Past participle agreement in French and Italian: A two-Agree analysis

In this study, past participle agreement (PPA) patterns in French and Italian are explained based on recent minimalist notions involving minimal search and labeling. For minimal computation, Agree minimally values a participle and an in-situ object (Minimal Agree). Hence, the participle is spelled out in a default form. If an object is displaced, a participle can choose to Agree with the object’s copy in its SPEC. Since the Agree operation is coupled with labeling, it fully values the participle (Full Agree), resulting in morphological agreement. In many cases, the optionality of PPA results from the participle’s free selection between the two types of Agree. The proposed analysis also deals with cases where PPA is either obligatory or absent. First, a derived subject obligatorily triggers agreement since Full Agree applies to the subject to label the so-called TP node, which also affects the participle. Second, Italian 3rd person clitic objects control agreement obligatorily, which is attributed to their internal structure. Third, agreement with a wh-object is absent in Italian because of criterial freezing. Since Full Agree is part of criterial licensing, a wh-phrase cannot select this option until it reaches its final criterial position unless some form of reconstruction is available.


Introduction
It is well known that a past participle in French and Italian can agree in gender and number with a preverbal object but not with an object remaining in situ. Observe that the clitic object in (1a) triggers feminine plural agreement on the participle whereas the postverbal object in (1b) does not. (1) French (Kayne 1989) a. Paul les a repeint-es. Paul them has repainted-f.pl 'Paul has repainted them(f).' b. Paul a repeint/*repeint-es les chaises. Paul has repainted/*repainted-f.pl the chairs[f] 'Paul has repainted the chairs.' Previous attempts to account for the mechanism of past participle agreement (PPA) have encountered several complicating factors. First, PPA is obligatory in some constructions but optional in others. Second, PPA affects semantics in some cases but not in others. Third, PPA patterns differ between French and Italian in several respects.
This study provides a minimalist analysis of PPA. Differences between French and Italian are attributed to different morphosyntax and parameterized criterial freezing. The remainder of this paper is organized as follows. In Section 2, I illustrate the PPA patterns in French and Italian. Section 3 examines the previous approaches and associated problems. Section 4 introduces two types of Agree operations derived from minimal search and labeling algorithm (LA). In Sections 5-7, I show how the two-Agree theory accounts for the PPA patterns. In Sections 8 and 9, I consider some further consequences of the analysis and the validity of parameterized criterial freezing, respectively. Finally, Section 10 concludes the paper.

PPA in French
In this section, we consider French PPA patterns. A lexical verb appears in past participle form in both perfect and passive sentences. A participle in an unaccusative perfect sentence or a passive sentence obligatorily agrees with a derived subject, that is, an A-moved object (Sportiche 1998;Belletti 2006). 1 In (2a,b), the derived subjects are 3rd person feminine singular, and the participles must be spelled out with the same gender/number properties: 1 These participles are typically preceded by être 'be'. A few unaccusative participles preceded by avoir 'have' reject agreement with a derived subject.
(2) Mathieu (2003: 87) a. Elle est allé-e/*allé en vacances. she is gone-f.sg/*gone[def] on holiday 'She went on holiday.' b. Elle a été réveillé-e/*réveillé. she has been woken-f.sg/*woken [def] 'She was woken up.' In contrast, PPA is optional if the preceding object is a clitic. 2 In the following examples, the participle may show agreement or appear in a default form.

b. Il t'
a pris-e/pris au jardin. he you has taken-f.sg/taken [def] to.the garden 'He took you(f) to the garden.' PPA is also optional with an A'-moved object and, if applied, has a semantic effect (Déprez 1998).
The following examples illustrate this point: (4) Déprez (1998: 10) a. Combien de fautes a-t-elle fait-es? how.many of mistakes has-she made-f.pl 'How many (amongst a known set of) mistakes has she made?' b. Combien de fautes a-t-elle fait? how.many of mistakes has-she made [def] 'What is the number of things that are mistakes and that she has made?' Déprez (1998) notes that the agreeing sentence (4a) presupposes a specific set of mistakes and asks how many of them are attributed to the subject. There is no such requirement for the non-agreeing sentence (4b). The object can be either specific or nonspecific when it does not trigger PPA.
PPA with a derived subject does not have this effect. Sportiche (1998) observes that the following sentence allows a non-generic non-specific reading of the indefinite subject: (5) Sportiche (1998: 155) Dans ce pays, une chaise est repeint-e toutes les heures. in this country a chair [f] is repainted-f.sg all the hours 'In this country, a chair is repainted every hour.' It is not clear whether the specificity requirement is relevant to clitics since they are intrinsically specific. 3 In sum, PPA results in a specific reading of an A'-moved object, but the effect is absent or unclear in other PPA cases.

