Actualistic interpretations in French

Actuality Entailments (AEs), which are standardly described in relation to modal predicates, are known to only occur in the perfective. This article argues that modal predicates are stative and, for that reason, only compatible with the perfective if coerced. Being the reflex of an aspectual coercion, which I label ‘actualistic’, the AE phenomenon is broader than usually assumed: it obtains with modal and non-modal predicates alike. At the core of the actualistic coercion is a presupposition, in the form of a necessary and sufficient condition, whose effects can be detected, for example,


Introduction
In languages which distinguish the perfective and the imperfective aspects morphologically, whenever an ability or circumstantial modal appears in the perfective in a positive matrix clause, it is possible to infer the truth of its complement in the actual world (Bhatt 1999, Borgonovo & Cummins 2007, Mari & Martin 2009, Hacquard 2006. This article discusses one such language, French. Sentence (1a) features present perfect * Earlier versions of some of the material presented here can be found in Homer 2011Homer , 2013. For helpful discussions and comments, many thanks to Philippe Schlenker, and also to Ana Arregui, Márta Abrusán, Nicholas Asher, Bart Geurts, Valentine Hacquard, Roumyana Pancheva, Barbara Partee, Benjamin Spector, Dominique Sportiche and Tim Stowell, and to the audiences at WCCFL 28 and at the 8 th JSM (Conference on Semantics and Formal Modeling) at LORIA-INRIA, Nancy.

©2021 Vincent Homer
This is an open-access article distributed under the terms of a Creative Commons Attribution License (https://creativecommons.org/licenses/by/3.0/). Homer morphology; in the indicative mood, this morphology correlates with the perfective aspect. The sentence not only says that at a past interval Olga had the capacity to lift a fridge, it also entails that she did. It is infelicitous to contradict this inference, called an actuality entailment (henceforth AE), with a continuation as in (1b) In addition to the contradiction test, one can use another test (from Homer 2011), which consists in using an AE triggered in the first member of a conjunction to satisfy the presupposition triggered by aussi 'too' in the second member (presuppositions triggered by aussi are notoriously hard to accom- The test discriminates between the perfective and the imperfective (which correlates with simple past morphology, a.k.a. imparfait). In (3a), the presupposition triggered by aussi projects globally, i.e., the first conjunct doesn't provide an inference that satisfies the presupposition locally. As a result, a presupposition failure obtains: 2 Generalizing, AEs can occur with all root modals, including deontic ones (as shown by Borgonovo &Cummins 2007 andHacquard 2009). The phenomenon is not modal suppression, i.e., the modal does contribute to meaning. If it were modal suppression, then (4) should have the same meaning irrespective of the force of the modal. An AE does obtain with each modal, but the quantificational force of the modal is felt: violin 'This afternoon, Olga was able/had to play the violin.' → Olga played the violin. → Olga was able to play the violin.
(from the pu version) → Olga had to to play the violin.
(from the dû version) Furthermore, under the modal suppression hypothesis, it should be possible, keeping the accessibility relation of the modals constant, to say (5a) felicitously with the same intended meaning as (5b), but it is in fact a contradiction: fait. done 'She was able to play the violin, but she didn't.' antecedent must entail the presupposition triggered by aussi; (iii) global accommodation can be appealed to to ensure that the entailment goes through. Suppose indeed that one accommodates ◇ → ; then the presupposition triggered by aussi in the second conjunct of (2a) is satisfied even without AE, and the test is not revealing. The deviance of (3a) shows that this analysis of (2a) is not promising. I owe this important comment to Philippe Schlenker (p.c.).

12:3 Homer
In their descriptions of AEs, previous researchers focus on modal verbs or socalled modal auxiliaries. Hacquard (2006Hacquard ( , 2009Hacquard ( , 2014 insists that the lexical status of the modal is important. But contrary to this claim, we find AEs triggered by nouns and adjectives, in a variety of syntactic configurations (the imparfait counterparts do not yield an AE): Under what conditions do AEs obtain? Previous researchers, especially Hacquard (2006Hacquard ( , 2009, have proposed that AEs obtain if and only if a root modal appears in the perfective (in a positive matrix clause). The main goal of this article is to show that this criterion is not warranted, for it is both too strong (AEs occur even when the predicate is not a modal) and too weak (the perfective doesn't suffice). Focusing for the time being on its excessive weakness, the standard criterion faces an immediate problem: AEs are not always mandatory under the perfective. It is possible, under certain conditions, to deny that the complement of the modal is true in the actual world, as Mari & Martin (2009) were first to show. 3 Quantificational temporal modifiers, for example, une fois 'once', toujours 'always', souvent 'often', chaque fois 'each time' (both in its restrictor and nuclear scope) are responsible for a subclass of exceptions to obligatory AEs. For example, the only difference between (10a) and (1a) is the presence in the former of the modifier à plusieurs reprises 'on several occasions'. Locational temporal adverbials such as cet après-midi 'this afternoon' do not have the same effect (10b).
AEs should be impervious to temporal modification if the presence of a root modal under the perfective were a sufficient condition for them (assuming that aspect is preserved under temporal modification). Therefore examples like (10a) are genuine counterexamples to any theory that relies on the aforementioned criterion. Now, if the perfective is not sufficient, something else must come into play: I therefore submit that AEs result from some enrichment of the meaning of sentences in the perfective. In order to capture the nature of the process, I propose that we look for a meaning-enrichment mechanism that applies specifically in the perfective. I will argue that (i.) root modals are stative predicates and that the perfective can only combine with quantized (hence non-stative) predicates; (ii.) aspectual coercion is a last resort mechanism which can turn a stative predicate into a quantized one; (iii.) AEs are the result of a certain kind of aspectual coercion, which I name 'actualistic'.
The article is structured as follows. In Section 1, I lay out my assumptions about the tense and aspect system of French, and explain the notion of aspectual coercion: I show how stative predicates in the perfective need to be reinterpreted, and define covert coercion operators that carry out the reinterpretation. Section 2 establishes that predicates formed by root modals are stative; therefore they need to be coerced in the perfective. I then show how coercion applies uniformly to modal and non-modal predicates alike and analyze AEs as instances of a hitherto undocumented kind of aspectual coercion, the actualistic one. Section 3 investigates AEs triggered under negation, and explains away apparent discrepancies between modal and non-modal predicates as resulting from a presupposition, in the form of a necessary and sufficient condition; this presupposition is the source of the inferences of effort or goal-orientedness often documented in relation to AEs. Section 4 compares my approach to Hacquard's (2006Hacquard's ( , 2009.

Passé composé and imparfait
I assume that each clause in French has a Viewpoint Aspect head Asp, located below T and above vP. The exponent of Asp is either perfective (pfv) or imperfective (impfv). A perfect head can intervene between T and Asp: it is only found in the perfect, which combines an auxiliary (the perf head) and a participle. In the indicative, the perfect requires a perfective Viewpoint Aspect. Tree (12) is a representation of sentence (11) I use an intensional system, with a time and a world parameters and intensional operators which shift these parameters. The (implicit) time argument of a predicate is controlled by the closest c-commanding time operator, or the original value of the time parameter, which is normally the time of utterance. I treat vPs, for example, John bake a cake, as denoting properties 4 All the key examples of this article are either in the passé composé or in the imparfait. In the indicative mood, the perfective aspect is also a component of the passé simple, only used in written French, and of the plus que parfait. The passé simple and the plus que parfait pattern with the passé composé as far as AEs are concerned.

