Japanese internally headed relatives: A hybrid analysis with Kuroda functions

ion over an individual variable corresponding to a dp gap in argument position. Neither operator nor gap are visible on the surface. In English, dp gaps are usually visible on the surface, because usually dp gaps occur in obligatory argument positions. Thus, for instance, in adverbial pps, if the dp moves out of the pp, the dp-gap is made visible on the surface by the stranded preposition. Gaps that are invisible on the surface are naturally associated with adverbial constructions. If it is the full pp in adjunct position that moves, the gap is invisible, because the adjunct position is an optional position. Whether or not an invisible gap is an ayay gap depends on the semantic interpretation of the abstraction involved (over an individual variable, or over a pp-entity variable), which is not an issue I want to resolve for pps here. True ayay gaps are found in English with bare np adverbs, discussed in Larson (1985) and Rothstein (1995). Bare np adverbs are expressions that look like dps but pattern in every way with adverbials. Examples are Tuesday in (9a) and every day in (9b): Landman: Japanese internally headed relatives Art. 36, page 7 of 35 (9) a. Tuesday, we visited Amsterdam. b. We visited a different city every day. Rothstein (1995) assumes that Tuesday and every day in (9) pattern with adverbials because they are pps with a null preposition (a null-version of on) in adverbial position: [pp [p e] [dp every day]] Larson gives a somewhat different account, but for our purposes the differences are irrelevant. What is relevant here is that we can make day in every day the external head of a relative clause, as in (10): (10) a. I wrote down in my notebook the day they told us we would visit Amsterdam. b. In fact, I circled in my notebook every day they told us we would be in Holland. c. I wrote down in my notebook [dp every day [cp opn they told us [cp we would be in Amsterdam [pp [p e] [dp en]]]]] The relevant reading in (10a) is the reading which expresses that the day in question is the day on which we would visit Amsterdam, according to ‘them’, not the day on which they told us so. The relative clause is part of a dp in argument position, and provides in all respects the same restriction on the determiner or quantifier that relatives do when the head noun is a property of individuals. Given this, it is reasonable to assume that (10b) is analyzed on the model of (10c). This means that the relativization in (10) is a true example of an ayay gap in English: the dp gap is invisible because the preposition is also null. Since pps with empty prepositions clearly constitute a phenomenon that exists across languages, and since the analysis I will give is most naturally formulated in terms of the semantics of a (null) preposition, I propose to take this case as a model for the analysis of Japanese internally headed relatives and suggest the following syntactic analysis. Note that Japanese has postpositions rather than prepositions. I take Japanese noun phrases in argument position to be dps rather than nps, but nothing hinges on this assumption. π stands for the internal head. The π-indices on the nodes are meant for easy reference: ppπ is the null pp containing the ayay-gap, xpπ the structure that contains the internal head and that ppπ adjoins to. 2.2 The semantics of ppπ With Grosu & Landman (2012), I assume a neo-Davidsonian semantics. I give a brief overview: Landman: Japanese internally headed relatives Art. 36, page 8 of 35 –Verbs and (extended) projections of the verb denote event types, sets of eventualities, events or states. I will use events for short. ‘→’ stands for ‘is interpreted as’. (12) [v butter] → λe.butter(e) The set of buttering events –Thematic roles are partial functions from events into event participants. The interpretations of dp arguments are combined with event type interpretations through thematic roles (specified in the theta grid of the verb). I assume that the dp-argument is interpreted, relative to a role in the theta grid, as an event type which intersects with the event type of the (extended) projection of the verb the dp combines with: (13) [dp a bun] + Th → λe.bun(Th(e)) The set of events with a bun as theme (14) [vp butter a bun] → λe.butter(e) ∩ λe.bun(Th(e)) = λe.butter(e) ∧ bun(Th(e)) The set of buttering events with a bun as theme In neo-Davidsonian semantics this same interpretation strategy applies to the combination of pps with (extended) projections of the verb, regardless of whether the preposition is selected by the verb or whether the pp is an adjunct. The p-element (preposition or postposition) is interpreted as a thematic role, the pp is interpreted as an event type, which intersects with the verbal event type: (15) [pp with a knife ] → λe.knife(Instr(e)) The set of events that have a knife as instrument (16) [vp butter a bun with a knife] → λe.butter(e) ∧ bun(Th(e)) ∩ λe.knife(Instr(e)) = λe.butter(e) ∧ bun(Th(e)) ∧ knife(Instr(e)) The set of buttering events with a bun as theme and a knife as instrument At the ip level, event existential closure takes place.6 Before existential closure (including the subject and past tense): (17) [ip Fred buttered a bun] → λe.butter(e) ∧ Ag(e)=Fred ∧ bun(Th(e)) ∧ Time(e) < now The set of buttering events with Fred as agent, a bun as theme and running time before now After existential closure: (18) [ip Fred buttered a bun] → ∃e[butter(e) ∧ Ag(e)=Fred ∧ bun(Th(e)) ∧ Time(e) < now] There is a buttering event with Fred as agent, a bun as theme and running time before now. The pp-interpretation follows the following general schema: If p → P and dp → DP then pp → λe.DP(λx.P(e)=x) 6 For extended discussion and caveats, see Landman (2000). Landman: Japanese internally headed relatives Art. 36, page 9 of 35 We come back to ppπ and xpπ: Assumption 2a: ppπ adjoins to structure xpπ and xpπ has an event type interpretation. This means that if xpπ is, say, an ip, ppπ is adjoined before event existential closure. With this, the basic semantics of ppπ and of xp is determined: (19) Let xpπ → Eπ An event type [pp en pπ] → λe.Pπ(e) = xn The set of events whose Pπ-participant is xn xp → λe.e ∈ Eπ ∧ Pπ(e) = xn The set of events in Eπ whose Pπ-participant is xn What is Pπ? Here I follow Grosu & Landman (2012): in the semantic derivation of the interpretation of xpπ, the interpretation of the internal head π fills a role Rπ. This role is chosen as the interpretation of the null preposition in ppπ: Assumption 2b: pπ is interpreted as the role Rπ that is used in the derivation of xpπ to connect the interpretation of internal head π to the event type of the relevant (extended) projection of the verb.