PPA in Italian
PPA in Standard Italian holds in contexts similar to those of French. First, a participle cannot agree with an in-situ object.
Maria is arrived-f.sg/*arrived-def 'Mary has arrived.' b. Due camicie sono stat-e lavat-e/*lavat-a. two shirts [f] are been-f.pl washed-f.pl/*washed-f.sg 'Two shirts have been washed.' However, different patterns are found elsewhere. First, PPA is obligatory if the clitic object is 3rd person. 3 Except for partitive clitic en (ne in Italian), which I consider in Section 8.

Summary of the data
The above observations are summarized as follows: 3 Previous approaches to PPA Kayne (1989) was the first to provide a generative account of PPA. Observing that only dislocated objects can trigger PPA, the author postulates Agr as a head responsible for PPA: PPA surfaces when Agr governs the object. PPA with an in-situ object is absent since no government relation holds between Agr and the object (see (12a)). If the object is displaced, Agr can govern (the trace of) the object, as in (12b). Sportiche (1998) assumes that SPEC-Agr is not an obligatory intermediate position, resulting in the optionality of PPA. The idea has led to the unification of PPA and finite verb agreement, both of which take place under government in AgrP.
The analysis, although simple and attractive, raises questions regarding its applicability.
Does obligatory PPA with a derived subject imply that A-moved DP must stop at SPEC-Agr? If so, why? What can account for the differences between French and Italian PPA?
Efforts have been made to develop Kayne's (1989) concept to answer these questions. This analysis, however, suffers from conceptual and empirical problems. From a minimalist perspective, an arbitrary stipulation of feature setups is not desirable. Empirically, the analysis does not address either obligatory PPA cases or differences between French and Italian PPA.

Explanation by recourse to feature arrangements
The same criticism applies to Déprez (1998), who accounts for French PPA patterns by arranging feature setups. Still, the author's idea of relating PPA to the Mapping Hypothesis (Diesing 1992) is incorporated into the analysis to be developed, as we will see in Sections 7 and 9.

Explanation by recourse to movement paths
Some researchers build on Kayne's (1989) insight that PPA results from a government relation between a dislocated object and Agr/v (e.g. Friedemann & Siloni 1997;Sportiche 1998;Guasti & Rizzi 2002;Belletti 2006). Different PPA patterns emerge from different movement paths of an object or a participle. Below, I illustrate the analysis proposed by Belletti (2006 (16e)). PPA with an A'-moved object is absent since the object and the participle never meet in the same AgrP (see (16b) and (16f)). 5 Supporting evidence for (16a, b) can be found in Pollock (1989), Belletti (1994), Cinque (1999, and Guasti & Rizzi (2002). Observing the relative order of participles and adverbials, these authors claim that (i) a participle has several possible landing sites (as in (17a, b) and (18b)); (ii) a passive participle may occupy a position lower than an active one (as in (18a, b)); and (iii) a French participle does not raise as far as an Italian one (as in (18a) and (19)).
By contrast, evidence for the assumptions (16c-f) is, to the best of my knowledge, nonexistent.
The assumptions are also conceptually problematic: There is no principled reason for language to be equipped with recursive AgrPs or escape hatch parameters. Moreover, as pointed out by D'Alessandro & Roberts (2008), there remains a question about how to accommodate SPEC-Head agreement under the Agree theory. 6 Considering these problems, Belletti's (2006) analysis is difficult to maintain. Agree holds between Prt-v and the in-situ object. Because vP is a strong phase, the complement domain, VP, is spelled out when the phase is completed. The Spell-Out domain contains an object, but not Prt-v. Therefore, the participle fails to show agreement with the in-situ object.

Explanation by recourse to PF
When the object is a clitic, it is in the same Spell-Out domain as Prt-v as a result of clitic movement, as shown in the following structure: When the phase CP is completed, the Spell-Out domain, TP, contains both the clitic and Prt-v.
Thus the participle shows morphological agreement with the clitic.
A derived subject is also contained in the same domain as the participle.
6 SPEC-Head agreement can be revived under the idea of minimal search, which I propose in Section 4.
The unaccusative/passive vP is not a phase. When the CP phase is completed, the participle is spelled out together with the derived subject with morphological agreement.
D'Alessandro & Roberts (2008) thus offer a simple explanation without ad hoc assumptions.
However, their discussion is limited to the obligatory PPA cases in Italian. It remains unclear how their analysis accounts for optional PPA with 1st/2nd person clitic objects. Moreover, it seems impossible to extend the analysis to PPA in French. For example, the analysis cannot consider PPA with a wh-object since a wh-object and a participle are obviously in different Spell-Out domains. The specificity requirement (as seen in (4)) also remains unexplained under the PF approach.
To conclude this section, we still lack a satisfactory account of PPA phenomena in French and Italian. In the next sections, I approach this problem based on recent minimalist notions involving minimal search and labeling.