12:6
Actualistic interpretations of eventualities (type ⟨ , ⟩; is the type of eventualities). For example, the vP John bake a cake denotes a property that holds of an eventuality if and only if is an eventuality of baking located in the world and time of evaluation, whose agent is John and whose theme is some cake (assuming a neo-Davidsonian framework): (13) ⟦John bake a cake⟧ , , , = . bake ′ ( )∧ Agent( ) = John ∧ [∃ ∶ cake ′ ( ) ∧ Theme( )= ] ∧ ( )∘ ∧ in (the function maps an eventuality to its runtime and '∘' designates temporal overlap) 5 This semantics provides information about the runtime and the world location of eventualities in the denotation of vP. Asp takes a property of eventualities (the denotation of vP) and returns a truth value (type ⟨⟨ , ⟩, ⟩). 6 It quantifies over eventualities whose temporal trace it locates w.r.t. an interval called 'topic time' by Klein (1994) (this is also Gerö & von Stechow's (2003) and Paslawska & von Stechow's (2003) reference time). For example, pfv includes the runtime of some eventuality in the denotation of vP in the topic interval (the latter is provided by the time parameter, a variable that ends up being bound by Perf): 7 (14) ⟦pfv⟧ , , , = ⟨ , ⟩ . ∃ ∶ ( ) ∧ ( )⊆ In the case of a perfect (the passé composé is a present perfect), the relation between T and Asp is mediated by a perfect head, realized as an auxiliary. Perf turns a property of times or intervals (⟨ , ⟩, with the type of times) into a truth value: in order to compose the denotation of Perf with that of AspP, we need to turn the latter into a property of times, using Intensional Functional Application (Heim & Kratzer 1998: 308). The effect of Perf is to backward shift the time parameter for expressions in its scope: The parameters of the interpretation function ⟦⋅⟧ are , a tuple made up of the speaker and the hearer, which is used to interpret indexicals; an assignment , a world variable , a time or interval variable . 6 This system is thus a two-component one, to use Smith's (1991) terminology, that is, a system in which the perfective-imperfective difference is not reduced to the telic-atelic difference, as in Kamp & Rohrer 1983, Krifka 1989or de Swart 1998 The lexical entries in this subsection are inspired by Kratzer 1998 andPancheva &von Stechow 2004. 12:7 Homer In a present perfect, we find prs under T; I assume prs to be semantically vacuous. The time parameter at the top of the clause is set by default to the time of utterance. The meaning that we derive for the LF in (12) (corresponding to sentence (11)) is thus: The information that the eventualities quantified over are located in the world of evaluation is inherited from the denotation of the vP (see (13)).
In the imparfait, Aspect is impfv, that is, imperfective: (17) Imparfait: Il it pleuvait. rain.pst 'It was raining.' With impfv, the topic time is said to be included in the runtime of an eventuality in the extension of vP: impfv and pfv operate temporal inclusions which are inverses of each other. There is no perfect head in the imparfait, but backward shifting is carried out by pst (which I assume has the same semantics as Perf) under T. We derive the meaning of (17): In this temporal-aspectual system with three independent components, Tense, Aspect and Perfect, many possible combinations are not in fact attested, but I will not attempt to explain why this is so. For example, I do not offer an explanation for why perfects require perfective in the indicative mood. 8 8 Interestingly this restriction does not hold in the subjunctive.

Aspectual classes
The temporal-aspectual system presented above is one where Viewpoint Aspect combines with predicates of eventualities (type ⟨ , ⟩). These predicates belong to aspectual classes, in the Aktionsart sense of the term (Ryle 1949, Vendler 1957, Kenny 1963. For example, the predicate Peter bake the cake is a telic predicate (I will refer to predicates of eventualities in this nonfinite form). And the predicate Peter be in the kitchen is an atelic predicate (more precisely a stative one). Following Krifka 1989Krifka , 1998 and much subsequent work, I take telicity and atelicity to be properties of predicates of eventualities (and by extension, of their denotations) rather than properties of eventualities (as in Rohrer 1983 andReyle 1993). Krifka structures the domain of eventualities D as a join semi-lattice (with no bottom) partially ordered by the part-of relation '⊑' (on the model of Link's (1983) lattice-theoretical analysis of plurals and mass nouns): The proper part relation is defined as follows: Telicity and atelicity are defined by Krifka using the proper-part relation in (22). A telic or quantized 9 predicate of eventualities, for example, Peter bake the cake, is only true of eventualities that have no proper parts to which the predicate also applies: No proper part of an eventuality of Peter baking the cake (e.g., an eventuality of Peter making a well in the dry ingredients) is itself an eventuality of Peter baking the cake. By this definition, atelic predicates such as Peter be in the kitchen and Peter walk in the park are non-quantized: eventualities in the extensions of these predicates do have proper parts that are also in the extensions of these predicates. 10 Among atelic predicates, a further distinction is usually made: Peter be in the kitchen is stative while Peter walk in the park isn't (it denotes 9 I do not distinguish the terms 'telic' and 'quantized' although they are not in fact synonymous: 'telic' applies to predicates and 'quantized' to properties. 10 These predicates are (at least) weakly homogeneous and also cumulative (see Rothstein 2004: p. 10): 12:9 Homer an activity). A stative predicate is only true of eventualities that have proper parts, each of which is also in the extension of the predicate: The predicate Peter walk in the park is not true of eventualities in which Peter moves forward but doesn't make at least one step: activities are only homogeneous down to small parts (they are neither quantized nor stative).

non-quantized stative
Pierre be angry

non-stative
Pierre walk in the park quantized Pierre bake the cake Pierre arrive Table 1 Aspectual classes of predicates after Bary 2009: Table 4.1, p. 77

Coercion
As explained in Section 1.1, the perfective locates within the topic time the runtime of an eventuality in the denotation of vP. Combining the perfective with an atelic predicate comes with some notable effect: it results in some semantic enrichment.

Complexive interpretation
For example, the predicate of eventualities Pierre run in the park, an activity, is interpreted as temporally bounded in (25) perfective should lead us to expect that (25) can be verified by an eventuality 1 of Pierre running in the park even if it is a proper part of an eventuality 2 of Pierre running in the park whose runtime includes the topic time (contributed by the frame adverbial this afternoon). But instead, we observe that the eventuality whose runtime is located in the topic time is locally maximal. The following dialogue is thus odd, because B's reply contradicts the boundedness inference: No such boundedness inference arises in the imparfait (i.e., the imperfective), that is, a variant of (26) in which courait (imparfait) replaces a couru is natural.

Inchoative interpretation
By changing the temporal adverbial (by making it punctual) we observe another enrichment in the perfective: an inchoative interpretation obtains, that is, it is the inception of an activity which is located in the topic time:

Complexive and inchoative interpretations with statives
Stative predicates can also give rise to a complexive or an inchoative interpretation in the perfective. But help from certain adverbials is usually needed. Out of the blue, the following sentence is infelicitous: It would be possible to continue with saying that Pierre has been seated/ angry nonstop every since.
Complexive reading A complexive interpretation of statives becomes available with quantificational adverbials, for example, à plusieurs reprises 'on several occasions', une fois 'once', chaque fois 'each time', à un moment 'at some point', as well as durational ones, for example, pendant n heures 'for n hours', entre 14h et 15h 'between 2pm and 3pm'… (as opposed to locational ones, e.g., cet après-midi 'this afternoon ', en 2016 'in 2016'): that is, the predicate of eventualities is interpreted as being temporally bounded. From the infelicity of (29) above, it is possible to infer that stative predicates are incompatible with the perfective. But then what about (31) and (32)-(34)? They are indeed felicitous, but note that they also come with a special interpretation (complexive or inchoative), which amounts to semantic enrichment. One can thus maintain that the incompatibility is real but a repair is possible, which is tied to semantic enrichment. What can be the role of the semantic enrichment? Of the two interpretations which appear in the perfective, the complexive one probably offers the best insight. We said that a property of eventualities is temporally bounded when the eventualities in its denotation are locally maximal. Here is a formal definition: 11 (35) A property is maximal iff ∀ , ′ ∈D ∶ if ( ) and ⊏ ′ then ¬ ( ′ ) A stative property like Pierre be seated is, by definition, not maximal. But it can be turned into a maximal property. The result is no longer stative, in fact it is quantized: if a property is maximal then if holds of then no proper subpart ′ of is maximal, hence a eventuality. So if is maximal, then it is quantized (per (23)).