1 The Scylla and Charybdis of Japanese internally headed relatives

The subsumption analysis and its problems
The bracketed expression in (1) is an example of an internally headed relative clause.
(1) üTaro-wa [Yoko-ga reezooko-ni kukkii-o sukunakutomo mit-tsu irete-oita-no]-o Taro-top [Yoko-nom refrigerator-loc cookie-acc at least 3-clf put-aux-no]-acc paatii-ni motteitta.party-to brought Taro brought to the party [the sum of all the cookies such that…] Yoko put at least three cookies in the refrigerator.'Yoko put at least three cookies in the refrigerator.Taro brought them to the party.' Example (1) shows the following properties of internally headed relatives.The relativebracketed in (1) -is a clausal structure, marked by the element no (the literature does not have a univocal opinion as to the status of this element).No gap or resumptive pronoun is visible in the clause in question, it looks like a full clause.However, the clause occurs in argument position (it is marked accusative in (1)), and has the interpretation of a noun phrase.This is the rationale for calling it a relative clause.In fact, the clause has the interpretation of a definite noun phrase ('the cookies that Yoko put in the fridge').It derives its noun phrase interpretation from a constituent inside the relative, the internal head (kukkii sukunakutomo mit-tsu-'at least three cookies').The internal head is not marked grammatically in any special way.The bracketed expression [the sum of all the cookies such that…] I will call the interpretation head.Ito (1986) and Watanabe (1992) (among others) proposed unified analyses of internally headed and externally headed relatives, assuming (in essence) the same mechanism for both, and taking the differences to lie in whether the head of the relative moves in the syntax or at some other level, and where it ends up (and at which level).Since the basic mechanism assumed is the standard mechanism for externally headed relatives, this approach tries to subsume internally headed relatives under the more familiar externally headed case.Hoshi (1995) argued extensively against this approach.He pointed out that the standard interpretation of the mechanism for externally headed relatives would predict that (1) has the same meaning as the comparable externally headed relative: Taro brought to the party at least three cookies that Yoko put in the fridge.
But (1) doesn't mean that, (1) expresses that Taro brought all of the cookies that Yoko put in the fridge to the party (see also Shimoyama 1999;2001). 1uroda , Hoshi (1995) and Shimoyama (1999) discuss various other semantic differences between internally and externally headed relatives.I will here discuss three types of differences that are particularly relevant for the present paper (all these cases have been discussed in the literature, and the examples are based on similar examples in Hoshi 1995;Kim 2007;Grosu 2010;Grosu & Landman 2012.Further differences are discussed in Grosu 2010; Grosu & Landman 2012;Grosu & Hoshi 2016).
In the first place, internally headed relatives, but not externally headed relatives, must satisfy the Kuroda relevancy condition (Kuroda 1976(Kuroda -1977;;1992;1999).This means that you cannot felicitously choose as the internal head an object that is not presented by the relative as sufficiently enough 'on the scene' of the main clause.
Look at the contrast between (2a) and (2b):2 (2) a. #[Daidokoro-no mado-kara siroi neko-ga haitte-ki-ta]-no]-ga kitchen-gen window-from white cat-nom came-in-past-no]-nom kesa mata yattekita.this morning again came [ [The cat such that…] a white cat came in from the window] came back this morning.'A white cat came in from the kitchen window; she came back this morning.'b.P[Daidokoro-no mado-kara siroi neko-ga haitte-ki-ta]-no]-ga kitchen-gen window-from white cat-nom came-in-past-no]-nom akana-o totte nigeta.fish-acc steal ran-away [ [The cat such that…] a white cat came in from the kitchen window] stole a fish and ran away.'A white cat came in from the kitchen window; she stole a fish and ran away.'In (2a), a white cat is introduced as a cat which was involved in some event: she came in through the window.In the matrix a second event is specified of this cat: she came in through the window again today.These are two event specifications that we do not naturally think of as one scene.In Kuroda's terms, the event described in the embedded clause does not put the cat enough on the scene of the event described by the matrix to allow siroi neko-'white cat' to be chosen felicitously as the internal head.
On the other hand, (2b) can naturally be understood as a scene that starts with the event of the relative, the cat coming in through the window (no doubt attracted by the smell of fish), while the matrix continues that scene with the event of the cat stealing the fish.The cat, hence, is directly on the scene of the matrix event in (2b) and siroi neko-'white cat' can serve as the internal head in (2b).
Japanese externally headed relatives, like externally headed relatives in other languages, show no such constraint.While this difference is not a fatal problem for the analysis that subsumes internally headed relatives under externally headed ones, it still is rather surprising and unexpected on that analysis. 3 second difference between internally and externally headed relatives -and one that is more problematic for the subsumption analysis -is the fact that internally and externally headed relatives differ in what they allow as the interpretation head of the relative.In internally headed relatives the interpretation head can be semantically derived from the interpretation of the internal head in a way that is impossible in externally headed relatives.Look at (3a) and (3b): (3) a üJohn-wa [Mary-ga gozentyuu-ni ringo-o sibottekureta-no]-o John-top [Mary-nom morning-in apple-acc squeezed-no]-acc gogo-ni hitoikide nomihosita.afternoon-in in-a-gulp drank-up John drank in the afternoon in a gulp [the juice such that …] Mary squeezed apples in the morning.
b. #John-wa [[Mary-ga gozentyuu-ni sibottekureta] ringo]-o John-top [[Mary-nom morning-in squeezed] apple]-acc gogo-ni hitoikide nomihosita.afternoon-in in-a-gulp drank-up 'John drank in the afternoon in a gulp the apples that Mary squeezed in the morning.' (3a) is an internally headed relative with internal head ringo-'apple'.And the example is felicitous.The interpretation head is not apples, but [the juice such that], i.e. apple juice.The corresponding externally headed relative with external head ringo-'apples' is infelicitous, as it is in English in corresponding examples (since you cannot drink apples).
A third difference concerns examples with 'accumulation' readings.Look at (4a-c): (4) a. Wasaburo-wa [dono gakusei-mo peepaa-o 3-bo dasita-no]-o Wasaburo-top [every student term-paper-acc 3-clf turned-in-no]-acc itiniti-de yonda.one-day-in read Wasaburo read in one day [the papers such that…] every student turned in three term papers.'Every student turned in three papers.Wasaburo read all the papers that all the students turned in in one day.' b.Wasaburo-wa [[dono gakusei-mo dasita ] 3-bon-no peepaa]-o Wasaburo-top [[every student turned-in ] 3-clf-gen paper]-acc itiniti-de yonda.one-day-in read c.Wasaburo-wa [[dono gakusei-mo dasita ] peepaa]-o 3-bon Wasaburo-top every student turned-in] paper-]-acc 3-clf itiniti-de yonda.one-day-in read 'Wasaburo read in one day the three papers that every student turned in.' As Shimoyama (1999) pointed out, (4a) has an accumulation reading, where if there were twenty students, Wasaburo read in one day sixty papers.The externally headed relatives in (4b-c) do not allow a similar accumulation reading; the only relevant reading that (4b-c) allow is the pragmatically odd reading where every student handed in the same three papers.
In this, Japanese externally headed relatives pattern with English relatives: if there are 24 cities, (5a) does not have a reading which describes the gathering of the 120 delegates from the 24 cities, and nor does the Japanese (5b): (5) a.The five delegates that every city elected gathered in Parliament Hall for the opening ceremony.b. [[dono tosi-mo eran-da] go-nin-no daigiin]-ga kokkai-gizidoo-ni atumatta.every city elected 5-clf-gen delegate-nom parliament-hall-in gathered These data show that an analysis which reduces the differences between internally and externally headed relatives just to the question of where in the syntactic chain the head of the relative is spelled out is inadequate: there are semantic differences that need to be accounted for. 4

1.2
The discourse anaphora analysis and its problems Hoshi (1995) and Shimoyama (1999) propose a radically different analysis for internally headed relatives.They assume that the name 'internally headed relative' is really a misnomer.These are not relative clauses at all, but they are what they look like: full clauses with a propositional meaning.They derive their nominal interpretation as a definite noun phrase from the assumption that there is an implicit discourse anaphor in the dp position in the matrix.While Hoshi and Shimoyama give slightly different analyses, they both assume that the interpretation of the discourse anaphor is as a definite whose predicative content is constructed with help of the embedded clause.Hence, the embedded clause functions as a discourse background for an implicit discourse anaphor in the matrix.Grosu (2010) and Grosu & Landman (2012) point out several differences between internally headed relatives and standard discourse anaphora constructions.
In the first place, since the embedded clause contains the internal head, both Hoshi and Shimoyama must assume that the discourse anaphor derives its content obligatorily, i.e. semantically, from the embedded clause.Discourse anaphora typically do not have such 4 Chris Tancredi points out that an accumulation reading is possible for externally headed relatives where the numerical is inside the relative and peepaa-'paper' is the external head, as in (i): (i) Wasaburo-wa [[dono gakusei-mo 3-bon dasi-ta ] peepaa]-o itiniti-de yonda.Wasaburo-top every student 3-clf turned-in] paper-]-acc one-day-in read I will come back to this case in Section 6.2.
semantic restrictions on where they need to look for their interpretation.Not in English, and not in Japanese either.(See Grosu & Landman 2012 for discussion.)Secondly, internally headed relatives are infelicitous when the internal head is interpreted in the scope of negation as in (6a): (6) a. #[Hitorino insei-mo doyoobi-no party-ni ika-nakat-ta-no]-ga [any grad-student Saturday-gen party-to go-Neg-Past-no]-nom jitsuwa uchi-de peepaa -o kaite ita.in-fact home-at paper-acc writing was [the students such that…] no graduate student(s) came to the party on Saturday were in fact writing term papers at home.
In contrast, (6b) with a discourse anaphor is felicitous:5 (6) b. üHitorino insei-mo doyoobi-no party-ni ikanakatta.any grad-student Saturday-gen party-to go-neg-past Karera-wa jitsuwa uchi-de peepaa-o kaite ita.they-top in-fact home-at paper-acc writing was No graduate student(s) came to the party on Saturday.They (i.e., the students) were in fact writing term papers at home.Thus, discourse anaphora allow accommodation of students in (6b).Internally headed relatives do not allow such accommodation.
Thirdly -and most problematically for the discourse anaphor analysis -internally headed relatives show island effects.When the internal head is in a syntactic island, the internally headed relative is infelicitous.This was first pointed out by Watanabe (1992;2003).Watanabe noted the contrast between (7a) and (7b): Grosu and Landman (2012) argue that, whereas there is systematic variation among speakers concerning the acceptability of the internally headed relative (7a) -judgements range between totally acceptable, somewhat odd, and totally unacceptable -there is no such variability with respect to (7b): the internal head is inside a complex noun phrase and (7b) is judged infelicitous by everybody.
Other cases of island sensitivity, in particular adjunct islands, are discussed in Grosu and Hoshi (2016), which also contains extensive discussion eliminating challenges to this and similar data, showing beyond doubt that indeed internally headed relatives are sensitive to island constraints.
In contrast with this, island sensitivity is unheard of for discourse anaphora.(8a) and (8b), which correspond to (7b) but have a discourse anaphor, are completely felicitous: (