Minimal Agree and Full Agree
As pointed out by Guasti & Rizzi (2002), PPA is a typical case of agreement asymmetry (cf. Greenberg 1966;Corbett 2006). Cross-linguistically, agreement tends to be richer when the controller (i.e. nominal) precedes the target of agreement than when the order is reversed.
(23) Controller … Target …. Controller |______________________| |_________________| richer agreement poorer agreement As for PPA, the object preceding the participle can trigger PPA (rich agreement), but the object following the participle cannot (poor agreement). Chomsky (2013; claims that richer agreement is related to LA. Consider the following structures: (24) a.

b.
When a lexical item (H) is merged with a phrase, as in (24a), LA selects H as the label of the syntactic object (SO). In this case, LA is just minimal search. When two phrases merge, as in (24b), LA cannot select one head for labeling. There are two ways in which the SO can be labeled: (i) Make XP or YP invisible to LA by raising it, or (ii) take the most prominent feature(s) shared by X and Y to be the label of the SO. The latter is a minimalist reformulation of SPEC-Head agreement. Chomsky (2015: 7) suggests that "in SPEC-head constructions rich agreement is necessary for labeling." Agreement elsewhere may not be rich, since there is no labeling issue.
In the above formulation, there are two distinct types of Agree: by Full Agree, it is spelled out with an agreement morpheme. Thus, the agreement asymmetry follows from the two types of Agree.
As for the timing and the domain of Agree and Transfer, I adopt the following assumptions: (26) a. Agree and Transfer take place at the phase level (Chomsky 2000: 131;2004: 116;2007: 18-19;2008: 143;2013: 42). b. Transfer applies to the complement of a phase head (Chomsky 2004: 108;2013: 42). The assumption (26c) may require justification. Why do we not simply assume that Agree, like Transfer, applies to the complement domain? In fact, (26c) is unavoidable under the minimalist assumptions. Consider, for instance, a matrix wh-question: C and a wh-phrase, both in the edge domain, must Agree. Another instance of edge-Agree is presented in (27a).
|___________________| Agree (i) Agree (ii) |___________| V-v in the edge must be able to Agree with an object in the complement domain. If Agee is applicable only to the Transfer domain, V with [uφ] must stay in the same domain as the object, as shown in (27b). However, this cannot be maintained. Since Agree and Transfer take place simultaneously (see (26a)), VP cannot be tampered with following Agree/Transfer; that is, V can no longer raise to v or higher. This is obviously a problem since (at least some instances of) V-raising are substantial (cf. Roberts 2010). Therefore, we have to assume that V-to-v raising occurs in syntax and that V-v in the edge is available for Agree. 9 8 Alternatively, the vocabulary insertion procedure may repair only the unvalued number value while retaining the gender value assigned to H. In this case, H will appear in a partially agreeing form. In Section 8.2, I touch upon partial agreement in Standard Arabic. 9 See Bobaljik & Wurmbrand (2005) for another argument for the mismatch between the Transfer and Agree domains.
I thank an anonymous reviewer for pointing out their work to me.
Notably, if an edge element can participate in Agree, movement creates more than one Agree option. Consider (27c): V-v may Agree with a copy of the object in situ or in the edge (though in the latter case, Agree can wait until the next higher phase). I assume that either option can be taken and that a restricting rule would be a burden on the computation. V-v, however, does not Agree with both copies. Since a chain is "a sequence of occurrences of a single α" (Chomsky 2000: 114), one Agree is enough for every copy of a chain to be valued.
In the following sections, I show that the two-Agree theory provides a simple account of the observed PPA patterns.

An account of PPA (I): PPA with an in-situ object and a derived subject
Let us first consider why an in-situ object cannot trigger PPA in either French or Italian.
I assume with Chomsky (2000; that only CP and non-unaccusative vP are phases. A participle raises to a higher functional head (v). The vP constitutes a phase and is dominated by an auxiliary phrase (v Aux P), which is also a phase if headed by avoir/avere 'have'. 10 When the vP phase is completed, Transfer applies to its complement domain and Agree to the entire phase.
Since nominal phrases are not phases, in (29), the probe Prt-v can search the entire object for a matching goal. From its agreement morphology, I assume that Prt-v has unvalued gender and number features. Agree in (29) is minimal because the SO is labeled by minimal search LA.
What is the minimal matching goal for Prt-v? To answer this, let us consider the morphosyntax of a nominal phrase. According to Ritter (1992), gender is an inherent feature of nouns, but number is not since a nominal can be either singular or plural (see Harbert & Bahloul 2002;Faß 10 Chomsky (2001: 12) argues that a verbal phase must have an external argument. If so, avoir/avere as well as v might take EA, making a control structure. The discussion of this topic is beyond the scope of this paper. See Kayne (1993) for an analysis of v Aux P. 2021 for similar remarks). Hence, the plural morpheme -s is separated from N, constituting a Number head. Carstens (2001) assumes that D, the highest head in the object, does not carry valued φ-features. Although definite/indefinite articles in French and Italian inflect for gender and number, it should be a reflex of φ-Agree within the nominal phrase. An argument for this is that determiners as well as possessive pronouns and adjectives share φ-information with a lexical noun.

