypic purpose or function (the telic quale). To these three structures we add a fourth: scale structure (SCSTR), which will identify the scale (the SNAME feature, e.g. "loaded") and specify whether the scale is open or closed (the OP/CL feature) and what the standard value is (STD, whose value is a degree). The exact configuration we have given to scale structure is not crucial for the analysis, so for reasons of space we will not justify it here.

Following K&M 1999 we treat well as a manner adverb which selects for adjectives.⁴ Our representation for well appears in Figure 1. We extend Pollard and Sag's treatment of prenominal adjectives to preadjectival adverbs. As would be expected of a manner adverb, well is not type-changing; that is, it inherits the index and event structure of its adjective argument (as represented in well's CONT feature). However, well does place conditions on the scale structure of the resulting well+participle combination: it has an open scale (see K&M 1999 for empirical support) whose standard value is boosted some ultimately context-dependent amount above that required by the participle alone.

Now let us turn to the conditions that well imposes on its adjectival argument. The MOD-ADJ feature specifies the one condition explicitly imposed: the adjective's scale must be closed. The other information represented in MOD-ADJ is characteristic of adjectives in general; since we follow Kennedy 1999 in taking adjectives to denote measure functions which are converted to properties of individuals only after combining with (possibly phonologically null) degree morphology, the adjective's INDEX and FORMAL qualia features have degree values. But in addition to the explicit condition that the adjective's scale be closed, the value of well's CONT feature places a crucial implicit condition on the semantics of the adjective argument: Since well denotes a measure function on events, the semantic representation for the adjective must make available an event argument for the measure function to operate on, though it does not specify anything else about that event argument.

Figure 1: Representation of well

This implicit condition is the key to understanding well's polysemy.

The polysemy associated with well is highly reminiscent of that associated with adjectives. Badia and Saurí 1999, extending Pustejovsky's 1995 treatment of verb polysemy and suggestions of his concerning the treatment of adjectives, propose that the different interpretations of e.g. fast in fast car (drives fast) vs. fast cake (made/baked fast) are a consequence of the adjective's ability to modify an event variable in either the telic quale of a noun (in the case of car, where the telic quale specifies a driving event) or its agentive quale (in the case of cake, where the agentive quale specifies a making/baking event; see also Bouillon 1999 for a similar treatment of vieux 'old' in French). Indeed, if adverbs are like adjectives in being able to modify different event variables in their complements' representations (via "selective binding", Pustejovksy 1995:129), and if adjectives and participles are like nouns in being potentially specified for telic and agentive qualia, the polysemy that well exhibits is exactly what we would expect.

Consider the representation of loaded-with in Figure 2.⁵

Figure 2: Representation of loaded-with

First, observe that loaded-with satisfies the explicit conditions imposed by well.⁶ It satisifes the implicit condition as well: Since the state of being loaded with some contents is achieved via a loading process, we can specify an agentive quale whose value is a description of a loading event. Since its being loaded with some contents is a result of a loading process, it is reasonable to assign the loaded state as the value of the telic quale. The representation of loaded-on in Figure 3 is identical, except that the arguments are crucially rearranged:⁷

Figure 3: Representation of loaded-on

In principle, either the event value in the agentive quale or that in the telic quale could be modified by well (note, interestingly, that the formal quale does not provide any event variable for modification). Modification of the event variable in the agentive quale corresponds to a manner/quality reading of well: The loading process is assigned a value on a scale of goodness which intuitively involves approval of objective aspects of the event-neatness, rapidity, skill, and, doubtless, degree of completion. All participles give rise to this reading. However, note that degree of completion will not be an interesting dimension of the loading event to be affected by well in the case of loaded-on, because truthful use of the phrase loaded hay entails that the entire referent of hay has undergone the loading process in question; in other words, the loading will have been completed to the maximal degree. Thus, no degree reading for well can be derived from its modifying the event variable in the agentive quale of loaded-on. In contrast, when well modifies the event variable in the agentive quale of loaded-with, it will yield a quality reading which need not be incompatible with implying that the loading was carried out to a high degree, though not completely-recall that truthful use of the phrase loaded truck doesn't entail that the truck is 100% loaded.

Be this as it may, we suspect that well's degree reading arises principally when it modifies an event variable in the telic quale of its argument.. Modification of the event variable in this quale corresponds to the assignment of a value on the goodness scale to the result state (here, the state of the contents or the vehicle being loaded). If the adverb is restricted, as seems to be empirically the case, to modifying objective aspects of this state as opposed to e.g. the speaker's opinion as to its utility or appropriateness, then there would appear to be little to be evaluated as "good" other than the degree to which the state holds-such parameters as rapidity or skill cannot be evaluated, and neatness is clearly a reflection of the manner in which the loading process was carried out. But, as noted, any interesting evaluation of the degree to which some contents is loaded on a vehicle is impossible because the standard for its being onsidered loaded at all is the maximum value on the scale. Thus, well will not have a degree reading when it modifies the event variable in loaded-on's telic quale, either. In contrast, it should now be clear why such a reading is possible when well modifies the corresponding variable in loaded-with's telic quale.