Relativization from an ayay-gap
The standard account of the syntax and semantics for externally headed relatives in languages like English postulates a gap in argument position inside the relative which is syntactically bound by an operator at the cp level.Semantically, the gap is interpreted as an individual variable, a variable ranging over individuals, which is abstracted over at the cp level.The analysis typically involves some account of how the external head fits into that, but since there is no external head in internally headed relatives, we can skip over the latter here.It is the syntax of the operator that accounts for the island effects.
The fact that internally headed relatives show island effects is easiest accounted for by the assumption that the same operator-variable construction mechanism is in fact operative in Japanese internally headed relatives.Since nothing of this is visible on the surface, I assume that the gap is an 'invisible individual gap' or in short, an 'ayay gap': Assumption 1: The internally headed relative contains an ayay gap.Internally headed relatives contain an operator-variable construction, which involves abstraction over an individual variable corresponding to a dp gap in argument position.Neither operator nor gap are visible on the surface.
In English, dp gaps are usually visible on the surface, because usually dp gaps occur in obligatory argument positions.Thus, for instance, in adverbial pps, if the dp moves out of the pp, the dp-gap is made visible on the surface by the stranded preposition.Gaps that are invisible on the surface are naturally associated with adverbial constructions.If it is the full pp in adjunct position that moves, the gap is invisible, because the adjunct position is an optional position.Whether or not an invisible gap is an ayay gap depends on the semantic interpretation of the abstraction involved (over an individual variable, or over a pp-entity variable), which is not an issue I want to resolve for pps here.
True ayay gaps are found in English with bare np adverbs, discussed in Larson (1985) and Rothstein (1995).Bare np adverbs are expressions that look like dps but pattern in every way with adverbials.Examples are Tuesday in (9a) and every day in (9b): (9) a. Tuesday, we visited Amsterdam.
b.We visited a different city every day.Rothstein (1995)  The relevant reading in (10a) is the reading which expresses that the day in question is the day on which we would visit Amsterdam, according to 'them', not the day on which they told us so.The relative clause is part of a dp in argument position, and provides in all respects the same restriction on the determiner or quantifier that relatives do when the head noun is a property of individuals.Given this, it is reasonable to assume that (10b) is analyzed on the model of (10c).This means that the relativization in (10) is a true example of an ayay gap in English: the dp gap is invisible because the preposition is also null.Since pps with empty prepositions clearly constitute a phenomenon that exists across languages, and since the analysis I will give is most naturally formulated in terms of the semantics of a (null) preposition, I propose to take this case as a model for the analysis of Japanese internally headed relatives and suggest the following syntactic analysis.
Note that Japanese has postpositions rather than prepositions.I take Japanese noun phrases in argument position to be dps rather than nps, but nothing hinges on this assumption.π stands for the internal head.The π-indices on the nodes are meant for easy reference: pp π is the null pp containing the ayay-gap, xp π the structure that contains the internal head and that pp π adjoins to.

The semantics of pp π
With Grosu & Landman (2012), I assume a neo-Davidsonian semantics.I give a brief overview: -Verbs and (extended) projections of the verb denote event types, sets of eventualities, events or states.I will use events for short.'→' stands for 'is interpreted as'.(12) [ v butter] → λe.butter(e)The set of buttering events -Thematic roles are partial functions from events into event participants.The interpretations of dp arguments are combined with event type interpretations through thematic roles (specified in the theta grid of the verb).I assume that the dp-argument is interpreted, relative to a role in the theta grid, as an event type which intersects with the event type of the (extended) projection of the verb the dp combines with: (13) [ dp a bun] + Th → λe.bun(Th(e)) The set of events with a bun as theme ( 14) [ vp butter a bun] → λe.butter(e) ∩ λe.bun(Th(e)) = λe.butter(e)∧ bun(Th(e)) The set of buttering events with a bun as theme In neo-Davidsonian semantics this same interpretation strategy applies to the combination of pps with (extended) projections of the verb, regardless of whether the preposition is selected by the verb or whether the pp is an adjunct.The p-element (preposition or postposition) is interpreted as a thematic role, the pp is interpreted as an event type, which intersects with the verbal event type: (15) [ pp with a knife ] → λe.knife(Instr(e)) The set of events that have a knife as instrument ( 16) [ vp butter a bun with a knife] → λe.butter(e) ∧ bun(Th(e)) ∩ λe.knife(Instr(e)) = λe.butter(e)∧ bun(Th(e)) ∧ knife(Instr(e)) The set of buttering events with a bun as theme and a knife as instrument At the ip level, event existential closure takes place. 6Before existential closure (including the subject and past tense): (17) [ ip Fred buttered a bun] → λe.butter(e) ∧ Ag(e)=Fred ∧ bun(Th(e)) ∧ Time(e) < now The set of buttering events with Fred as agent, a bun as theme and running time before now After existential closure:

bun(Th(e)) ∧ Time(e) < now]
There is a buttering event with Fred as agent, a bun as theme and running time before now.
The pp-interpretation follows the following general schema: If p → P and dp → DP then pp → λe.DP(λx.P(e)=x) Landman: Japanese internally headed relatives Art.36, page 9 of 35 We come back to pp π and xp π : Assumption 2a: pp π adjoins to structure xp π and xp π has an event type interpretation.
This means that if xp π is, say, an ip, pp π is adjoined before event existential closure.With this, the basic semantics of pp π and of xp is determined: The set of events whose P π -participant is x n xp → λe.e ∈ E π ∧ P π (e) = x n The set of events in E π whose P π -participant is x n What is P π ?Here I follow Grosu & Landman (2012): in the semantic derivation of the interpretation of xp π, the interpretation of the internal head π fills a role R π .This role is chosen as the interpretation of the null preposition in pp π : Assumption 2b: p π is interpreted as the role R π that is used in the derivation of xp π to connect the interpretation of internal head π to the event type of the relevant (extended) projection of the verb.
So we derive: where R π is the role specified in assumption 2b This means that, if we choose, say, the Theme role Th for R π , we derive, for the structure in which pp π is adjoined to the ip before existential closure: The set of past buttering events with Fred as agent, and as theme a bun and x n as theme Thus, de facto the theme role is constrained twice.7

Participant relations and the locality of the internal head
The analysis given above is formulated not in terms of the internal head π, but in terms of the role R π that connects π to the event type interpretation of the relevant (extended) projection of the verb.
In fact, the analysis does without the notion of internal head.I will make this aspect of the analysis explicit by introducing a notion of participant relation.I will concentrate here on the basic case.
We consider a structure xp, an (extended) projection of a lexical verb v, where v → V and xp → XP, and V and XP are event types such that XP ⊆ V.The neo-Davidsonian theory sketched above uses the same semantic mechanism for interpreting dp-arguments in xp, relative to roles in the theta grid of v, as it does for dp objects of pp-adjuncts in xp, where the role is provided by the preposition.
The participant relation for xp interprets the xp semantically as an n-place relation between the interpretations of the n dps that are in one of these two ways grammatically realized in xp:

Participant roles
Let R be a thematic role defined on the events in XP.R is a participant role for xp if there is a dp realized in xp, as an argument or the argument of an adjunct pp, and R is the role that adds the interpretation DP of dp via intersection of λe.DP(λx.R(e)=x) and the event type interpretation of the relevant (extended) projection of v, i.e. the one that is the sister of the dp or its pp.

