Two types of quantifier particles: Quantifier-phrase internal vs. heads on the clausal spine

The paper discusses two types of quantifier particles in Hungarian that both participate in reiterated constructions. One type follows and the other precedes its host, which makes it easy to compare them. The particles that follow their hosts are argued to be heads on the clausal spines of independent propositions. Host+particle does, but need not, occur in reiterations, and the particles do not build quantifier words. In contrast, the particles that precede their hosts are argued to be quantifier-phrase internal. Particle+host must occur in reiterations, and the particles build quantifier words. The two types of reiterated constructions also differ in having their own distinctive internal “connectives” and in forming strict vs. non-strict negative concord expressions. The paper focuses on syntax, with some attention to semantics. It argues for propositional coordination for both types, and propositional quantification for the second type. Constituent-size reiterations are derivable via ellipsis, raising the question whether they are necessarily so derived. The paper concludes with data from Bosnian, French, Japanese, Malay-alam, Mandarin, Persian, Russian, Sinhala, Telugu, and Turkish, which indicate the cross-linguistic interest of recognizing the two types of particle constructions.


Introduction
There is a substantial literature on English both_and, either_or, whether_or, and neither_nor constructions, especially relating to how the possibly mismatched positions of either and or come about and how the position of either correlates with the scope of the disjunction.The Hungarian (Turkish, Russian, Telugu, etc.) counterparts present a somewhat different descriptive profile that has received less attention.Here the particles take the same shape in all the juncts, occur at the same structural height in all the juncts and, in a subset of the cases, are obligatorily present in all the juncts. 1 Moreover, the same particles may show up as additive or negative concord elements and as building blocks of quantifier words.They are quantifier particles in the sense of Szabolcsi (2015).
The reiterated quantifier particle constructions are propositional (type t) coordinations, Junction Phrases in the sense of den Dikken (2006).They involve ellipsis or structuresharing when they look like constituent coordinations.In the focus of the paper is the fact that they come in two distinct types.The difference pertains to syntactic structure and, accordingly, to the way the meanings are composed.It cannot be predicted from the basic truth-conditional semantics.The overall meanings of the two constructions may be similar or identical, and the same particle may participate in both constructions.
In one type, the particles are heads on the clausal spine, with a focus-accented constituent of the complement in their specifier.In the other type, the particles are uninterpreted and realize a silent propositional quantifier on each junct.Propositional quantification was introduced in Kratzer & Shimoyama (2002) for cases where the set of propositions quantified over are alternatives generated by an indeterminate pronoun.Our case aligns with this nicely, but here the propositions quantified over are those expressed by the juncts.
The bulk of the paper analyzes data from Hungarian, a language in which particles in the first type follow and those in the second type precede their hosts, making the distinction especially convenient to keep track of.The detailed investigation of Hungarian is followed by a look at ten languages that likewise exhibit reiterated quantifier particle constructions, some of them plausibly both types.These data are interesting, among other things, because they raise questions about how to provide a unified semantics for the particles in their various roles.More generally, they bear on the syntax of the logical operators that make up some of the critical scaffolding of sentence meanings.
Below is a preview of the analyses and the Hungarian diagnostics they are based on.
(1)-( 2) represent the type where each particle is argued to be a head on the clausal spine, with a focus-accented constituent of the complement in its specifier.The reiteration is a coordination of self-contained propositions.For readability, the schematic Junction Phrase in (1) shows just two juncts: (1) 2 accordingly, to the way the meanings are composed.It cannot be predicted from the basic truth-conditional semantics.The overall meanings of the two constructions may be similar or identical, and the same particle may participate in both constructions.
In one type, the particles are heads on the clausal spine, with a focus-accented constituent of the complement in their specifier.In the other type, the particles are uninterpreted and realize a silent propositional quantifier on each junct.Propositional quantification was introduced in Kratzer & Shimoyama (2002) for cases where the set of propositions quantified over are alternatives generated by an indeterminate pronoun.Our case aligns with this nicely, but here the propositions quantified over are those expressed by the juncts.
The bulk of the paper analyzes data from Hungarian, a language in which particles in the first type follow and those in the second type precede their hosts, making the distinction especially convenient to keep track of.The detailed investigation of Hungarian is followed by a look at ten languages that likewise exhibit reiterated quantifier particle constructions, some of them plausibly both types.These data are interesting, among other things, because they raise questions about how to provide a unified semantics for the particles in their various roles.More generally, they bear on the syntax of the logical operators that make up some of the critical scaffolding of sentence meanings.
Below is a preview of the analyses and the Hungarian diagnostics they are based on.
(1)-( 2) represent the type where each particle is argued to be a head on the clausal spine, with a focus-accented constituent of the complement in its specifier.The reiteration is a coordination of self-contained propositions.For readability, the schematic Junction Phrase in (1) shows just two juncts: (1) (2) a.
A hó is esik, a szél is fúj, a gyerek is nyűgös.the snow too falls the wind too blows the child too cranky 'The snow is falling, likewise the wind is blowing, and likewise the child is cranky.' b.