Aspectual mismatch and coercion operators
To sum up then, the examination of stative predicates suggests that they can only compose with the perfective if they are turned into quantized (telic) predicates. This is the gist of the aspectual coercion view: 12 after de Swart (1998), Gerö & von Stechow (2003) and Bary (2009), I assume that pfv imposes a restriction on its complement, which must be a quantized predicate of eventualities; 13 the semantic enrichment, a reinterpretation process, comes down to the transformation of a non-quantized property into a quantized one. Reinterpretation is a way of avoiding an impending mismatch; furthermore it is a last resort, since the complexive and the inchoative interpretations, as we saw in the imperfective variant of (26) and in (28), are not available in the imperfective. The reader will probably wonder: the need for coercion might be attested with stative predicates, for they are (for the most part) infelicitous in the absence of appropriate adverbials (29), but activities (e.g., Pierre run in the park) seem to dovetail with the perfective effortlessly. So do these need to be coerced as well? The fact that activities in the perfective mandatorily come with semantic enrichment (see (26) and (27) above) indicates that they too need to be coerced; but a complete answer to the query would require understanding the role of adverbials. I do not know why coercion seems to necessitate the presence of appropriate adverbials in the case of statives. But I note that this statement is too strong anyway, as certain statives can be coerced with no appropriate adverbial, for example, Pierre être ministre des affaires étrangères 'Pierre be minister of foreign affairs'. The reading that obtains is a complexive one: étrangères. foreign 'Pierre once was minister of foreign affairs.' sentence-internal mechanism, triggered as a response to a semantic mismatch between two expressions; for a different view, see Dölling 2014. 13 The reason for the restriction is not well understood. Bary (2009) and Bary & Egg (2012) offer an explanation in terms of competition and pragmatic strengthening. In a nutshell, the proposal is the following. Let be an imperfective sentence with a non-quantized vP predicate; the imperfective locates the topic interval within the runtime of an eventuality in the denotation of vP; if is true, there is an eventuality 1 which verifies this inclusion, and ′ , which only differs from in having pfv instead of impfv, is also true: the property denoted by vP is homogeneous at least down to a minimal threshold, and the topic interval thus contains the runtime of 2 , an eventuality in the denotation of vP, and a part of 1 . The selectional restriction of pfv can thus be seen as rooted in a semantic overlap, which Bary and Egg claim to be unwanted. These authors use Egg's (2005) Duration Principle, a principle which holds that 'properties of eventualities must be compatible with respect to the duration they attribute to an eventuality', to explain how the choice of a particular coercion operator is determined by the temporal modifiers present in the clause.

12:14
Actualistic interpretations The boundedness of the resulting predicate is evidenced by the following test (with the locational adverbial en 2016 'in 2016', which doesn't by itself trigger or license coercion): The imparfait variant of (37), in which était replaces a été, is not odd. Going back to the issue of adverbials, we can dismiss a possible hypothesis about their role in coercion: one could imagine that they apply to predicates of eventualities and make them quantized (as suggested to me by Ana Arregui); the fact that aspectual coercion can happen without adverbials (witness activities and Pierre être ministre des affaires étrangères), shows that they do not effect coercion by themselves or are not the only coercion agents. 14 Coercion operators I will assume, with Bary, that coercion is performed by covert operators, present in the syntax. These operators intervene between vP and pfv: 15 14 It is also plausible that not all adverbials are alike. It seems quite clear, for example, that durational adverbials, which can attach as low as vP, might suffice to turn an atelic predicate into a quantized one, by imposing temporal boundaries (it is harder to make the same case about quantificational adverbials). For example, while John run is atelic (and as such can be modified by for five hours), John run for five hours is quantized (under an exactly interpretation of the numeral). 15 In Section 2.3, I provide a gapping test to show that coercion operators are present in the syntax.

12:15
Homer There isn't just one coercion operator. Bary describes four of them in her study of Ancient Greek: in this language, in addition to the complexive and inchoative ('ingressive' in Bary's terms) interpretations, two more can be found, namely the tragic and the generic interpretations. For French we only need two (for the time being), labelled 'incho' (for the inchoative reading; Bary calls it 'ingr') and 'max' (for the complexive reading). Let's consider max first: its input is, in set talk, a set of eventualities and its output is a subset thereof, namely a set of eventualities with a maximal span, that is, eventualities not properly contained in other eventualities. The following entry delivers the desired meaning (i.e., a quantized property obtains): 16 Bary 2009] In the picture below in (40), 1 is an eventuality which is locally maximal and whose runtime ( 1 ) is located within the topic time: so if it is an eventuality of Pierre running in the park, it will verify (41): Now, how does the inchoative operator incho output a quantized property? Bary proposes that it returns (in set talk) a set of punctual eventualities. A predicate of punctual eventualities is vacuously quantized, because a punctual eventuality has no proper parts (23). The instantaneous eventualities in the output of incho abut the runtime of an eventuality in the denotation of the vP argument: where the initial bound function ib maps an interval ′ to the latest moment just before ′ . [from Bary 2009] The negative condition on the second line ensures that no eventuality in the denotation of vP starts before an eventuality in the output of the coercion operator. In the picture below, 1 is an eventuality in the output of incho and its runtime ( 1 ) (an instant, represented as a dot) is located within the topic time; the eventuality 2 , whose runtime ( 2 ) begins right after the runtime of 1 , is an eventuality in the denotation of vP: Unlike 2 , which is an eventuality in the denotation of vP, the nature of the instantaneous eventuality 1 , which is targeted by the inclusion performed by pfv, is left unspecified.
In the next section, I argue that root modals, which take front stage in standard descriptions of the actuality entailment phenomenon, form (i.) predicates of eventualities (ii.) which are atelic, specifically stative. My goal is to show that aspectual coercion, which targets atelic predicates in the perfective (Section 1.3), applies to them too.

Root modals form stative predicates of eventualities
The semantics that we gave for Viewpoint Aspect heads in Section 1.1 leads us to assume that in the sentences that interest us, for example, (1a), Asp combines with a predicate of eventualities of type ⟨ , ⟩. The root modal is the head of the complement of Asp, 18 and as such it forms a predicate of eventualities, for example, the predicate Olga can lift a fridge. If a predicate formed with a modal is indeed a predicate of eventualities, it should be possible to locate the eventualities it is true of in space and time, using appropriate modifiers. Let's verify that this is so. As for a time coordinate, in sentence (47)  We see that Viewpoint Aspect (impfv in (47)) locates the runtime of a legal situation (now over and superseded by a new one) w.r.t. the topic interval. It doesn't have access to eventualities in the denotation of the complement of the modal, that is, eventualities of Pierre turning in his homework (these are located in a time interval set by the modifier la semaine prochaine 'next week'). We can generalize: eventualities in the denotation of the complement of a root modal are never quantified over by matrix Viewpoint Aspect (despite appearances to the contrary, when an actuality entailment occurs); this is a point of contention with Hacquard (2009Hacquard ( , 2010, see Section 4. In the next sentence, the matrix adverbial fixes the space coordinate of a legal situation (Pierre being allowed to have received his surgeon degree abroad), which is not the same as the spatial location of the eventuality of Pierre receiving his surgeon degree.