Two examples:
(22) Fred quickly buttered a bun with a knife.
In ( 22), the roles Ag, Th, Instr, Manner and Time constrain the ip-event type grammatically, Time is introduced by the tense, Manner by the adverb, the others link interpretations of syntactically realized dps intersectively to the event type.This means that the participant relation of the ip is:8  With this revision of the theory, we can in fact introduce π, i.e. define π: the interpretation of p π is identified with a role R π in the participant relation of xp π ; the dp in xp π whose interpretation fills that role is π.
We derive the following corollary: , the ayay-gap and the internal head π are co-arguments in the participant relation of xp.
The participant relation of xp π is an n-place relation, and π is an argument of that relation.But pp π is an adjoined pp, hence xp, the mother of xp π and pp π , determines an n+1-place participant relation (adding role R π once more, this time in relation to the ayay-gap), and both the ayay-gap and π are arguments of that participant relation.The fact that this corollary follows directly from the theory is the main reason why I prefer to take the phrase containing the ayay-gap to be a null pp, rather than some new kind of null functional category, as was assumed in Grosu & Landman (2012).
Let me take stock.In the hybrid analysis of internally headed relatives, the relative contains a dp-gap (the ayay-gap) as part of a null pp, pp π , and this gap forms a standard operator-variable relation with an operator at the cp-level of the relative: that is, the ayay-gap is interpreted as an individual variable x n which is bound by an operator at the cp-level.pp π is adjoined to a node xp π which we take to be an (extended) projection of a verb with an event type interpretation.
The second plank of the hybrid analysis concerns the interpretation of the null preposition p π .I associate with [ XP xp π pp π ] a semantic object, the participant relation of xp, and restrict the interpretation choice for p π to the other participant roles specified in that relation.
While the participant relation is a semantic object, it is constructed from a syntactic structure containing an (extended) projection spine from a lexical verb up to xp, with dps -the internal head π among them -connecting to it as arguments or via prepositions.What this means is that on the hybrid analysis, pp π is adjoined to the extended projection that π belongs to.π can occur embedded in a clause in the relative, but only if the ayaygap can.So embedding is to do with the operator-ayay gap relation, not with the ayay gap-internal head relation.This means that in the relative in the felicitous example (7a), with internal head p = juuyouna kasetsu-'important hypothesis', pp π is attached to ip 2 , the lowest ip dominating the internal head: pp π could not be adjoined to the higher ip, ip 1 , because π is not an argument of the participant relation of ip 1 .
π is an argument of the participant relation of ip 2 , so pp π can be adjoined to ip 2 .We assume that from pp π , adjoined to ip 2 , the operator o n can move freely to cp, hence the grammar allows (26a), and (7a) is felicitous.
In the infelicitous example (7b), with internal head p = atarashii kasetu-'new hypothesis', we similarly cannot adjoin pp π to the higher ip, ip 1 , as in (26b 1 ): The reason is the same as for (26a): π is not an argument of the participant relation of ip 1 .As above, π is an argument of the participant relation of ip 2 , so pp π can be adjoined there, as in (26b 2 ): But then the operator o n cannot move to cp, because the ayay gap is inside the island (ip inside dp).So we predict the island effect: (7b) is infelicitous.

Comparison with Grosu & Landman (2012)
The present analysis in terms of participant relations is inspired by Reinhardt & Reuland's (1992) relational analysis of reflexivity in terms of the notion co-argument of a semantic predicate (but building relations at a higher level than they did).While the basic analysis as given here suffices for the cases discussed in this paper, obviously both the notion of participant relation and the role identification mechanism need to be extended to deal with more complex cases.
With respect to the participant relation, I am here only looking at ips where the event type interpretation is a subset of the event type interpretation of the verb: this does not deal, for instance, with the possibility of the derivation involving a more articulated event structure, either as part of a more complex v structure (with dp-arguments relating to subevent structure), or through aspectual or modal operations (with dp-arguments relating to super-event structure, event structure derivationally introduced), nor does it address predicative structures.Similarly, extension of the analysis to conjunction cases, like the ones discussed in Grosu & Landman (2012: Section 6.2), requires an extension of the notion of participant relation.
Other cases are more straightforward to deal with: Grosu & Landman (2012: Section 6.1) discusses cases where the interpretation of p π is derived from two roles in the participant relation.Their analysis can be taken over here without much change. 10he main difference between the present analysis and that of Grosu & Landman (2012) lies in what we accept as a role in the event type interpretation of ip π .In the theory presented here, I propose a strict view on thematic roles: thematic roles specify event participants.While I am well aware that there is leeway in what we may or may not intuitively count as a participant of a given event, I want the theory to be as strict as possible about this.So, to give an extreme example, I do not want -without solid grammatical reason -to allow the interpretation of the dp a bun in the relative clause in ( 27) to fill a participant role on the main clause event type of Fred typing a letter: (27) Fred, who was eating a bun, typed a letter.
In an unconstrained theory of roles, the function that maps letter-typing event e onto the theme of accompanying bun-eating event could be a perfectly well defined role.But, if this function can be a participant role, the notion of participant relation obviously no longer corresponds to a syntactic structure that encodes any notion of syntactic locality, and the locality condition on the relation between the ayay-gap and the internal head would have to be stipulated independently.
This is, of course, an extreme case, but I now believe that Grosu & Landman's analysis suffers from exactly this problem: at the basis of their analysis lies what they call a 'liberalized' notion of role which is meant to allow for what they call 'bridging' cases.Look at the contrast between (28a) and (28b):11 (28) a # [Taro-ga zibun-no musume-no hito-ri-no sushi-o kyaku-ni [Taro-nom his daughter-gen 1-clf-gen sushi-acc guest-dat dasita-no]-o kyaku-ga suguni home-ta.served-no]-acc guest-nom immediately praise-past The guest immediately praised: [the one of his i daughters such that…] Taro i served to the guest the sushi of one of his i daughters.
b ü[Taro-ga daidokoro-no zibun-no musume-no hito-ri-no sushi-o [Taro-nom kitchen-gen self-gen daughter-gen 1-clf-gen sushi-acc kyaku-ni dasita-no]-o kyaku-ga suguni home-ta.guest-dat served-no]-acc guest-nom immediately praise-past The guest immediately praised: [the one of his i daughters such that…] Taro i served to the guest the sushi of one of his i daughters, who was in the kitchen.
(28a) derives from an example originally discussed in Shimoyama (2001).Shimoyama noted the infelicity of the example similar to (28a) and suggested that this infelicity is due to the fact that the genitive dp zibun-no musume-no hito-ri-no-'one of his daughters' is not an argument of the participant relation for the ip; to cite Shimoyama: "It seems to be the case that only thematic role bearers of the event in the lower clause can be the internal head."(Shimoyama 2001: 143).This is, of course, exactly what I am proposing here.
Against this, Grosu & Landman suggested that the infelicity of examples like (28a) is due to Kuroda relevancy effects, and they give an example (due to Koji Hoshi), similar to (28b), which like (28b) and unlike (28a), is felicitous.Grosu & Landman's idea is that the extra information about the daughter being in the kitchen while the meal goes on provides the more intimate connection between the sushi serving and praising that allows (28b) to satisfy the Kuroda relevancy condition, where (28a) does not.
In (28b) the internal head is zibun-no musume-no hito-ri-no-'one of his daughters' which is neither an argument in the participant relation of the ip, nor linked to the serving event type via a normal thematic role (the sushi is, the daughter is not).
The contrast in (28) plays a fundamental role in the analysis of Grosu & Landman (2012) (and in fact, in presentations of earlier versions of this paper).To deal with the felicity of cases like (28b), Grosu & Landman allow the role R π to be identified with a 'liberalized' role, a role that is defined on the event type interpretation of xp π , but is not a participant role in my sense.The role in question is the function which takes events e of Taro serving the theme of e and maps them onto the person who fills in e the role of being the agent of an accompanying event of preparing the theme of e, or an accompanying state of having prepared the theme of e. 12The problem is that this is, of course, exactly the kind of role that we didn't want to allow in (27).And the problem for Grosu & Landman's analysis is that, if you allow R π to pick up this kind of 'bridging role', there is actually no constraint on where in xp π the internal head is located.This means that, on closer inspection, there is actually nothing in Grosu & Landman's analysis that enforces locality, i.e. nothing that guarantees that the ayay-gap and the internal head are not separated by an island.And this means that, in order to predict the island effects observed, their analysis actually needs to be supplemented with a further syntactic locality constraint.Note that the problem is not to do with the syntactic theory, but with the fact that, by allowing bridging roles, Grosu & Landman's analysis does not properly constrain where the internal head can be inside xp π .
The idea of the present analysis is, of course, that further locality constraints are not needed, because the present analysis tries to define the role-identification relation from the start as affecting co-arguments in a participant relation which is derived from a syntactic structure in which these arguments are 'local'.
So the present analysis does predict the island effects without further locality conditions.But then the obvious question is: what about the bridging data that motivates the analysis of Grosu & Landman, the felicity of (28b)?
This is where Grosu & Koji (2016), comes in.If (28a) and (28b) are internally headed relatives, and the difference in felicity is due to Kuroda relevancy, then the felicity contrast between (28a) and (28b) will be preserved if the examples are put in the context of the tests provided for internally headed relatives in Grosu & Koji (2016).In particular, Grosu & Koji (2016)  In this case hito-ri-'one'-clf can not have a partitive meaning, hence the purported meaning expressed is his one daughter.The classifier selects for humans, so the sushi cannot be the internal head.And the example is infelicitous.This is, of course, not surprising given the infelicity of (28a).We look at (29b), which corresponds to (28b): (29) b. #[Taro-ga [daidokoro-no zibun-no musume]-no sushi-o kyaku-ni Taro-nom kitchen-gen his daughter-gen sushi-acc guest-dat dasi-ta-no]-o hito-ri kyaku-ga suguni home-ta.serve-past-no-acc 1-clf guest-nom immediately praise-past The guest immediately praised [the daughter such that…] Taro served to the guest the sushi of his one daughter who was in the kitchen.
The crucial observation is that (29b) is judged as infelicitous as (29a).This means that the phrase that expresses the connection between the serving and praising, that supposedly allowed (28b) to satisfy Kuroda relevancy, has actually no effect on felicity.
But that means that bridging examples like (28b), which formed the basis for the 'liberalized role analysis' of Grosu & Landman (2012), are a red herring: according to the tests, the felicity of (28b) can not be attributed to Kuroda relevancy effects in internally headed relatives, because in that case we would expect (29b) to be felicitous.The felicity of (28b) must be due, thus, to the possibility of analyzing (28b) as some other construction than as an internally headed relative.
This obviously doesn't address the very interesting question of what does account for the contrast in (28a,b), if it isn't the Kuroda relevancy condition for internally headed relatives.But that is not something to be resolved in the present paper.For our purposes here, the relevant conclusion is that the contrast in (28a,b) is no reason to liberalize the notion of role along the lines of Grosu & Landman (2012).Hoshi's example (28b) turns out to be a red herring.This means that Shimoyama's suggestion, taken up by me here, that in internally headed relatives the internal head must fill a participant role can be maintained.With that, the present analysis provides better results than that of Grosu & Landman (2012), with a semantically simpler, and grammatically more constrained notion of role.