(30)
Italian ( Multiple agreement within DP is well captured if we assume that D and the modifiers carry [uGr] and [uNr] which are valued by N and Number, respectively. These features on D are unvalued at the stage (29), since DP is not a phase. Therefore, Prt-v skips D and continues searching until it encounters a head with a valued φ-feature. A more detailed illustration of the Agree operation in (29) is provided below: Num (-s) with a plural feature, made active by the unvalued Case feature, is found as the closest goal. The search stops here and assigns a plural value to Prt-v. Since both gender and number are necessary for morphological agreement, the participle shows up in a default form. 11 11 N (chaise) raises above Num (-s) either in syntax or at PF to derive the surface order. In the former case, Prt-v would find the N as the closest goal. Here, too, PPA is absent since Prt-v receives only a gender value from the N.
In this connection, an anonymous reviewer asked me where [uCase] resides, which I had not specified in the previous draft. If we assume that "uninterpretable features render the goal active" (Chomsky 2000: 123), it must appear on a head with a valued feature. Thus, [uCase] resides on either Num or N. I assume that either option is possible: [uCase] can be added to either of the nominal heads when they enter a derivation (cf. Chomsky 1995). In Let us next consider why PPA is obligatory with a derived subject in both French and Italian.

(32)
Elle est allé-e/*allé en vacances. (=(2a)) she is gone-f.sg/*gone[def] on holiday 'She went on holiday.' Neither unaccusative vP nor v Aux P (headed by être/essere 'be') is a phase. Transfer does not apply until the CP phase is complete. At Transfer, the SO1 in (33) needs to be labeled by Full Agree: Search picks all φ-values in the derived subject to fully value v Aux -T. At this stage, Prt-v should also have its [uφ] valued. Full Agree, therefore, continues and assigns the picked φ-values to Prt-v (Multiple Agree). The agreement morpheme thus shows up on the participle as well as the finite auxiliary.
One might suspect that Prt-v should be valued by Minimal Agree since the SO2 is labeled without the help of Full Agree. However, it is uneconomical: Search picks all the φ-values of the subject to fully value v Aux -T and then forgets all the φ-values except one to minimally value Prt-v. It is more economical to continue one Full Agree operation as far as possible.
To summarize, the two-Agree theory provides a simple account for why PPA is absent with an in-situ object and obligatory with a derived subject. Minimal Agree applies to a participle and an in-situ object. A minimally valued participle must show up in a default form. If an object is A-moved, Full Agree holds between the derived subject and a finite auxiliary to label the so-called TP node, which also affects the participle. The fully valued participle appears in an agreeing form.
However, there is an apparent problem that needs consideration. In Italian, an internal argument of a passive/unaccusative verb seems to trigger PPA even from a postverbal position: Under the present analysis PPA is not expected if le ragazze 'the girls' really remains in situ, leaving the subject position empty. One way to solve this problem is to assume that PPA is triggered by the subject pro, which has the same φ-values as le ragazze (cf. Burzio 1986). As long as this explanation holds, PPA in (34) is not a major problem in the current analysis.

An account of PPA (II): PPA with a clitic object
We will now consider PPA with clitic objects. In French, PPA with clitics is optional. In contrast, in Italian, PPA is obligatory with 3rd person clitics and optional with 1st/2nd person clitics. A rough sketch of the argument presented in this section is shown below:

b.
A clitic stops at SPEC-v before reaching its final landing site. Prt-v can Agree with a copy of the clitic in its SPEC or in the object position, as shown in (35). In the former case, Full Agree applies to label the so-called vP node, which results in PPA. In the latter case, Minimal Agree applies. If the highest φ-bearing head of the clitic does not have enough φ-information, as in (36a) In the remainder of this section, I first discuss the structures of clitics, and then explain the observed PPA patterns.