(48)
Context: Where he lives now, is Pierre allowed to practice as a surgeon with his French degree?
18 That root modals are generated below Asp is a claim that is also defended by Hacquard (2009Hacquard ( , 2010, and Homer (2013)  The fact that spatial modifiers can be used to locate a legal situation is consonant with an analysis of the main vP headed by the root modal as a predicate of eventualities.
I propose a (simplified) semantics for root modals, 19 whereby they take as arguments a proposition (they create biclausal structures) and an eventuality: The accessibility relation Acc takes as input an eventuality, for example, the existence of certain conditions, rules or circumstances (I draw on situation semantics when I say that accessibility is not relative to a world but to an eventuality), and the modal domain is projected from this eventuality. 20 It is enough to change the quantificational force to get a lexical entry for devoir root 'must'. Second, if root modals form predicates of eventualities, what aspectual class do these belong to? A conceptual argument can be made. The predicates of eventualities headed by root modals are expected to be stative, since our definition of stative predicates applies to them: any eventuality that can be conceived as a state in which worlds are accessible from certain conditions, rules or circumstances, has proper parts, each of which is itself a eventuality.
A standard test confirms that predicates formed by root modals are nonquantized. They can be modified by for time-adverbials, and cannot be modified by in time-adverbials: 19 Simplified because I ignore the Kratzerian distinction (Kratzer 1981(Kratzer , 1991) between two conversational backgrounds, and because I do not specify how the accessibility relation is determined. 20 The notion of projection is taken from Hacquard 2010 and Kratzer 2013, and it has roots in Arregui 2005Arregui , 2007Arregui , 2009. A modal has an anchor, which is a part of the evaluation world; modal alternatives are fashioned according to the anchor. I use as anchor certain conditions of the world of evaluation, and I feed this anchor to the Acc function.  (50), I use a simple modified vP, not a tensed structure, to stay away from the interference created by coercion when Asp is introduced. Furthermore, to control for attachment ambiguity, I choose, in the complement of the modal, a predicate that cannot be modified by the relevant adverbial (hence the non-minimality of the pair). In (50a), the embedded predicate x send back the proofs of the manuscript is quantized; in (50b), x watch television is atelic. There is another aspect under which predicates headed by root modals pattern with atelic predicates. Unlike quantized predicates, they do not yield an obligatory future orientation in antecedents of subjunctive conditionals. (51) feels odd because it is hard to see how a future event of meeting with Michael Jordan would lead to the person in question playing professional basketball right now. Note that this test shows that predicates formed by root modals can be stative, not that they have to be (one could imagine that they are ambiguously stative or non-stative). Another test, specific to stativity, can be applied, which uses the incompatibility of the periphrastic progressive être en train de 'be in the process of' with stative predicates, as illustrated in (54)-(55)  As expected, the modal predicate pouvoir faire le gâteau ' can bake the cake' is infelicitous under the periphrastic progressive. It bears saying that the aspectual properties of the complement of the modal are not 'visible' to the periphrastic progressive above the modal (56); thus the aspectual class of the predicate headed by the root modal does not depend on the complement (a point which is ignored by Hacquard (2009Hacquard ( , 2010, see Section 4). Now, if a modal predicate of eventualities is stative, it should be incompatible with the perfective, barring coercion. In the next subsection, I show that the complexive and inchoative interpretations, which are reflexes of coercion, are available with root modals. Establishing this point is crucial, for 12:21 Homer if modal predicates of eventualities can be coerced, then they must be, given that coercion is a repair for a mismatch.

Inchoative interpretation
Recall that statives can receive an inchoative interpretation in the perfective (Section 1.3.2). The inchoative interpretation illustrated in (31) comes about with modal predicates as well, with the right adverbial. Suppose that Olga's wish was granted by a genie; she dreamt of being able to lift heavy objects: This time, soudain indicates that an event of Olga lifting a fridge happened suddenly, not (just) that the ability came to exist suddenly. As will become clearer in Section 2.3, the optionality of the AE under soudain is a case of ambiguity between two kinds of coercion, the inchoative one in (58) and the 'actualistic' one (which yields AEs) in (59).

Complexive interpretation
The second kind of special interpretation that arises when the perfective is confronted with an atelic predicate is a complexive interpretation, whereby the existence of a locally maximal state is asserted (33). Modal predicates pattern with non-modal ones in being subject to the same kind of coercion. (60) merely says that at some point in the past, there was a temporally maximal capacity: The continuations in (60) and (61) show again an ambiguity, this time between a complexive reading in the former, and an actualistic one (a.k.a. AE) in the latter.
The fact that modal predicates are amenable to at least two kinds of aspectual coercion in the perfective suffices to show that they are not suitable under the perfective, and that they need to be coerced, because coercion is a last resort. Another point must be made: the so-called exceptions to AEs in French follow a clear pattern: (62) Generalization: The very same adverbials that allow for the complexive and inchoative interpretations with non-modal predicates license a complexive or an inchoative reading, hence a reading without AE, with modal predicates.
This is another indication that modal predicates form a natural class with non-modal stative predicates. An actuality entailment is, like the complexive and the inchoative interpretations, a semantic enrichment: since modal predicates need to be coerced, as we have just shown, it stands to reason that an actuality entailment is a reflex of a hitherto unnoticed coercion mechanism. It is now time (i.) to show that there exists a kind of coercion with non-modal stative predicates which gives rise to an entailment about the occurrence of an event and (ii.) to propose that canonical AEs (with modals) are nothing but the result of this coercion. The next subsection is devoted to the exploration of the third way of coercing stative predicates.

Actualistic interpretation
I first illustrate this mode of coercion, which has gone unnoticed so far, 22 with non-modal predicates; I define a dedicated coercion operator act. And I then propose that it is the culprit in the triggering of canonical AEs.

Non-modal predicates
When placed in the scope of pfv, a number of stative predicates (importantly, not all predicates are eligible) give rise to a reading whereby the existence of some pragmatically determined event is entailed; 22 It has been unnoticed as far as the perfective is concerned. But it might well occur in the progressive, e.g., She's being smart, Goldsmith & Woisetschlaeger 1982, Moens 1987, de Swart 1998, Bary 2009.