The basic semantics, an example
We illustrate the semantic derivation of the relative (more details in Grosu & Landman 2012): (1) üTaro-wa [Yoko-ga reezooko-ni kukkii-o sukunakutomo mit-tsu Taro-top [Yoko-nom refrigerator-loc cookie-acc at least 3-clf irete-oita-no]-o paatii-ni motteitta.put-aux-no]-acc party-to brought Taro brought to the party: [the sum of all the cookies such that…] Yoko put at least three cookies in the refrigerator.'Yoko put at least three cookies in the refrigerator.Taro brought them to the party.' We assume we have put together the ip-semantics: ip → E π : Next, event existential closure takes place at the ip-level, and at the cp-level, where the operator is, abstraction takes place over variable x n , binding that variable: The set of all sums of at least three cookies that were put in the fridge by Yoko (in some sum of events) We have derived at the cp-level a predicate interpretation for the relative clause.The cp is in argument position in the matrix.14I assume that the implicit definiteness operation s brings the relative in argument position from a predicative meaning to a definite interpretation at the type of individuals.15This is similar to what Jacobson (1988;1995) assumes for English free relatives in argument position.
With this, we derive as the interpretation of the internally headed relative clause: The sum of all cookies that Yoko put in the fridge (in some sum of events), presupposing that she put at least three cookies in the fridge And this means that we derive as the interpretation for (1): Taro brought the cookies that Yoko put in the fridge to the party.Presupposition (brought in by the definiteness operator): Yoko put at least three cookies in the fridge.

The Kuroda relevancy condition
Kuroda showed that felicitous interpretation of the internally headed relative requires a relevancy connection.The Kuroda relevancy condition (Kuroda 1976-77;1992;1999) can be formulated as follows: The Kuroda relevancy condition a.The Relevancy Condition For an internally headed relative to be acceptable, it is necessary that it be interpreted pragmatically in such a way as to be directly relevant to the pragmatic content of its matrix clause.

b. Sub-condition
The two events represented by the internally headed relative and the matrix clause involve the same temporal interval and the same location.
For discussion and modification of the sub-condition, see Kim (2007), Grosu (2010), Grosu & Landman (2012) and Grosu & Hoshi (2016).While I am in this paper mainly concerned with the question of how to enforce the Kuroda relevancy condition as a felicity condition, I will suggest a reformulation here.The Kuroda relevancy condition was illustrated with the examples in (2): (2) a. #[Daidokoro-no mado-kara siroi neko-ga haitte-ki-ta]-no]-ga kitchen-gen window-from white cat-nom came-in-past-no]-nom kesa mata yattekita.this-morning again came [ [The cat such that…] a white cat came in from the window] came back this morning.'A white cat came in from the kitchen window; she came back this morning.'b. ü[Daidokoro-no mado-kara siroi neko-ga haitte-ki-ta]-no]-ga kitchen-gen window-from white cat-nom came-in-past-no ]-nom akana-o totte nigeta.fish-acc steal ran-away [ [The cat such that…] a white cat came in from the kitchen window] stole a fish and ran away.'A white cat came in from the kitchen window; she stole a fish and ran away.'I note first that, while the examples in (2) allow other structural analyses besides internally headed relatives, the contrast in felicity judgements in (2a) and ( 2b) is preserved under the applicable test for internally headed relatives proposed in Grosu & Hoshi (2016).I will stick with the examples that are potentially structurally ambiguous, but the facts are the same for the more complex disambiguated examples.Kuroda relevancy is the observation that the event of the white cat coming in does not bring her enough on the scene for (2a) to be felicitous.In (2b) the scene with the white cat coming continues in the main clause with her stealing the fish.This is enough to bring her on the scene, and (2b) is felicitous.This fits with the spatio-temporal overlap clause: the sentence is presented as observing one extended region including the coming in, the stealing, and the leaving.
However, the temporal overlap clause is too strong for felicitous examples like ( 18 Taro-nom evening-in sushi-acc guest-to served-no-acc asa daidokoro-de tukutta.morning kitchen-in made Yoko made in the kitchen in the morning [the sushi such that] Taro served the guest sushi at night. In these examples it is presumably what we could call the rhythm of the events: 'made-inthe-morning -served-in-the-evening' which provides the relevant connection.Note too that the felicity of both these examples requires a symmetric formulation of the Kuroda connection (it won't do to require, say, that the matrix event should overlap a result state of the internal event, because that cannot deal with (34b)).I propose a (still very informal) formulation in terms of group-event or singular process formation:

The Kuroda relevancy condition (reformulated):
The two events represented by the internally headed relative and the matrix clause must be in the context naturally interpretable as part of a single natural process (a group event).
Events e 1 and e 2 are Kuroda-related iff e 1 and e 2 satisfy (in context) the Kuroda relevancy condition.
Thus, in the context of ( 34), the relevant events can be seen as part of a single processmake the sushi-let it rest-serve the sushi -which is contextually present in the matrix both in (34a) and (34b).In (2a) the event of the cat coming in the past and the event of the cat coming in today are presented as two single events, and not as one process.
That the notion of single process is on the right track is suggested by the following examples.Compare the infelicitous (2a) with ( 35): (35) [Haiiro-no neko-ga kinou mado-kara haitteki-ta-no]-ga gray-gen cat-nom yesterday window-from came-in-past-no-nom kesa mata soto-ni tobi-dasita.this-morning again jumped out [ [The cat such that…] a gray cat came in from the window yesterday] jumped out again this morning.
The main difference between ( 35) and ( 2a) is that the event of the cat coming in yesterday and the cat jumping out again today are naturally seen as (part of) one process, and ( 35) is felicitous.
Even stronger is the following observation.Landman & Rothstein (2009) show that certain interactions of various kinds of plural noun phrases with aspectual operators are best understood by assuming that pluralities of events get reanalyzed as single processes: e.g. they argue that aspectually, iterations of events are no longer event pluralities, but singular processes.Inspired by this, (36) varies (2a) by introducing an iteration: (36) [Haiiro-no neko-ga iti-nen-mae-ni mado-kara haitteki-ta-no]-ga gray-gen cat-nom one-year-ago window-from came-in-past-no-nom sore-o soreirai zutto mai asa yattei-ru.that-acc since ever every morning has done [ [The cat such that…] a gray cat came in from the window a year ago] has done that every morning since.
In (36), the event introduced in the relative clause is not simply regarded as one of a multitude of events, but as the first stage of a single iterative process.Unlike (2a), ( 36) is felicitous.This is rather compelling evidence that what is at stake in Kuroda relevancy is indeed single process formation.
While I think that the heart of Kuroda relatedness is indeed the plausibility of regarding the events as forming in context a singe process, I think that the role of context here should not be over-emphasized.While the context obviously plays a role, it cannot all by itself provide the clues that make the events form a natural single process.Thus, take any internally headed relative which is infelicitous because the relevant events involved do not naturally form a single process.Set up a pragmatic context where you make these events explicitly part of a single process.It is not clear that that will, in general, be sufficient to make the relative felicitous.If so, the notion of Kuroda relatedness is more semantically constrained than assumed in Kuroda's own formulation of the condition: the natural, contextual interpretation as a single process must be derived not just from the context, but from the context and the semantic material provided by the sentence interpretation.Kuroda relatedness, then, should be constrained accordingly. 16