Morphosyntax of clitic objects
The proposal in this section is twofold: (i) clitic pronouns involve a projection encoding φ-information (PhiP); (ii) PhiP may be decomposed into two layers. The discussion is based on Déchaine & Wiltschko (2002) and . Déchaine & Wiltschko (2002), examining the morphosyntax of pronouns cross-linguistically, argue that pronouns of languages are classified into the following three types: The DP pronoun has three projection layers. Either sublayer, PhiP or NP, can also be a pronoun.
Déchaine & Wiltschko note that PhiP is "a cover term for any intermediate functional projection that intervenes between N and D and that encodes φ-features" (p. 410). PhiP may be decomposed into several projections.
The three types of pronouns have different semantics and syntax. DP pronouns are always definite and occur only in argument positions. PhiP pronouns can be arguments or predicates, and can also function as bound variables. NP pronouns are inherently constants, and allow modification by adjectives and demonstratives.
Déchaine & Wiltschko argue that clitic pronouns in French (and other Romance languages) are PhiPs. 12 This is evident from the fact that a 1st/2nd person clitic object can be bound by its subject.
12 Partitive clitic en is an exception, which they identify as NP. One might suspect that 3rd person clitics should be DPs since they have the same form as definite articles (Fr. le, la, les; It. lo, la, li, le), as maintained by . For Kayne, definite articles are Ds, regardless of their semantics. However, Déchaine & Wiltschko argue that Romance "definite" articles should also be analyzed as Phi since they are not necessarily definite. To resolve this conflict, I assume that Romance 3rd person clitics are DPs whose head may be active or inert. If inert, the clitics show PhiP properties, as in (39a, b).  morphological decomposition of pronouns. Kayne first observes that French 1st/2nd person possessives may show agreement with the head noun, claiming that they consist of person + agreement (+ abstract possessive) morphemes. 13 13 Agreement morphology is absent when the head noun is masculine singular.

(40)
Kayne ( In (40), m-and t-are 1st and 2nd person morphemes, respectively, and -es and -a represent agreement. We can interpret "agreement" as a spell-out of [uφ]  I adopt the idea that redundant φ-marking on a pronoun represents agreement within the pronoun.
Kayne (2000) then analyzes accusative clitics in French and Italian as follows: 'my book' Kayne assumes that -on is a possessive morpheme which surfaces only when agreement morphology is null. 14 If tables is analyzed as table [f] and -s [pl] (see Section 5), it would be more precise to assume that lower Phi [uφ] is decomposed into Phi [uGr] and Phi [uNr] : The values assigned under Agree are underlined for the sake of illustration.
Let us now consider the structure of 3rd person accusative clitics. They are all headed by l-, which Kayne identifies as D. l-is followed by a morpheme representing gender. In French, -a marks masculine and -e feminine. However, this distinction is blurred in the plural les. Les may be decomposed into D (l-), blurred gender morpheme -e and plural -s. Based on these observations, I propose the following structure of French 3rd person clitics: [D [Phi2 [m, sg]

PPA explained
We are now in a position to account for PPA with clitics. Consider example (3a), repeated here as (51).
(51) Ces sottises, Jean ne les a jamais fait-es/fait. (=(3a)) these stupid.things[f] Jean not them has ever done-f.pl/done[def] 'These stupid things, Jean has never done them.' Clitic raising, though apparently head movement, should be considered a type of A'-movement since clitics have a complex internal structure. They should move successive-cyclically to their final landing site. Therefore, the accusative clitic object should move via SPEC-v and SPEC-v Aux . I assume, with Sportiche (1998) and Matushansky (2006), that clitics target (the inner) SPEC of T and then morphologically merges with a finite (auxiliary) verb in the PF component.
When Agree applies at the vP phase, Prt-v (fait-v in (52) If Prt-v chooses to Agree with Clitic 1 , as in (53b), it is Minimal Agree. That is, search stops when it encounters the closest goal in the clitic. With this in mind, let us consider (50a, b) again.
(55) Minimal Agree with 3rd person clitics in French: [Prt-v [uNr, uGr] … [D [Phi2 [Gr, uNr]  Minimal Agree with Italian 3rd person clitics leads to a different outcome: (56) Minimal Agree with 3rd person clitics in Italian: [Prt-v [uNr, uGr] … [D [Phi2 [Gr, Nr] [N]]] ] |_____________________________| Minimal Agree → full valuation → PPA Professeur 'professor', a masculine noun, induces masculine agreement within the nominal phrase, whereas it induces feminine agreement on content 'satisfied' if the professor is female. The latter type of agreement is called notional or semantic agreement since the target agrees with the sex of the referent, not with its formal gender. To explain notional agreement, we need to posit a notional gender feature, which is visible to the syntactic computation.
A 1st/2nd person pronominal subject can also induce feminine agreement on a predicate if the referent of the subject is female.
I am satisfied-f 'I(f) am happy.' Je 'I', however, has no formal gender. A natural assumption would be that this is also notional agreement, that is, agreement with the pronoun's notional feminine value.