12:24
Actualistic interpretations no adverbial is needed to license this reading. We find it, for example, with predicates formed with the verb coûter 'cost': (63a) not only says what the price of the house was, it also entails that the house was bought (or sold) for that price. No such entailment occurs if we substitute the imparfait (hence imperfective aspect) for the passé composé (which correlates with the perfective aspect), as in (63b) (Imperfective) The lack of entailment in (63b) can be evidenced by the aussi-test (not shown here). I submit that the entailment in (63a) is a reflex of an aspectual coercion, which is neither complexive nor inchoative; I label this coercion 'actualistic'; note that no adverbial is needed for it. The stative la maison coûter 100 000 € is also amenable to the inchoative or the complexive coercion, brought up by the relevant adverbials:  (66) and (67), the entailment is derived from an infinitival complement (which is reminiscent of canonical AEs with modal verbs; the commonality is not an accident, see Section 3). It bears saying that the entailments depend on the meanings of the predicates of eventualities, not on their particular linguistic form (a point that was already made in the Introduction, about standard AEs). For example, we can replace the house cost €100,000 with the price of the house be €100,000, or replace the tough-construction of (66) with a near equivalent, without changing the entailment pattern: The fact that these entailments only occur when a stative predicate is in the perfective strongly suggests that they result from aspectual coercion. This coercion doesn't require particular adverbials. I posit a coercion operator, which I call 'act': 25 It seems plausible that in this case, aspectual coercion coexists with another kind of coercion, which supplies a verb under like/hate such as read, see, etc., the same way that finish a book can be interpreted as 'finish reading/writing a book' (Pustejovsky 1995). The output of the latter coercion is part of the entailment. I submit that act takes two ⟨ , ⟩ arguments: the first one is provided by a variable (P 2 in the above tree); 26 the value of this variable is the property of eventualities that is existentially closed in the entailment. For the time being, I do not say how the value of this free variable can be predicted -I will do so in Section 3 -but one can safely assume that it is dependent on the utterance context, i.e., on the meaning of some other part of the sentence, namely vP. 27 The second ⟨ , ⟩ argument is provided by vP. Here is a provisional entry for act: Note that this coercion operator, like max (39) and incho (44), yields a conjunctive meaning. Unlike the former but like the latter, it yields (in set talk) a set of eventualities of a different nature than the set of eventualities denoted by vP. incho yields a set of instantaneous eventualities, whose nature is unspecified; act yields a set of eventualities whose nature is contextdependent. In order to satisfy the selectional requirement of pfv, the property returned by act is quantized: this is the role of the second conjunct in 26 The variable assignment function is defined as thus: for each ∈ { , }, for each k≥ 0, ( ) ∈ . 27 Another example of expressions whose meaning depends on the utterance context is provided by non-intersective adjectives in Heim & Kratzer 1998, p. 71. In the sentence Jumbo is a small elephant, it is not said that Jumbo is absolutely small, only that he is small for an elephant: a standard of size is determined by the noun elephant, present in the sentence.
(i) ⟦small⟧ , , , = . 's size is below , where is the size standard made salient by the utterance context.
With (P 2 ) the property the house be bought, we derive that the sentence asserts that there was an event of buying the house in a past interval in the world of evaluation, while its price was €100,000, as desired. The quantization condition applies vacuously since the property the house be bought is intrinsically quantized. This seems to be a fairly good approximation of the intuitive meaning. The output of act is fed to Asp. We verify that pfv quantifies over eventualities taken from the first argument, as shown by the clash in (80b): here the value of the first argument of act is determined (in a way to be explained) by the complement of the matrix adjective, which contains a predicate true of eventualities located after the time of utterance: We said that the utterance context determines the property of eventualities used in the actualistic coercion. Can we say a bit more? We have shown that x coûter y 'x cost y' can easily give rise to an actualistic interpretation (63a). Its near synonym x valoir y 'x be worth y' cannot, and in the absence of appropriate adverbials which could license an inchoative or complexive reading, it gives rise to an odd sentence: There is a crucial difference in the lexical semantics of cost and be worth. The value of an object is independent of a monetary transaction: even without being for sale, or after being sold, an object can retain its value, but not its price. Only objects that are up for sale have a price, and lose it once they have been purchased. This difference, which is rooted in the lexical entry of the two verbs, illuminates the workings of act: it is sensitive to the inference x can be bought triggered by the vP x coûter y. As shown in (82a), it is an inference that is preserved in questions, as evidenced by a clash with world knowledge (it is notorious that the Mona Lisa is not for sale): paradigm thus plays a role in deriving the actualistic interpretation; more will be said about this in Section 3.

Modal predicates
We can now put the pieces together and address the standard examples of actuality entailments. We have shown root modals to be coercible and thus obligatorily coerced in the perfective (Section 2.1 and 2.2); they give rise to what seems to be an actualistic interpretation, in the absence of adverbials that license other reinterpretations. I thus propose that AEs with root modals, for example (1), (10b), (59) and (61) (85) ⟦(84)⟧ , , , = True iff there is a past interval ′ s.t. there is an eventuality of (P 6 ) in in ′ s.t. no proper part of is an eventuality of (P 6 ), and there is a state of Olga being able to lift a fridge in whose runtime overlaps with ′ With (P 6 ) the property Olga lift a fridge (an inherently quantized property, which is inferred from context, and indirectly determined by the complement of the modal verb), 29 the perfective locates an eventuality of Olga lifting a fridge in the topic interval in the actual world (the world parameter, which is not shifted); it is also asserted that a state of Olga being able to lift a fridge existed in the actual world, and its runtime overlaps with the topic time (this information comes from the denotation of vP (13)). We verify that the eventuality whose existence is determined contextually cannot be temporally ordered after the topic time (hence pfv quantifies over eventualities taken from the first ⟨ , ⟩ argument (80b)): Angeles. Angeles 'This is how I was able to live in Los Angeles.' The result of coercion is a temporally bounded property of living in L.A. (act outputs a quantized property), which is then fed to pfv. The lexical entry in (76) states that act together with its arguments outputs True only if its first argument is quantized. Since the value of the first ⟨ , ⟩ argument is inferred, I have to assume that it is possible to infer an eventuality which is a temporally bounded state, based on the information provided by the utterance context.

Ambiguity: How AEs can be made optional
All stative predicates need to be coerced in the perfective (Section 1.3), which means, in the present system, that they require the presence of some coercion operator. Temporal adverbials license certain types of coercion (Table  2). For the predicates that are amenable to the actualistic one, temporal modifiers are not necessary to get the interpretation: therefore in the presence of temporal modifiers, ambiguity ensues (cf. (58) & (59) and (60) & (61), the latter two repeated below for convenience), and in their absence, only the actualistic interpretation is available.
(Act ic ) (88a) and (88b) taken together show that in the presence of a quantificational or durational adverbial, an AE is not mandatory (contradiction test) but possible (aussi-test). As for predicates that are not amenable to the actualistic interpretation, e.g., Pierre be seated, the only way they can be made acceptable in the perfective is through the inchoative and the complexive interpretations, licensed by the appropriate modifiers (they are otherwise generally excluded (29)).  This confirms that our analysis of AEs as stemming from the actualistic coercion is on the right track, and that quantificational temporal modifiers do not block AEs: they simply make them optional, by licensing another interpretation. It also bears saying that ambiguity shows that temporal adverbials are not per se the agents of coercion: therefore covert coercion operators are needed. 30 I would like to close this section by showing that the coercion operators that I posited are indeed present in the syntax (the demonstration is about 30 If we follow Hacquard's (2009Hacquard's ( , 2014 suggestion, temporal adverbials optionally remove the perfective, that is, a key ingredient of AE. I discuss this option in Section 4. [Jean] also escaped on Tuesday.' The first conjunct of the first sentence of (90a) mandates a complexive interpretation (since no prisoner escaped more than once), which the temporal modifier licenses; the constituent that is gapped in the second conjunct is identical with some constituent of the first conjunct which is at least as large as AspP. Importantly, there is no quantificational temporal modifier in the second conjunct, but a complexive interpretation obtains nonetheless: it is forced by syntactic means (i.e., copying). The continuation with aussi 'too' yields a presupposition failure in the above context: the AE is unavailable. The gapped constituent contains max -instead of act -because its antecedent does too. We have evidence that the complexive interpretation -i.e., max insertion -obtains through at least two routes: either max is licensed by certain quantificational temporal modifiers, or it is copied from another clause. In (90b), which is a control and where no copying takes place, 12:34 the AE in the second conjunct is possible (the aussi-test is successful) and in fact necessary (in the absence of modification or copying).
We can apply the same strategy to show that act is syntactically represented when an actualistic interpretation obtains.