Kuroda functions in a Lombardian presupposition mechanism
I am not concerned in this paper with giving more content to Kuroda relevancy than the suggestions in the previous subsection.I am concerned with how to enforce the constraint as a felicity condition in the grammar.This section works out a proposal to that effect.
Let us fix some notation: E π is the event type which is the interpretation of xp π , the structure that pp π adjoins to.E μ is the event type which is the interpretation of the matrix, the structure in which the relative clause fills an argument position.(μ is mnemonic for matrix) R π is the role in the participant relation of xp π that the interpretation of p π is identified with.
Kuroda relevancy relates events in event type E π to events in event type E μ .We will enforce Kuroda relevancy via a function from E π into E μ , which I call a Kuroda function: A Kuroda function is a contextually salient partial function k from E π into E μ such that for every e ∈ E π : if k(e) is defined, then e and k(e) are Kuroda-related (in the context).
Standard notion of domain: dom(k) = {e 1 ∈ E π : k(e 1 ) is defined} The semantics is going to make reference to a Kuroda function in the course of the derivation.But this is actually not quite trivial.The reason for this is that at the level of xp π , event type E π is accessible, but event type E μ , the event type of the matrix, is not: at the level of xp π there isn't yet an accessible event type of the matrix, because there isn't yet a matrix.On the other hand, at the level of the matrix, where event type E μ is accessible, event type E π is no longer accessible, because event existential closure has taken place, making E π semantically inaccessible.
In other words, in order to implement the felicity condition, we need a presuppositional mechanism that allows for a connection between event types E π and E μ , even though there is no derivational stage at which both are accessible.I propose a presuppositional mechanism that works somewhat along the lines of Renaissance economics.I call the mechanism Lombardian:

Lombardian banking:
Stage 1: You take out a loan -the bank checks your credit rating.Stage 2: You pay back the loan -you pay the interest.
The Lombardian presupposition mechanism is a mechanism that regulates the establishment in context of an appropriate salient Kuroda function.It is a presupposition mechanism that operates along Lombardian principles in the course of the semantic derivation: borrow at E π -pay back at E μ .
We start out at the level where pp π adjoins to xp π , with E π the interpretation of xp π .
We are building a semantic derivation.We have come to level E π and the interpretation of pp π .It is our task to link E π to a salient Kuroda function.We can't do this, because we don't have a Kuroda function, for the reasons given.What do we do?We borrow a function: we extend the interpretation of pp π , and introduce a functional variable and an event variable over its range:

Stage 1a: Borrowing
Let k be a variable over (partial) functions from events into events and let e μ be a variable over events.pp π → PP π , where: Variable k ranges over functions, but this variable will stay free and its value will ultimately be fixed as a salient function in the context.So instead of the expression k ranges over functions such that… I will use the expression: k stands for a function such that… Next, we undergo a credit check: we presuppose at this stage that k stands for a function from E π , i.e. a function whose domain is a subset of E π .We introduce this presupposition by making the intersection operation, connecting the interpretations of pp π and of xp π , presuppositional: Note that the presupposition that k stands for a function from E π does not mean that it is presupposed that all events in E π are in the domain of k -that would be an unreasonable requirement -but only that some are.So far we are presupposing that k is a Kuroda function from E π into some other set of events.We cannot at this stage require more.The next Lombardian activity happens when we reach the matrix and the event type interpretation of the matrix.We derive an event type in which the borrowed variable e μ is still unbound, and we haven't yet fixed more about k than that it is a function from events into events with domain E π .I will call this event type E μ (note: with a superscript μ).We now need to pay back the loan, with interest.Paying back means that we bind the free event variable by abstracting over it:

Stage 2a: Paying back
Given event type E μ .Form event type E μ by binding e μ in E μ : λe μ .eμ ∈ E μ The interest is the presupposition introduced at this stage: that E μ is the range of the function k and that k is a Kuroda function into E μ .We do that by making the semantic binding operation presuppositional: We have already presupposed that k stands for a Kuroda function with domain E π .We now set the range of k to E μ , making sure, of course, to continue to presuppose that k is indeed a Kuroda-function.Thus, in two stages the Lombardian presupposition mechanism has built a presupposition linking E π and E μ via a Kuroda function.We will show, by discussing two examples, that this indeed means that 'matrix events' are presupposed to be Kuroda related to 'internal relative events'.

Two examples
The first example is (1), for which we have already gave the basic derivation in Section 2.5 above: (1) üTaro-wa [Yoko-ga reezooko-ni kukkii-o sukunakutomo mit-tsu Taro-top [Yoko-nom refrigerator-loc cookie-acc at least 3-clf irete-oita-no]-o paatii-ni motteitta.put-aux-no]-acc party-to brought Taro brought to the party: [the sum of all the cookies such that…] Yoko put at least three cookies in the refrigerator.
The new derivation follows that given in Section 2.5.We derive at the ip level of the relative: This means that we derive as the interpretation of the relative in the matrix: (38) σ(λx .∃e ∈ E π : Th(e)=x ∧ k(e)=e μ ) Presupposition: k is a Kuroda function and dom(k) ⊆ E π .
The matrix event type E μ with variable e μ still free is: This presupposes, as before, that Yoko put at least three cookies in the fridge.Look at the sum of all events of Yoko putting at least three cookies in the fridge.This sum is itself an event of Yoko putting at least three cookies in the fridge and its theme is the sum of all cookies that Yoko put in the fridge, hence the sentence expresses that there is an event of Taro bringing the theme of the sum of in-fridge-putting events to the party, an event which is presupposed to be Kuroda related to the sum of in-fridgeputting events.This derivation is felicitous if variable k can be linked in the context to a salient Kuroda function.That is possible, if the context naturally allows the event of putting the cookies in the fridge and the event of taking them to the party to be regarded as stages of a single process.Since such an interpretation is readily available, there is no problem assuming that there is such a salient Kuroda function.The sentence is felicitous and we derive, informally: (42) Taro brought the cookies that Yoko put in the fridge to the party.Presuppositions: -Yoko put at least three cookies in the fridge.
-The event of putting the cookies in the fridge and the event of bringing them to the party are Kuroda-related.
As a second example, we look at the contrast between (2a) and (2b): (2) a. #[Daidokoro-no mado-kara siroi neko-ga haitte-ki-ta]-no]-ga kitchen-gen window-from white cat-nom came-in-past-no]-nom kesa mata yattekita.this-morning again came [ [The cat such that…] a white cat came in from the window] came back this morning.
b. ü[Daidokoro-no mado-kara siroi neko-ga haitte-ki-ta]-no]-ga kitchen-gen window-from white cat-nom came-in-past-no ]-nom akana-o totte nigeta.fish-acc steal ran-away [ [The cat such that…] a white cat came in from the kitchen window] stole a fish and ran away.
(43) E π = λx.comein(e) ∧ white cat(Ag(e)) ∧ through the kitchen(Path(e)) ∧ Time(e)<now The set of events of a white cat coming in through the window in the past The internal head is siroi neko-'white cat', so we set the interpretation of p π to the Ag role.
From here on the derivation is just as in example (1), and we derive, on the condition that k is a Kuroda function, for the matrix: (44) λe.come back(e) ∧ this morning(Time(e)) ∧ Ag(e) = σ(λx .∃e' ∈ E π : Ag(e')=x ∧ k(e')=e) The set of events of the cat that came in coming in today again But, of course, we only derives this, if k is a Kuroda function, which means that there must be a natural salient sense in the context in which the event of the cat coming in in the past (before today) and the cat coming in today are regarded as a single process.But, as argued before, there is no such natural salient sense: the natural salient sense is to regard these entrance events as two, not as one.This means that E μ is undefined, and the derivation stops.(2a) is infelicitous.
We have the same derivation for (2b) and derive, on the condition that k is a Kuroda function, for the matrix: (45) λe.stole a fish and ran away(e) ∧ Ag(e) = σ(λx .∃e' ∈ E π : Ag(e')=x ∧ k(e')=e) The set of events of the cat that came in stealing a fish (then) and running away (after that) I am skipping over the technicalities of connecting the coming-in event to the plural sum of a fish-stealing event and a running-away event.The point is: there is a very natural interpretation of these events as part of one unrolling scenario, hence in this case there is a salient Kuroda function, E μ is defined, and after event existential closure we derive a felicitous interpretation along the lines of: Concerning the cat that came in through the window: there is a sequence of events continuing its coming in: namely, it stole a fish and then ran way.