4 Conclusion

We have sketched an account of well's polysemy in combination with participles which improves substantially upon our previous account. While it may appear that we have simply moved the puzzle from well to the participle insofar as we posit two lexical entries for the latter, this is not in fact the case. The ambiguity in the participle is independently motivated on argument structure grounds and has been claimed to have semantic consequences (by e.g. Dowty 1991). Moreover, placing the ambiguity in the participle correctly predicts that the phenomenon found in (1) occurs only with participles for which multiple semantic representations can be independently motivated. The fact that the source of the polysemy becomes so clearly evident in a GL representation underscores the promise of GL as a framework for lexical semantic research.

References

Badia, T. and R. Saurí. 1999. Semantic disambiguation of adjectives in local context: A generative approach. In P. Bouillon and E. Viegas (eds.), Proceedings of TALN 99, Cargèse, Corsica.

Badia, T. and R. Saurí. 2000. Enlarging HPSG with lexical semantics. In A. Gelbukh (ed.), Proceedings of CICLing 2000, Computer Research Center, National Polytechnic Institute, Mexico City, 101–122.

Bolinger, D. 1972. Degree words. The Hague, Mouton.

Bouillon, P. 1999. The adjective "vieux": The point of view of "Generative Lexicon". In E. Viegas (ed.), Breadth and depth of semantic lexicons, Kluwer, Dordrecht, 148–166.

Dowty, D. 1991. Thematic proto-roles and argument selection. Language 67, 547–619.

Kennedy, C. 1999. Projecting the adjective: The syntax and semantics of gradability and comparison. Garland Press, New York.

Kennedy, C. and L. McNally 1999. From event structure to scale structure: Degree modification in deverbal adjectives. In T. Matthews and D. Strolovitch (eds.), Semantics and Linguistic Theory 9, CLC Publications, Ithaca, NY, 163–180.

Koenig, J.-P. 1999. Lexical relations. CSLI Publications, Stanford, CA.

Levin, B. and M. Rappaport-Hovav. 1999. Two Structures for Compositionally Derived Events. In T. Matthews and D. Strolovitch (eds.), Semantics and Linguistic Theory 9, CLC Publications, Ithaca, NY.

Pollard, C. and I. Sag. 1994. Head-Driven Phrase Structure Grammar. CSLI/University of Chicago Press, Chicago.

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Endnotes

¹ Since Jorge is a man of few (though, needless to say, always well-chosen) words, we'll just say, "Happy Birthday!" Here's your present: Homework Problem #1: Show that our analysis correctly predicts the attested reading of well in the first sentence of this note. Homework Problem #2: Suggest how the restriction that well combines only with adjectives which are closed on at least one end (see note 1) might be made to follow from our independently motivated claims (a) that adjectives denote measure functions and (b) that scale structure is homomorphically related to event structure. [Back]

² To account for the degree uses of well with certain nonparticipial expressions, this condition will eventually have to be weakened to "closed on at least one end". However, since we restrict our attention in this squib to participles, we maintain the stronger condition. [Back]

³ It also seems that in some cases the loading of the last bit of x onto y defines the maximum value of the scale as applied to y as well. If we're going on a trip and you ask me whether the car is completely loaded or if I have finished loading the car, I can respond truthfully even if more things could be put in the car. What matters for truth in these cases is that all of the contents in question have been put into the car. This observation indicates that a reexamination is needed of Dowty's (1991) suggestion that the direct object is consistently the incremental theme in spray-load alternations. [Back]

⁴ Obviously, a fully general analysis of well should try to unify its adjective-modifying use with its verb-modifying use. In the interest of space we do not pursue such a unification here. Our analysis will similarly ignore certain other such generalizations which do not bear directly on the issue of how both the degree and nondegree readings of well can be derived from an unambiguous well. [Back]

⁵ Although we assign loaded two different lexical entries correponding to its two argument structures, these two entries are highly redundant and could be partially unified in a hierarchical lexicon like that proposed in Koenig 1999. Also note that to save space we have representated the values of the qualia as linear formulae, rather than as feature-structures. [Back]

⁶ We assume that past participles can be adjectival, i.e., classified as a subtype of adjective. [Back]

⁷ The standard value for the participle is that degree which corresponds homomorphically to the smallest event of the type described by the participle involving (all of) the participant described by the participle's argument. [Back]