(91)
Context: Same as in (90) The first conjunct of (91a) has an actualistic interpretation (i.e., an AE) because it lacks a quantificational temporal modifier. Copying of AspPincluding the act operator it contains -into the second conjunct ruins the coherence of the discourse (in the context, no prisoner ever escaped more than once) but it is syntactically forced, hence the incoherence marked with the # sign. In the control sentence (91b), the first conjunct receives an actualistic interpretation and the second conjunct a complexive interpretation, and no incoherence ensues (the asymmetry is possible because no copying is involved).
To sum up, we have shown that AEs are instances of a kind of aspectual coercion which targets modal and non-modal predicates alike (the actualistic coercion). We have shown that syntactically represented coercion operators are operative in satisfying the need of the perfective to combine with a quantized predicate of eventualities.

Presupposed AEs
As it stands, the foregoing theory makes no distinction between modal and non-modal predicates w.r.t. the actualistic interpretation: the same coercion mechanism is said to apply to both kinds of predicates. There is however a striking asymmetry, which might cast doubt on the unified picture proposed here: the actuality inference is a presupposition in the case of non-modal predicates, while it is a 'plain' entailment in the case of modal predicates. The preservation of the inference in (92)-(94) shows that it is a presupposition. Under negation, a 'negative' entailment obtains with modal predicates, whether the modal has existential or universal force (as already observed by Hacquard (2009)), and the modal is negated as well: We are now faced with two challenges. First, the asymmetry seems to suggest that either standard AEs are not the result of coercion, or if they are, modal predicates get coerced by a different operator than the one that applies to non-modal predicates. The first option is inconsistent with the evidence adduced here, and the second option is implausible, as it is hard to conceive of operators with a selectional restriction for or against modal predicates of eventualities. I actually think we can reject the alternative. And in doing so, we will also address the second challenge: our semantics for act yields a conjunction of two statements, a modal one and a non-modal one (75), but we observed that under negation the second component always gets negated; our account is a priori not well suited to explain why we get this 'negative' entailment (and worse yet, there are two negative entailments in the case of modal predicates, see (97)-(98)).

A necessary and sufficient condition
The solution to the two challenges is inspired by the observation of the presuppositions triggered by the non-modal predicates involved in actualistic coercion (66)-(71): we noticed (Section 2.2.3) that they all come with a modal presupposition. For example, the house cost €100,000/a lot presupposes that the house can/could be bought. Now suppose that act triggers a 'necessary 12:37 Homer and sufficient condition' presupposition, which holds that the house was bought just in case it could be bought. Combining these two inferences results in the simple presupposition that the house was bought. And this is precisely the outcome we observed: the actuality entailment is presupposed. With modal predicates, we also find a modal inference, for example, that Olga can lift a fridge, contributed by the modal predicate itself. But this inference is not a presupposition; consequently, despite the 'necessary and sufficient condition' presupposition of act, the actuality inference will not be presupposed; and because of the necessary and sufficient condition, the entailment will be a negative one.
Let's now implement this idea in a revised definition of act. The only change is the addition of a presupposition, the 'necessary and sufficient condition'. 31 I use the -notation, borrowed from Beaver & Krahmer 2001: ( ) is defined iff is true. I also use the ' Qu ' abbreviation introduced in (76) for quantized predicates: with Ω the strongest entailment of ∃ ∶ ( ) of the form [Mod(∃ + ∶ ( + ))], with Mod ∈ {◇, □} and some predicate of eventualities [final version] What this says is that the existence of a eventuality ( is the ⟨ , ⟩ argument whose value is context-dependent) has a necessary and sufficient condition. 32 This necessary and sufficient condition Ω is given as an entailment of '∃ ∶ ( )', where is the ⟨ , ⟩ argument saturated by vP. Let be the predicate Pierre devoir rendre son devoir 'Pierre have to turn in his homework'. Then '∃ ∶ ( )' has entailments of the form [Mod(∃ * ∶ ( * ))], with some predicate of eventualities and Mod∈ {◇, □}, namely: 31 A similar presupposition is introduced in Alxatib 2019. This proposal and mine were developed independently. 32 For reasons of simplicity, I use a biconditional symbol, although I am aware that analyzing necessary and sufficient conditions in terms of material implication (see e.g., Blumberg 1976 andHintikka &Bachman 1991) is problematic. 12:38

Actualistic interpretations
The second entailment (with □) is logically stronger than (asymmetrically entails) the first one (with ◇): we would thus only retain the second entailment, as prescribed by the presupposition. With a modal predicate like Olga pouvoir soulever un frigo 'Olga can lift a fridge' there is only one modal entailment (101a); similarly with our non-modal predicates, for example, la maison coûter 100 000€ 'the house cost €100,000', except that in this case, the modal entailment is a presupposition (101b): The presupposition of act restricts the choice of the first argument of act (the variable): it requires that the existence of a eventuality be conditioned (necessarily and sufficiently) by another eventuality, which is a possibility, a capacity, an obligation, etc., drawn from the meaning of vP. I thus submit that the presupposition of act is what determines the value of the free property variable argument of act.

Examples
Let's now apply the new lexical entry to examples. These examples should help us understand two things: (i) how the value of the free property variable gets determined (i.e., which actuality inference is derived) and (ii) how the actuality inference is in some cases (but not all) a presupposition. First, consider again (94) Now we consider the presuppositions. We know that (P 2 ) is determined by the context of utterance, and I assume that the necessary and sufficient condition attached to act (99) provides the information needed for this determination. The strongest modal entailment of la maison coûter cher is: act presupposes that the possibility that the house is bought is a sufficient and necessary condition for the existence of (P 2 ), a quantized property. Let's see why the best choice for (P 2 ), given this restriction, is the property the house be bought. The possibility of buying the house is certainly a requirement for its purchase. Now, it is not sufficient for the purchase in just any context. But it is in contexts in which all relevant circumstances (the existence of a plan on the part of a buyer, approval by a lender, etc.) converge toward the realization of the purchase. Provided that such circumstances can be accommodated by the conversationalists, the property the house be bought can be inferred. Now why is it that this property and none other is indeed inferred? Any more specific (hence stronger) property would require more accommodation and is presumably ruled out for this reason. Why not a weaker property? An obvious candidate would be someone try to buy the house. But does an attempt to buy the house require the possibility to buy it? I find this doubtful (but matters that rely so heavily on world knowledge are, I must admit, difficult to decide). Let's abbreviate the inferred property the house be bought (a quantized property) as . The presupposition of act projects through negation, and so does the presupposition triggered by the vP predicate; so we get (notice the ' Qu ' abbreviation for quantized predicates (76)): I assume that the statement '◇(∃ ′ ∶ ( ′ ))' is time-dependent, and that the time parameter of the interpretation function serves to specify its location in time (the time at which the possibility holds): it is thus equivalent to '∃ ″ ∶ ⟦vP⟧ , , , ′ ( ″ )'. 33 We now simplify the presupposition, and consequently the truth conditions: The sentence presupposes that the house was bought in the topic interval in the world of evaluation and asserts that it didn't cost much at the topic interval, as desired.
Let's now turn to modal predicates, and derive the semantic value of (97).
(108) LF of (97) The strongest modal entailment of Olga pouvoir soulever un frigo is: Olga's ability to lift a fridge is a necessary and sufficient condition for the existence of (P 8 ). Again, an event of Olga attempting to lift a fridge does not require her ability to do so. But an event of Olga lifting a fridge does. Turning to sufficiency now, we again need to accommodate circumstances, which together with Olga's ability, suffice to bring about an actual lifting. In other words, we can see Olga's ability as the only missing piece in a larger set or system of circumstances leading to the actualization of her ability. It has often been noted that AEs are accompanied with a second inference, which is 33 The vP the house cost a lot triggers the presupposition that the house can be bought; the presupposition is not intrinsically tensed, but when the predicate is modified by tense, the presupposition becomes relativized to a time: (i) The house will cost €100,000. Presupposition: It will be possible to buy the house.