A hó is ellen-ünk van, a szél is ellen-ünk van. the snow too against-1PL is the wind too against-1PL is 'The snow, as well as the wind, is against us.' where is 'too' sem 'nor' (2) a.A hó is esik, a szél is fúj, a gyerek is nyűgös.the snow too falls the wind too blows the child too cranky 'The snow is falling, likewise the wind is blowing, and likewise the child is cranky.' b.A hó is ellen-ünk van, a szél is ellen-ünk van. the snow too against-1pl is the wind too against-1pl is 'The snow, as well as the wind, is against us.' The type in (3)-(4) has not, to my knowledge, been scrutinized in the literature on Hungarian or other languages.The reiterated construction is argued to represent one big quantifier, interpreted in terms of propositional quantification in the spirit of Kratzer & Shimoyama (2002).The overt particles are uninterpreted and merely signal the presence of a contentful but unpronounced quantifier.Again, for readability, the JP schema in (3) shows just two juncts: (3) 3 The type in (3)-( 4) has not, to my knowledge, been scrutinized in the literature on Hungarian or other languages.The reiterated construction is argued to represent one big quantifier, interpreted in terms of propositional quantification in the spirit of Kratzer & Shimoyama (2002).The overt particles are uninterpreted and merely signal the presence of a contentful but unpronounced quantifier.Again, for readability, the JP schema in (3) shows just two juncts: (4) a. Vagy a hó esik, vagy a szél fúj, vagy a gyerek nyűgös.or the snow falls or the wind blows or the child cranky 'Either the snow is falling, or the wind is blowing, or the child is cranky.' b.Vagy a hó esett, vagy az eső esett.or the snow fell or the rain fell 'Either the snow or the rain was falling.' Section 2 motivates the proposed analyses with reference to the descriptive properties in (5).Throughout the paper, reiterations will be referred to as "tuples" for short. (5) Head on the clausal spine, cf. ( 1)-( 2): Quantifier-internal, cf. ( 3)-( 4): is, sem mind, vagy, akár, sem Particle follows host.Particle precedes host.Need not be part of a tuple.
Must be part of a tuple.Tuple-internal connective: és 'and'.
Builds quantifier words.Builds non-strict negative concord items.
Builds strict negative concord items.
To make parsing the data easier for the reader, Section 2 focuses on examples like (2b) and (4b), with superficially constituent-size juncts, temporarily pushing the propositional aspect to the background as much as possible.
Sections 3 and 4 flesh out the syntax of the two types in terms of propositional coordination and propositional quantification.The treatment of ellipsis connects to Valmala (2012;2013) regarding two types of Right Node Raising, and to Hirsch (2017) regarding constituent coordination as vP-coordination.The basics of the semantics are outlined.
Section 5 explains how the syntactic difference between the two constructions correlates with strict vs. non-strict negative concord (NC) in Hungarian.Chierchia (2013) proposed that non-strict NC involves a null functional head NEG with an n-word in its specifier.Szabolcsi (2016)  Section 2 motivates the proposed analyses with reference to the descriptive properties in (5).Throughout the paper, reiterations will be referred to as "tuples" for short. (5) Head on the clausal spine, cf. ( 1)-( 2): Quantifier-internal, cf. ( 3)-( 4): is, sem mind, vagy, akár, sem Particle follows host.Particle precedes host.Need not be part of a tuple.
Must be part of a tuple.Tuple-internal connective: és 'and'.
Builds quantifier words.Builds non-strict negative concord items.
Builds strict negative concord items.
To make parsing the data easier for the reader, Section 2 focuses on examples like (2b) and (4b), with superficially constituent-size juncts, temporarily pushing the propositional aspect to the background as much as possible.
Sections 3 and 4 flesh out the syntax of the two types in terms of propositional coordination and propositional quantification.The treatment of ellipsis connects to Valmala (2012;2013) regarding two types of Right Node Raising, and to Hirsch (2017) regarding constituent coordination as vP-coordination.The basics of the semantics are outlined.
Section 5 explains how the syntactic difference between the two constructions correlates with strict vs. non-strict negative concord (NC) in Hungarian.Chierchia (2013) proposed that non-strict NC involves a null functional head NEG with an n-word in its specifier.Szabolcsi (2016) adapted this proposal to Hungarian, identifying the sem in (1) as an overt counterpart of Chierchia's NEG and as a spell-out of is under clause-mate negation.In contrast, the sem in (3) naturally instantiates strict NC.
Section 6 links the present investigation to a programmatic proposal in Szabolcsi (2015) to offer a unified semantics for the various uses of quantifier particles.The question is how the syntactic differences affect the prospects of unification.This section lays out new data from nine languages, with many examples of both types of quantifier particles, placing the discussion into a wider cross-linguistic context.
Finally, some comments on how the particles are glossed.Finding transparent glosses is not trivial, because English does not have identical reiterating particles, irrespective of linear order, but the reader still deserves some crutches.
The universal quantifier particle mind, which also serves as a floating quantifier, is glossed as 'all', although 'all' may look awkward in combination with singulars.
The free-choice particle akár is etymologically related to akar 'want', a cross-linguistically not unusual situation (Haspelmath 1997).Abrusán (2007) analyses akár as 'even' in one non-reiterated use.Neither of these connections yield appealing glosses, so 'whether' will be used in its unconditional sense (Rawlins 2013).
The remaining glosses are more straightforward, with an eye on better-known Indo-European counterparts.Vagy_vagy 'or_or' builds jointly exhaustive and mutually exclusive disjunctions, much like Russian ili_ili and French ou_ou (Spector 2014).The negative concord item sem_sem 'nor_nor' is reminiscent of Russian and French ni_ni.The fact that is_is 'too_too' builds distributive conjunctions is paralleled by Russian i_i and Romanian şi_şi; like is, i and şi also serve as additive particles.
The tuple-internal connective pedig mentioned in (5) will be glossed as pedig.Although Section 6 points out various cross-linguistic counterparts, no morpheme of English presents itself as a good gloss option.