The highest Phi (Phi2) has both gender and number values (see (50bii)). Prt-v is,
therefore, fully valued and shows up in an agreeing form. Full Agree, as in (53a), also results in full valuation. Consequently, Italian 3rd person clitics always trigger PPA.
In sum, the observed PPA patterns follow from the two-Agree theory and the internal structure of clitics. Prt-v can have its [uφ] valued under Minimal or Full Agree with a clitic. In most cases, Minimal Agree results in partial valuation and no PPA, and Full Agree in full valuation and PPA.
Hence, most clitics optionally trigger PPA. 3rd person clitics in Italian are exceptional in that they always fully value Prt-v since their highest Phi head has both gender and number values.

An account of PPA (III): PPA with an A'-moved object
Let us now turn to PPA with an A'-moved object. PPA is optional in French and absent in Italian.
(57) French: optional PPA with an A'-moved object (=(4a, b)) a. Combien de fautes a-t-elle fait-es? how.many of mistakes has-she made-f.pl 'How many (amongst a known set of) mistakes has she made?' b. Combien de fautes a-t-elle fait? how.many of mistakes has-she made [def] 'What is the number of things that are mistakes and that she has made?' (58) Italian: no PPA with an A'-moved object (=(10b)) Quanti libri hai lett-o/*lett-i? how.many books[m] have.2sg read-def/*read-m.pl 'How many books have you read?' Below, I use a wh-object as a representative example of A'-moved objects.
Optional PPA in French conforms with the proposed analysis. A wh-object stops at SPEC-v and SPEC-v Aux before reaching SPEC-C. (59)

Prt-v has its [uφ] valued when the vP phase is completed. It can choose between Minimal Agree
with Wh 1 or Full Agree with Wh 2 . The former results in no PPA, and the latter in PPA. Thus, the two Agree options result in optional PPA with a wh-object.
The proposed analysis can also explain the specificity requirement of a PPA-inducing wh-object: The agreeing sentence (57a) presupposes a specific set of mistakes and asks how many of them are attributed to the subject. In the non-agreeing sentence (57b), the wh-object may or may not be specific. The specificity requirement can be considered a result of criterial interpretation.
To understand this point, let us first consider how C in (59) contributes to labeling and interpretation. According to Rizzi (2015), C is a criterial head that attracts a wh-phrase to its SPEC, thus creating a SPEC-Head configuration (criterial configuration) under which the shared feature, Q, labels the SO1 as <Q, Q>. At LF, the criterial head carries instructions for interpreting its SPEC as an interrogative quantifier. Thus, so-called SPEC-Head agreement brings about labeling and mapping instructions to LF.
According to this idea, we should expect Prt-v to be a criterial head. Suppose that Full Agree holds between Prt-v and Wh 2 to label the SO2 as <φ, φ>. In this case, Prt-v is a criterial head and carries instructions on how to interpret Wh 2 . A similar proposal was made by Déprez (1998), who, considering Diesing's (1992) tripartite LF representation, claims that a PPAinducing object is mapped to the restrictive clause by which it receives a presuppositional/specific reading. Integrating Déprez's idea into the present analysis, I propose that the criterial head Prt-v instructs LF to interpret its SPEC (Wh 2 ) as a specific entity. PPA with a wh-object, thus, induces a semantic effect.
Incidentally, a derived subject, which obligatorily triggers PPA, does not need a specific interpretation. Recall that in (5), repeated here as (60), the subject allows a non-specific reading: Dans ce pays, une chaise est repeint-e toutes les heures. in this country a chair[f] is repainted-f.sg all the hours 'In this country, a chair is repainted every hour.' This interpretation also follows from the present analysis. Full Agree holds between the derived subject and T to label the so-called TP node. T, the criterial head, instructs LF to interpret its SPEC as "Subject" (something related to aboutness; see Section 9). Since the instruction does not necessarily entail specificity, the derived subject does not need to have a specific reading.
However, the proposed analysis cannot readily explain the absence of PPA with wh-objects in Italian. In Italian, an independent factor might block the application of Full Agree between Prt-v and Wh 2 in (59). I assume that criterial freezing is active in Italian, but not in French:
If Full Agree applies between Prt-v and Wh 2 in (59), the wh-phrase can no longer move to SPEC-C. Hence, the derivation is convergent only if Prt-v chooses to Agree with Wh 1 in the object position (Minimal Agree). Consequently, PPA does not appear with a wh-object in Italian. Burzio (1986) regards PPA with a wh-object in Italian as "stylistically rather marked" (p. 80), unlike other researchers who simply exclude it. There might be a speaker variation as to whether (61) is a rigid rule or a preferred one.
In summary, the proposed analysis explains optional PPA with a French wh-object and the total absence of PPA with an Italian wh-object while assuming parameterized criterial freezing.
PPA implies that a wh-object has entered into two criterial configurations: one with a participle (Prt-v), and the other with interrogative C. The violation of criterial freezing is not tolerated in Italian. However, in French, it poses no problem: A PPA-inducing wh-object is qualified as an interrogative quantifier (by C) and as a specific entity (by Prt-v). The specificity requirement for the PPA-inducing wh-object follows from labeling.
One might naturally wonder about the validity of parameterized criterial freezing. I make a few remarks about this in Section 9. (62) (62a) from Belletti (2006: 506); (62b) from Déprez (1998: 6) a. Il en a repeint /*repeint-es deux. he of.them has repainted[def]/*repainted-f.pl two 'He has repainted two of them.' b. Des bombes, je peux vous assurer que cette usine en a produit-es, of bombs I can you assure that this factory some has produced-f.pl mais je ne peux pas vous dire lesquelles. but I not can not you tell which.ones 'Bombs, I can assure you that this factory has produced some, but I could not tell you which ones.' An unclear acceptability status is expected under the proposed analysis. PPA implies that the clitic has entered into a criterial configuration with Prt-v and hence has a specific interpretation, that is, PPA-inducing en should be both partitive and specific. A speaker would accept PPA with en if they managed to come up with a situation in which such a reading of en is natural.