12:41
Homer not easy to pinpoint. Is it an inference of difficulty or of goal-orientedness? 34 For example, Mari (2016) gives examples such as (110), which indicate the existence of a plan or intention (the same test can be applied to (97) [Mari 2016, ex. (9)] Note that the sentence is still deviant if we negate the first part of the sentence. I don't think such examples indicate that the modal is inherently goaloriented (and that AEs are thus limited to such modals, pace Mari), for we observed AEs with all root flavors of modality. Instead, I propose that the necessary and sufficient condition presupposition, which projects in the case of modal predicates, is the source of the inference. For a possibility to be a necessary and sufficient condition for an event, it must be the case that the possibility is the only missing piece in some plan (a plan to lift a fridge, which requires specific circumstances, including an effort on Olga's part).
With non-modal predicates, for example the house cost a lot, no such additional inference (of effort or desire) is observed: for example, one doesn't infer from (63a) or (94) that a certain plan succeeded. But our semantics actually predicts that, for the necessary and sufficient condition presupposition doesn't project with non-modal predicates (107). 35 Let's abbreviate the property Olga lift a fridge (a quantized property) as . ⟦vP⟧ , , , ′ denotes a possibility of Olga lifting a fridge, such that this ability holds in the world of evaluation at the time of evaluation ′ . Factoring in the presupposition of act, we get (the vP predicate doesn't trigger a presupposition): 34 It seems to me that it is the same inference that is attached to implicative verbs, e.g., manage.
I do not pursue the parallel here but I think that what I say about the presupposition of act can fruitfully be compared to Baglini & Francez's (2016) analysis of manage. 35 The condition is still used of course, in the determination of the value of the ⟨ , ⟩ variable.
I submit that the calculation of the value of the variable occurs at the point where act composes with its two ⟨ , ⟩ arguments; the information that the possibility to buy the house is a necessary and sufficient condition for the buying becomes lost in the course of the semantic derivation (it doesn't project), due to the incorporation of other presuppositions.

12:42
Actualistic interpretations We can conclude: the biconditional in the presupposition of act leads to negating the two conjuncts of the assertive content. That is, the sentence asserts that Olga didn't lift a fridge in the world of evaluation (negative AE) and that she didn't have the ability to do so, as desired. If we remove the negation from (97), we get that Olga lifted a fridge and that she had the ability to do so.
Mutatis mutandis, we also derive the right denotations for sentences with a universal modal. 36 (112) LF of (98) The sentence asserts that Olga didn't lift a fridge in the world of evaluation and that she didn't have an obligation (if the modal is deontic) or constraint 36 For reasons of space, I do not discuss negative AEs triggered by 'intrinsically' negative predicates: (i) L'obstacle the-obstacle a has été be.pp impossible impossible à to franchir. overcome → The obstacle was not overcome.
In this case, the predicate yields an entailment of the form □(∃ ′ ∶ ( ′ )), with standing for the obstacle not be overcome. Actuality entailments provide a strong case for the existence of negative events, although these are a subject of skepticism among linguistics and philosophers. The following example drives this point home, I think: Bernard & Champollion (2018) provide a linguistic account of negative events, which, as far as I can tell, can be incorporated in the current proposal.

12:43
Homer (if the modal is circumstantial) to do so. This is as desired. Why is the inferred property Olga lift a fridge? Obviously an obligation or constraint, e.g., Olga have to lift a fridge, is not a necessary condition for Olga lifting a fridge. Or for any event property for that matter. Therefore one needs to do some accommodation, once again: one needs to assume a context in which an obligation or constraint can be a requirement (as well as a sufficient condition) for some event. This explains the inference that one gets from (98) that Olga didn't behave according to her desires, but only lifted a fridge because of a moral obligation or a constraint. Had the constraint (or obligation) been absent, it is natural to assume that Olga wouldn't have lifted a fridge (hence that she didn't want to).
To better appreciate the effect of this 'reluctance' inference, consider propriétaire. owner 'The thieves had to return the money to its owner.' (114) should be a felicitous sentence if its overall meaning amounted to saying that the thieves were morally or legally obliged to return the money to its owner and that they did (both statements are true). But it isn't, and the problem seems to be that the context establishes no connection between a deontic obligation and the restitution of stolen goods. If the context is one where the thieves become consumed with remorse, and guilt makes them return the money, then the sentence is perfectly natural. Another supporting context would be one where the obligation is not moral: the thieves returned the money because Superman caught them and told them to do so. Either way, the restitution wouldn't happen without the obligation, and the obligation suffices for it to happen.
The semantics of act (99) appears (i) to correctly derive the 'negative' actuality entailments in (97) and (98) (and lack thereof in (94)) and (ii) to account for additional inferences (of difficulty, goal-orientedness or reluctance). In closing, I would like to address two issues raised by this entry. 12:44

Two issues
First, the reader might wonder why I insist that the first ⟨ , ⟩ argument is contextually determined. Wouldn't it be simpler to equate the value of the free variable with the predicate which appears in the strongest modal entailment drawn from the second ⟨ , ⟩ argument? The reason is that we sometimes need weaker inferences. Take predicates headed by vouloir 'want'. In the perfective these typically yield attempt inferences: Were Margot to continue with saying that he didn't try to strangle her, she would be inconsistent (contradiction test); in the imperfective, such an attempt inference wouldn't occur. If we think about the presupposition of act, it makes sense that an attempt event is inferred, since a desire to can reasonably be seen as a necessary and sufficient condition for an attempt to . I do not have an explanation for why Italian volere in the perfective yields a stronger inference, i.e., the realization of its complement (Hacquard 2006: Chapter 4). But I note that the same is true for some verba volendi in French, e.g., tenir à 'be intent on', which are intuitively 'stronger' than vouloir. Second, why is it that many stative predicates, e.g., Pierre être assis (29) and la maison valoir 100 000 € (81), 37 are out in the perfective, barring ap-37 This is also true of certain modal adjectives, e.g., fragile 'fragile' and cassable 'breakable': propriate adverbials? That is, why can't they be coerced with act? The entry for act requires a modal entailment. Maybe this can account for the house be worth €100,000. But, as an anonymous reviewer points out, it is likely that Pierre be seated entails and even presupposes that Pierre can bend his legs. Obviously, a modal entailment is not enough. And the coercible predicates meet some extra condition that I am currently unable to single out. Hacquard's (2006Hacquard's ( , 2009 theory is a landmark in the study of AEs, and the first account extensively based on French. The thrust of the proposal lies in what Hacquard takes to be a syntactic peculiarity of modal verbs. She claims that they create monoclausal structures: in her view, the complement of pouvoir and devoir, unlike that of other modal expressions, for example, the noun possibilité, is devoid of an Aspect head. The Asp head above ModP quantifies over eventualities in the extension of the embedded predicate of eventualities.