Extending the analysis: Change relatives
We are now concerned with examples like (3a): (3) a üJohn-wa [Mary-ga gozentyuu-ni ringo-o sibottekureta-no]-o John-top [Mary-nom morning-in apple-acc squeezed-no]-acc gogo-ni hitoikide nomihosita.afternoon-in in-a-gulp drank-up John drank in the afternoon in a gulp [the juice such that …] Mary squeezed apples in the morning.
As we have seen, (3a) is felicitous, even though the interpretation head (apple juice) is not the same as the interpretation of the internal head (apples).Similar examples are the felicitous (46a) and ( 46b It is hard to construct a similar contrast for the examples in ( 46), because it is hard to find examples that naturally satisfy Kuroda relevancy.This is not a problem in (47): arguably, (47) satisfies Kuroda relevancy in the same way as (3), so failure to satisfy Kuroda relevancy is not the source of the infelicity in (47).
Internally headed relatives like the above examples were first discussed in Hoshi (1995) and came to be called change relatives in the literature.While the actual examples discussed here are structurally ambiguous between an analysis as internally headed relatives and an analysis involving a bi-clausal adverbial construction, it is argued in Grosu & Hoshi (2016) that such cases can be disambiguated, and examples of internally headed change relatives, which do not allow an analysis involving a bi-clausal adverbial construction, do indeed exist.The analysis presented in this section, then, applies to cases like ( 3) and ( 46) on their analysis as internally headed change relatives.
What is the difference between the felicitous example in (3) and the infelicitous example in (47)?Let's first see what the similarity is.Both in (3) and in ( 47), E π is a set of events where the internal head is a sum of count objects and the presumed interpretation head is a liquid that this sum of objects is turned into via a transition procedure (squeezing).The main difference between the felicitous example in (3) and the infelicitous example in (47) seems to be that in (3) the transformation is entailed by the semantics of E π , whereas in the examples in (47), it is not entailed by the semantics of E π , but pragmatically induced.Thus in (3) the events in the event type are themselves events of turning the theme into liquid, while the events in (47) are not.The generalization then is:

Internally headed change relatives:
In internally headed change relatives, where E π expresses semantically a transformation of π, the interpretation head can be taken to be the result of the transformation.
What we see, then, is that in contrast to non-change internally headed relatives, in change relatives the relation between the interpretation of π and the interpretation head can be more relaxed. 17s we observed, change-relatives are only possible if in xp π the verb expresses a phasetransformation on the role R π .Let us call this a change-event type (on role R π ): This is the theory.We can now come back to the example: (3) a üJohn-wa [Mary-ga gozentyuu-ni ringo-o sibottekureta-no]-o John-top [Mary-nom morning-in apple-acc squeezed-no]-acc gogo-ni hitoikide nomihosita.afternoon-in in-a-gulp drank-up John drank in the afternoon in a gulp [the juice such that …] Mary squeezed apples in the morning.
The internal head p is ringo-'apple', which here clearly has a count interpretation.The change presupposition is that the matrix event contains a role Th k that maps the squeezing event e onto tr[e,Th(e)], the juice that results from event e of squeezing its theme.This presupposition is satisfied in the example by the natural assumption that Th k is the theme role on the matrix, the role that the interpretation of the relative fills.With that, we derive the interpretation given under the formula above.The Kuroda presupposition that the event of squeezing apples and the drinking the resulting apple juice in one gulp are in context naturally regarded as a single process is, we assume, naturally satisfied by k.
The idea, then, is that change relatives use the derivational mechanism that brings a Kuroda function into the interpretation: the Kuroda function k takes on a second role as a change function, which allows a liberalization via k of the relation between the interpretation of p π and the ayay gap interpretation x n in the interpretation of pp π .

Conclusion and discussion
Unlike the operator-gap construction in externally headed relatives or antecedent-anaphor structure in discourse anaphora, internally headed relatives require for felicity a relevancy relation between the interpretation of the internal head inside the relative and the interpretation of the matrix.The relevancy relation is interpreted as 'being contextually interpreted as part of a single process'.In the present analysis, this semantic connection is made via Kuroda-functions, functions mapping events onto events that are in context relevantly related in the right way.
The felicity requirement is implemented via a Lombardian presupposition mechanism which takes as input the event type that the internal head associates with, and links it to the matrix event type when that becomes available (on the conditions that such a link is possible, that is the felicity condition).
We have seen that the nature of the Kuroda-function-linking can be relaxed: while the internally headed relative expresses in the matrix properties of the object that fills the internal head role in the relevant internal head event type (or the sum of the objects that fill that role across that event type), internally headed relatives allows change-interpretations where the internally headed relative semantically expresses an event type of change with respect to one of its roles, and the matrix expresses properties not of the thing that fills that role, but of the stuff it gets changed into.
Any analysis of Japanese internally headed relatives will have to incorporate one way or another something that enforces the Kuroda constraint, but also allows for the required flexibility.I have presented a hybrid analysis: a standard operator-gap construction, with the gap the complement of a null preposition in pp π , adjoined to xp π .I have proposed that the semantics of the null preposition selects a role from the participant relation of xp π , and I have argued that this forces the gap and the internal head to be syntactically local.I then showed how the event type and role analysis allows the notion of a Kuroda function to tie together in the semantic derivation the event type levels that are relevant for formulating the Kuroda constraint.For this we needed to develop a Lombardian presupposition mechanism, a mechanism where the input conditions and output conditions of the Kuroda function are expressed at different stages of the derivation.It was shown that the mechanism of Kuroda functions is flexible enough to incorporate the relaxations required for analyzing change relatives.Thus the sword cuts both ways: the hybrid analysis opens the way for implementing the Kuroda relevancy condition via Kuroda functions.The relative ease with which the latter extends to 'difficult' cases -like change relatives -provides support for the hybrid analysis, given that the analysis does need to account for island effects as well.
The Lombardian presupposition mechanism is, of course, an extension of classical presupposition mechanisms.We need such an extension because we are dealing with a doubly complex case.
In classical presupposition cases the actual presupposed information (like, say, a factive presupposition, deictic link, or a uniqueness condition) is usually not that complex; what is complex is the projection problem: determining the level of discourse information structure at which the presupposed information can be and/or must be assumed to be integrated.That question is just as relevant here, but I have not focused on it at all.
What is different in the present case is that the presupposed information is itself relational (or, as I have assumed, functional).Relational presuppositions are found in bi-clausal constructions, for instance, adverbial phrases that presuppose a certain temporal relation -like temporal overlap -between the time expressed in the adverbial and the time expressed in the main clause.This by itself is not necessarily very complex: in standard bi-clausal cases the semantics has two event types available at the same stage of derivation, and the actual presupposed relation can be readily expressed compositionally.
But, as the current paper argues, Japanese internally headed relatives are not bi-clausal structures.What internally headed relatives share with presuppositional bi-clausal Once we realize the need for an operation creating an event type of absence states, the obvious semantic structure of the internally headed relative in (51) becomes: Thus, what happens semantically is that in the scope of PP π , there are two semantically relevant event types: the lower one that is existentially closed before ¬ can apply, and the higher absence one that the internal head π relates to.This means that PP π semantically adjoins to the higher of the two event types and, since Grosu & Landman's scope constraint is formulated semantically, it is not violated by this derivation: (51c) is correctly predicted to be felicitous.Koji Hoshi p.c. points out that nani-ka muzukashii hon-'what difficult book' is functioning as a positive polarity item in examples like (51c), in particular, an item that does not want to be semantically interpreted in the scope of the negation.The felicity of (47c) depends on the interpretation of nani-ka muzukashii hon as taking scope over negation, not on its position: (51c) stays felicitous if we put nani-ka muzukashii hon in its non-scrambled position after the negative polarity item dono kyooju-'any professor'.This is quite compatible with the analysis presented here.The analysis presupposes a mechanism giving nani-ka muzukashii hon scope over negation.What the analysis adds is a mechanism constructing semantically an event type at the level where nani-ka muzukashii hon is interpreted.And this is the event type that PP π adjoins to.
In a way, then, the assumption is that with the syntactic node xp π a more extensive semantic interpretation strategy is associated (event existential closure -negation -event type opening -indefinite -PP π adjunction).And the assumption is that this is a local mechanism in the sense that is relevant for the interpretation of pp π .