Another type of agreement asymmetry
A second welcome result is another type of agreement asymmetry. Recall that in Section 6, I have argued that PPA with Italian 3rd person clitics is obligatory because Minimal as well as Full Agree leads to full valuation of the participle. French 3rd person clitics partially value a participle under Minimal Agree because their highest Phi only carries a gender value.
(66) a. Italian: Minimal Agree with a 3rd person clitic [… Prt-v [uGr, uNr] Phi2 [Gr,Nr]  This indicates another type of agreement asymmetry: A controller whose φ-information is assembled in one head triggers richer agreement than a controller whose φ-information is scattered in different heads.
This type of asymmetry may be observed in, for example, Welsh. In this VS language, a finite verb agrees with a pronominal subject in person and number whereas a verb always occurs in the default 3rd person singular form with a lexical subject.
(67) Welsh (Borsley et al. 2007: 199)  A similar agreement asymmetry is observed in Standard Arabic, which allows both VS and SV word orders. In a VS sentence, a finite verb agrees with a pronominal subject in person, gender and number, as in (69). In contrast, the verb shows agreement in gender but not in number with a lexical subject. Observe that the finite verb in (70) appears in a feminine singular form, whereas the subject is dual.

Lexical Controller |____________________________| poorer agreement
The target shows richer agreement with a pronominal controller than with a lexical controller. Kobayashi (2020a;b) argues that this type of agreement asymmetry can be attributed to the different distributions of φ-features. Syntactic and morphological evidence suggests that pronouns in these languages are PhiPs whose highest head Phi carries a full set of φ-features.
When Minimal Agree applies to the target and the pronominal controller, the target is fully valued by Phi and shows up in an agreeing form. In contrast, the highest head of a lexical controller has a partial set of φ-features: In Welsh, D carries gender and number values but lacks a person value; in Standard Arabic, the highest head is N with a gender value as a result of N-to-D raising (see Kobayashi 2020a;b for details). When Minimal Agree holds between a verb and a lexical subject, the verb is partially valued. In Welsh, the partially valued verb is spelled out in its default form. In Standard Arabic, the verb appears in a partially agreeing form.

PPA with an in-situ object
The discussion so far has been based on the observation that PPA with an in-situ object is absent in both French and Italian. Some Italo-Romance dialects, however, do allow PPA of this type, as  This proposal is only a possibility. If we want to pursue this direction further, we will need to explain why the participle's [uφ]-features appear on a single head in some dialects and not in others, which I leave for future research.

A note on criterial freezing
In Section 7, I propose a criterial freezing parameter that is active in Italian, but absent in French.
The proposal is apparently problematic since the strongest minimalist thesis holds that the core computational system of I-language is (close to) uniform across languages (cf. Chomsky 2017; Chomsky et al. 2019). In this section, I provide further evidence for the proposal, although a fullscale reformulation of criterial freezing is beyond the scope of this paper.
The sentence allows either an existential or generic reading of the bare plural subject. That is, (75) can mean either that there are some firemen available at the speech time, or that firemen are such people that are available anytime. Diesing (1992) claims that the subject position (SPEC-T) is mapped to the generic reading at LF. The existential reading is obtained by lowering the subject to its theta position (SPEC-v) at LF (reconstruction). Under the copy theory of movement, we can reinterpret this as follows: Either a higher or lower copy of the subject can be chosen to be mapped to the generic/existential reading.
However, a question arises here. Rizzi (2006; claims that the subject position is a criterial position. The subject is a phrase about which an event is presented. Put differently, the criterial head T maps its SPEC (i.e. subject) to the "aboutness" reading. 18 To receive the reading, the copy of the subject at SPEC-T must be visible at LF even if it is reconstructed to SPEC-v to have an existential reading. How can a subject be interpreted at both SPEC-T and