Comparison with Hacquard 2006, 2009
(116) Jane a pu circ prendre le train. The system is extensional, with indexed abstractors over world variables (à la Percus 2000) and over eventuality variables. Tenses are treated as pronouns with presuppositional features (after Partee 1973, Heim 1994, Schlenker 1999, von Stechow 2004; the assignment function assigns values to indices carried by individual, time, eventuality and world variables. pfv takes a world 12:46 and a property of eventualities as arguments, and returns a property of times; it carries out the inclusion of an eventuality in the denotation of vP inside the topic time and in its world argument; root modals take a world argument and a ⟨ , ⟨ , ⟩⟩ argument, and return a property of eventualities (I adapt and simplify some of the entries): ∧ Theme( , ′ )=the train ∧ Agent( , ′ )=Jane ( and are respectively the time and the world of the context) 'There is an event in located in a past interval, and there is a world compatible with Jane's abilities in where that event is a taking-the-train event by Jane.' The sentence asserts the existence of some eventuality in the actual world. With an existential quantification over possible worlds (i.e., the modal) mediating between Viewpoint Aspect and vP, this eventuality is said to be, in some accessible world, an eventuality in the denotation of vP. Hacquard claims that the properties of an eventuality in an accessible world are the same as the properties of in the actual world, which derives that in (116) an eventuality of Jane taking the train took place in actuality. (120)

Principle of Preservation of Event Description (Hacquard 2009):
For all worlds 1 , 2 , if eventuality 1 occurs in 1 and 2 , and 1 is a event in 1 , then ceteris paribus, 1 is a event in 2 as well.
In this account, the stativity of root modals plays no role, no more than the perfective per se or any restriction imposed by it; it is also silent about the actuality inferences that obtain with non-modal predicates. AEs are predicted to obtain if and only if a root modal is placed under the perfective. The imperfective, according to Hacquard, is more complex, as it brings in modal quantification: therefore the events whose existence is asserted happen in non-actual worlds, hence the absence of AE. The claim that the complement of modal verbs lacks an Asp head runs counter to some of the evidence discussed in this article. We showed that 12:47 Homer the Aspect head above the modal doesn't have access to eventualities in the denotation of the complement: in (47), the Asp head was impfv, and it didn't quantify over eventualities in the denotation of the embedded vP; in (89), the Asp head was pfv, and again, there was a temporal mismatch, but no infelicity. It is also implausible that full CP complements would lack an Asp head, and yet AEs are observed with modals that embed (subjunctive) thatclauses: Hacquard highlights the purported lack of AE with the noun possibilité, and argues that it lends support to her claim, since she assumes that nouns create biclausal structures: (122) Olga a eu la possibilité circ de prendre le train de 7 heures, mais ne l'a pas fait. 'Olga had the possibility to take the 7 o'clock train but she didn't do so.' Granted, (122) is not contradictory, but avoir la possibilité de is in fact ambiguous: under one reading, it does not yield an AE (122) In light of the principles I advocate in this article, the reason no AE is triggered in one reading of (122) is either that no aspectual coercion occurs, or that a kind of coercion other than the actualistic one is available (without adverbial modification). To account for the apparent lack of AE in (122), it is enough that one of these two options is viable. I think there is evidence that the first option is, since the verb avoir 'have', which is part of the modal expression, has some eventive usages, for example, in (124), where it means 12:48 get, in the absence of any aspectual coercion (the sentence is in the simple indicative present). ans. years 'One gets their A-levels at the age of 18.' Whenever the auxiliary is être 'be' (as in être capable, see (6)-(9)) rather than avoir 'have' (as in avoir la possibilité de), the contradiction test is passed. It thus follows that (122) cannot be used to support the view that modal nouns differ from modal verbs with regard to the presence of Asp in their complement; all (122) shows is that the actualistic coercion is not the only option (in the absence of licensers of other coercions) with predicates headed by the verb avoir.
The so-called 'exceptions' to AEs which obtain in the presence of certain temporal modifiers, for example, (10a), (57) and (60), are genuine counterexamples to Hacquard's theory, for which AEs are derived if and only if a root modal is placed in the perfective. One cannot claim that temporal modifiers change Viewpoint Aspect from perfective into imperfective (this attempt is made in Hacquard 2006, fn. 73 on p. 164 about sempre 'always' in Italian). There is no evidence that temporal modifiers have this effect. In fact, we see clearly that perfective sentences have none of the characteristic aspectual properties of their imperfective counterparts. For example, accomplishments in the imperfective give rise to the so-called imperfective paradox (i.e., the lack of entailment illustrated in (125) Hacquard (2014) proposes that temporal modifiers can license a perfect construal of the passé composé, which might be compatible with imperfective or neutral aspect. The first option is not viable, as we've just shown. As far as neutral aspect is concerned, I suppose that it doesn't carry out a temporal inclusion in an interval. But even with the addition of quantificational temporal modifiers, we observe that inclusion in the topic interval is compulsory in French: the inchoative and the complexive coercions, which we discussed extensively (Section 1.3), and which are licensed by the adverbials in question (the same for modal and non-modal predicates (62)), are ways of facilitating the inclusion. (127) makes the same point with a quantized predicate: the sentence is odd because it asserts that an event of running the Paris marathon (which takes at least two hours) fits in the duration of the 1pm news report (approximately thirty minutes): heures. hours Intended: 'On several occasions she ran the Paris marathon during the 1pm news report.' In some languages, AEs remain obligatory under quantificational modifiers and suddenly: Hacquard (2014) provides examples from Bulgarian and Hindi-Urdu. By itself, such an observation is not a problem for the theory I advocate. One needs to first check how coercion works in these languages, and ascertain whether the complexive and the inchoative interpretations are ever available with statives. For what makes (10a), (57) and (60) and the like exceptional is not that they lack an AE; it is rather that they are ambiguous examples, due to the licensing of an alternative construal.
Lastly, in this system, certain inferences fail to be derived. There is no semantic encoding (and there cannot be one) of a necessary and sufficient connection between the event in the actual world and the possibility/necessity contributed by the modal predicate. Given the semantics in (119), it is not predicted that (110) would sound like a contradiction. And as Hacquard 2009 acknowledges, the negative entailment about Olga's ability which obtains under negation in (97) is not derived qua entailment. The predicted truth conditions of (97) hold that there was no event in the actual world that in some world compatible with Olga's abilities is an event of Olga lifting a fridge; but there might be worlds compatible with Olga's abilities in which some event 12:50 of her lifting a fridge occurs (not the same event as the one in the actual world). With a universal modal (98) the prediction is also incorrect. The sentence is predicted to assert that there is no actual event such that in all worlds compatible with Olga's circumstances, is an event of Olga lifting a fridge. These conditions are met when there is an actual event which only exists in some accessible worlds and is, in those worlds, an event of Olga lifting a fridge. This time, the negative AE is missed (contrary to what is claimed in Hacquard 2009: p. 307).

Conclusion
Provided that the stativity and the coercibility of root modals are taken into consideration, it becomes apparent that aspectual coercion must play some role in the derivation of actuality entailments. This article documents a hitherto unnoticed mode of coercion of stative predicates in the perfective, with I call 'actualistic'. Like other aspectual coercion processes, it applies to modal and non-modal predicates alike. The covert coercion operator act reinterprets a stative predicate into a quantized one, in such a way that the existence of an event in the world of evaluation is entailed, and this occurrence is contingent on a condition, which is, by presupposition, necessary and sufficient. This condition is the existence of a possibility or a necessity, provided by the core meaning of the original stative predicate. The presupposition has detectable effects, as it manifests itself in the often described effort or goalorientedness inference; these effects are derived in the article, as well as the rather intricate entailment pattern under negation.