Internal scope dependencies
We come back to Shimoyama's example (4a).(4a) allows an accumulation reading that corresponding externally headed relatives do not allow: (4) a. Wasaburo-wa [dono gakusei-mo peepaa-o 3-bo dasita-no]-o Wasaburo-top [every student paper-acc 3-clf turned-in-no]-acc itiniti-de yonda.one-day-in read Wasaburo read in one day [the papers such that…] every student turned in three term papers.'Every student turned in three papers.Wasaburo read all the papers that all the students turned in in one day.' The internal head peepaa-o 3-bon-'three term papers' is in the scope of a universal quantifier dono gakusei-mo-'every student'.In event theories, the universal quantifier takes scope over the event existential quantifier (for each student x there is a set of events e x of x turning in three term papers).If we derive this with the scope mechanism, dono gakusei-mo-'every student' takes scope over E π .There are two problems with this.
In the first place, this is incompatible with the scope blocking constraint: PP π adjoins to the event type interpretation of xp π and π is local in xp π .But that means that PP π adjoins before existential closure.This means that if we give the universal quantifier wide scope over the event existential quantifier, we necessarily give it wide scope over PP π and we violate the scope blocking constraint.
In the second place, we don't want to think that this is a legitimate exception to the scope blocking constraint, because the reading derived by giving the universal quantifier wide scope with the scope mechanism is a reading that (4a) doesn't naturally have, and a reading which is not the natural one indicated above: Wasaburo read in one day three papers, the same three papers that every student turned in.Grosu & Landman (2012) propose a different analysis for these cases.They argue, following Landman (2000), that cases like (55a) allow, besides the scopal analysis (55b), an analysis with a dependency relation, interpreted along the lines of (55c): The cumulative event type interpretation of students turned in term papers is called the Scha-event type in Landman (2000).Following Scha (1981), analyses of scopeless readings, cumulative readings, absorption readings, binary quantifier readings, dependency readings, etc. have generally involved something equivalent to the Scha-event type.The particular analysis in (55c) was inspired by the analysis of Moltmann (1992) of reciprocals and same and different.
In the analysis suggested in Landman (2000), the interpretation of each student -three term papers is an event type adjoined to the cumulative Scha event type.This adjoined event type is the set of all events such that the sum of its subevents with a single agent has as theme a sum of three.Intersected with the Scha event type, this gets the right interpretation for (55c) (for details of the semantics, see Landman 2000).
If we now assume that the internal head is peepaa-'papers', we see that the situation created in this derivation is similar to the one in the previous subsection: the analysis involves two event types, the dependent event type which contains the scopal element each and the cumulative event type to which the latter is adjoined: The internal head of the relative is, on this analysis, not in the event type which is in the scope of the quantifier (per student, the set of subevents of that student turning-in the papers (s)he turned-in), but in the higher cumulative event type: papers in the set of events of students turning in papers, as restricted by the adjunct.This means that, once again, the scope constraint is not violated and this is a felicitous derivation for (4a).
The rest of the derivation is just a question of technical diligence.The reading derived for the relative clause in (4a) is the correct one: The sum of all term papers turned in by students, where every student turned in three term papers This analysis, then, solves both problems: the analysis does not violate the scope blocking constraint and it derives the correct interpretation for (4a).The Scha event type is cumulative, and the internal head connects to its theme role.Hence, the internally headed relative accumulates the themes of all the events in the Scha event type, i.e. all papers written.This means that the analysis derives the correct reading for (4a).The reading is, in fact, support for the scopal analysis, because the correct reading derives from the fact that the higher event type is in essence the cumulative Scha event type.We come briefly back to the issue mentioning in Section 1, footnote 4. Chris Tancredi points out that an accumulation reading is also possible for externally headed examples like (i) (from footnote 4), where the numerical 3-bon-3-clf is inside the relative and the head is peepaa-'paper': Wasaburo-wa [[dono gakusei-mo 3-bon dasi-ta ] peepaa]-o itiniti-de yon-da.Wasaburo-top every student 3-clf turned-in] paper]-acc one-day-in read 'Wasaburo read the sum of all term papers turned in by students, where every student turned in three term papers.' To derive this reading we only need to assume that the ip inside the relative allows for the same semantic analysis with a Scha event type and dependency relation as the ip as in (4a) above, but, of course, without an internal head: i.e. with variable x n corresponding to the gap of the external relative, which is abstracted over at the cp-level and constrained there by the external head peepaa-'paper': definite interpretation of this will derive the same accumulation reading.Coming back to internally headed relatives, note that similar cumulative examples exist for change relatives: (7) a. üMary-ga [John-ga [zibun-no gakusei-ga juuyouna kasetsu-o Mary-nom [John-nom self-gen student-nom important hypothesis-acc teian-shi-ta to] jimanshite-ita-no]-no kekkan-o shiteki-shi-ta.propose-do-past-to] boasted-had-no]-gen defect-acc point-out-do-past Mary pointed out a defect in: [the important hypothesis such that …] John had boasted that his student proposed an important hypothesis.b. #Mary-ga [John-ga [atarashii kasetu-o teianshita gakusei-o] Mary-nom [John-nom [new hypothesis-acc proposed student-acc] homete-ita-no]-no kekkan-o shitekishita.praise-had-no]-gen defect-acc pointed-out #Mary pointed out a defect in: [the new hypothesis such that …] John had praised [the student who proposed a new hypothesis].
π [ ip Fred buttered a bun]] → λe.butter(e) ∧ Ag(e)=Fred ∧ bun(Th(e)) ∧ Time(e) < now ∧ Th(e)=x n is the participant relation of xp iff R 1 …R n are the participant roles for xp.I will call the dps corresponding to the participant roles in the participant relation of xp the arguments of the participant relation.
, Th, Instr>, where IP is: λe.butter(e) ∧ Ag(e)=Fred ∧ bun(Th(e)) ∧ knife(Instr(e)) ∧ quick(Manner(e)) ∧ Time(e)<now (24) Fred buttered a bun at midnight.In (24), the roles Ag, Th and Time are participant roles.Note that the Time role is, so to say, introduced twice, by the tense and by the pp at midnight.The latter makes the Time role a participant role in (24): (25) <IP, Ag, Th, Time>, where IP is: λe.butter(e) ∧ Ag(e)=Fred ∧ bun(Th(e)) ∧ midnight(Time(e)) ∧ Time(e)<now We can now reformulate Assumption (2b) from the previous section without making reference to the internal head π: Assumption 2b: p π is interpreted as one of the roles in the participant relation of xp π .
By this construction, the relation between xp, the dp arguments of the participant relation of xp and v is 'local' in the following sense: 'Locality': 9 -The arguments of the participant relation of xp cannot occur in a clause embedded in xp.-There cannot be a syntactic island in xp between v and any of the arguments in the participant relation of xp.Corollary: -The internal head cannot occur in a clause embedded in xp π-There cannot be a syntactic island between the ayay-gap and the internal head π.
a. üJohn-wa[[[mizu-ga  hiruma-ni kootta]-no]-no ue]-de John-top water-nom day-during frozen-no-gen surface-on moosudeni yuugata-ni sukeeto-o sita.already evening-in skate-acc did John skated in the evening already on [the ice such that] the water froze during the day.b.üMary-wa [[[koori-ga hiruma-ni toketa]-no]-no naka]-deMary-top ice-nom day-during melted-no-gen inside-in moosudeni yuugata-ni oyoida.already evening-in swam Mary swam in the evening already in [the water such that] the ice melted during the day.It is instructive to compare the felicitous example (3) with the infelicitous (47):(47) #John-wa [Mary-ga gozen hachi-ji-ni fuudopurosessaa-ni John-top Mary-nom morning 8-o'clock-dat foodprocessor-dat kakeru-tame-ni put-into-purpose-dat ringo-o kirikizanda-no]-o gogo-ni hitoikide nomihosita.apple-acc cut-into-pieces-no-acc afternoon-in in-a-gulp drank-up John drank in the afternoon in a gulp [the juice such that …] Mary cut apples into pieces for the foodprocessor at eight in the morning.
le. squeeze(e) ∧ Ag(e)=Mary ∧ apples(Th(e)) ∧ morning(Time(e)) The set of events of Mary squeezing apples in the morning R π = Th E π is a change event type on role Th. pp π → λe.Th k (k(e))=x n ∧ k(e)=e μ We adjoin to E π , do event existential closure, abstract over x n and derive the definite interpretation of the relative: (49) σ(λx.∃e[squeeze(e)∧ Ag(e)=Mary ∧ apples(Th(e)) ∧ morning(Time(e)) ∧ Th k (k(e))=x ∧ k(e)=e μ ]) We form the matrix event type E μ on the presupposition that k is a Kuroda function and a change function from E π into E μ and apply event existential closure over the matrix event type and derive: (50) ∃e[drink(e) ∧ Ag(e)=John ∧ in one gulp(Manner(e)) ∧ afternoon(Time(e)) ∧ Th(e) = σ(λx.∃e'[squeeze(e')∧ Ag(e')=Mary ∧ apples(Th(e')) ∧ morning(Time(e')) ∧ Th k (k(e'))=x ∧ k(e')=e])There is an event of John drinking in the afternoon in one gulp the stuff that results from what Mary did to apples in the morning in a squeezing transformation event.
dono gakusei-mo peepaa-o 3-bon dasita-no]-o.[every student term-paper-acc 3-clf turned-in-no]-acc b.Every student turned in three term papers.c.Students turned in term papers, each student three term papers.

pp [ p e] [ dp e n ]]]]]
assumes that Tuesday and every day in (9) pattern with adverbials because they are pps with a null preposition (a null-version of on) in adverbial position: argues that internally headed relatives can be split headed.The examples in (29) are split-headed versions of the examples in (28).13Taroserved to the guest the sushi of his one daughter.