SPEC-v?
Let us assume that mapping can be applied to a subpart of a copy. Firemen is decomposed into null D and N. Suppose that D of the higher copy and N of the lower copy are separately mapped to an interpretation, as illustrated in (76a) The D part at SPEC-T is mapped to the aboutness reading and the N part at SPEC-v to the existential reading. If the whole subject is mapped to interpretation, as in (76b), it receives aboutness as well as the generic reading.
This implies that we cannot obsolete reconstruction even under the copy theory of movement  German (Diesing 1992: 37-38) a. … weil Professoren ja doch verfügbar sind since professors 'indeed' available are '… since (in general) professors are available' b. … weil ja doch Professoren verfügbar sind since 'indeed' professors available are '… since there are professors available' The sentence particle ja doch 'indeed' indicates the position of the subject. The subject in (77a), which is to the left of the particle, is in SPEC-T, whereas the subject in (77b), which is to the right of the particle, remains in vP. As the translations show, the raised subject in (77a) has a generic reading and the in-situ subject in (77b) has an existential reading. That is, "in German the S-structure position of the subject correlates with the most readily available reading for a bare plural subject" (Diesing 1992: 37). This indicates that copy-splitting reconstruction is unavailable in German. Once the subject occupies SPEC-T, the entire copy is mapped to interpretation. In Italian, the two criterial configurations created in syntax are not properly interpreted.
Parameter (79b) prohibits mapping of (a part of) the lower copy to a specific reading: A coordinated subject triggers plural agreement on a finite verb, as shown in (82a). If a subject remains in a postverbal position, as in (82b) and (82c), a finite verb agrees only with the first conjunct of the subject. If a coordinated subject is A'-moved, it triggers plural agreement.
(83) [Which man and which woman] do you think are in the house?
If the subject had to move directly to the A'-position, skipping subject position (SPEC-T), the copular would show singular agreement. Plural agreement indicates that the wh-subject stops at SPEC-T and SPEC-C, creating two criterial configurations. Presumably, reconstruction allows the wh-part to be interpreted at SPEC-C and the rest to be interpreted at SPEC-T.
Data from an Italian dialect suggest the opposite. In Fiorentino, a preverbal subject must occur with a subject clitic agreeing with it, as shown in (84a). When the subject is postverbal, the clitic takes the default form (gli), as in (84b). When a subject is A'-moved, the subject clitic must be the default gli.

(85)
Fiorentino (Brandi & Cordin 1989: 124-125) a. Quante ragazze gli è venut-o con te? how.many girls 3sg is come-def with you 'How many girls have come with you?' b. *Quante ragazze le sono venut-e con te? how.many girls 3.f.pl are come-f.pl with you This indicates that the wh-subject must skip the criterial subject position. Because reconstruction cannot split a copy for mapping, the wh-subject can enter into at most one criterial configuration. 19 In summary, the assumed criterial freezing/reconstruction parameter is given empirical support to some extent. Different possible readings of a bare plural subject in English and German, and different agreement patterns with a wh-subject in English and Fiorentino appear to suggest that some languages allow reconstruction at LF, but others do not. Although Rizzi (2010), based mainly on Italian data, argues that a criterial requirement is "unsatisfiable through reconstruction" (p. 23), the above data suggest that Rizzi's observation might not hold for every language.

Conclusion
The proposed analysis is a revival of the AgrP analysis developed by Kayne (1989) and Sportiche (1998): PPA surfaces if government holds between the object at SPEC-Agr and Agr; PPA is often optional since a dislocated object may or may not occupy SPEC-Agr. The present study has approached the idea of PPA from a minimalist perspective. Since a dislocated object leaves a copy in the object position and at SPEC-v, a past participle can Agree with either copy. Agree with a copy in the object position minimally values the participle (Minimal Agree), which is then spelled out in a default form. Agree with a copy at SPEC-v, however, is not minimal because it is coupled with the labeling operation (Full Agree). The participle is fully valued and spelled out in an agreeing form. Thus, optional PPA results from the two Agree options.
The proposed analysis, however, has a wider empirical implication than the AgrP analysis. The reconstruction parameter is empirically supported, but apparently inconsistent with current minimalist assumptions. Further elaboration is necessary on this issue as recommended by an anonymous reviewer, but I leave it for future research.