Systematic differences between is-type and mind-type particles
This section demonstrates that the two constructions and the particles in them are syntactically quite different.It enumerates arguments for the structures in (1) and (3) above.Sections 3 and 4 will follow with theoretical aspects of the syntax and the semantics.

Constituent order: Particle follows vs. precedes host
We begin with the most straightforward difference between the two types of particles, already highlighted in Section 1: one type follows and the other precedes its host.Hungarian orthography mandates a comma between the members of the iterations.The commas will help structure the examples for the reader, so they are retained.These contrasts unambiguously point to a global difference between the two constructions, postulated in (1) and (3).Even though the particles that follow their focused hosts (is, sem) participate in "reiterated" constructions, those arise from the coordination of independent and self-sufficient propositions.In contrast, in the case of the particles that precede their hosts (mind, vagy, sem, and akár), grammar must ensure that the hosts form a tuple.

Different optional connectives inside the tuples
Reiterated constructions of both types optionally contain what I will call "connectives" -but different connectives, és vs. pedig.És is the default Junction head corresponding to and (Szabolcsi 2015). 4It optionally occurs in iterations with particles that follow the host, confirming that those iterations are vanilla conjunctions.The optionality of és is due to the fact that Hungarian generally allows asyndetic (connectiveless) conjunctions.Pedig requires a more elaborate introduction, see below.
We first demonstrate that és and pedig are not interchangeable and do not combine.( 11)-( 12) illustrate the lack of interchangeability and combinability with particle sem, whose two versions offer minimal pairs.Afterwards only the grammatical examples are given, see ( 13)-( 14).Notice that unlike és, pedig intervenes between the particle and the host.
( To my knowledge, the connective pedig has not been discussed in the modern literature on Hungarian (although data of the type of ( 14) are cited in Lipták 2001).
Pedig has what seem to be two distinct versions. 5One version, which may be called adversative, occurs in clause-initial position and can be translated as 'even though' or 'despite the fact'.The present paper will not be concerned with this version. (15) Mari elkésett, pedig Peti figyelmeztette.Mari was.late pedig Peti warned.her'Mari was late, even though Peti warned her.' The pedig that interests us follows the topic in the last member of a propositional coordination or list, and its contribution can be approximated as 'on the other hand' or 'however' or 'lastly'.It marks the last member of a set of two or more partial answers to an overt or covert question, and thus indicates that the answer is now complete.Pedig is an entirely opaque element.It will be glossed as pedig, for lack of a non-misleading option.
or Kati or Mari or pedig Peti (is at.home) 'Either Kati or Mari or, lastly, Peti.' The interpretation of pedig jibes with the fact that it occurs in that construction which always comes in tuples.The tuple as a whole provides an answer to an overt or implicit question under discussion, enumerating propositions that serve as partial answers.If pedig is present, the list is complete.The particle mind 'all' tells us that all the propositions in the tuple are true; vagy 'or' tells us that one of them is true.In the next subsection we will see this even more vividly.

Particles that precede their hosts build quantifier words, those that follow do not
Hungarian forms its quantifier words by combining particles with indeterminate (wh-) pronouns.They are built with the particles that are confined to tuples.Those particles precede their hosts both in the reiterated construction and in combination with indeterminate pronouns.Vala-'some' is an allomorph of vagy 'or'.(19) Particle precedes host7,8 a. mind-en-ki, mind-en(*-mi), mind-en-hol all-en-who all-en-what all-en-where 'everyone, everything, everywhere' b. vala-ki, vala-mi, vala-hol some-who some-what some-where 'someone, something, somewhere' c. akár-ki, akár-mi, akár-hol whether-who whether-what whether-where 'whoever, whatever, wherever' d. sen-ki, sem-mi, se-hol nor-who nor-what nor-where 'no one, nothing, nowhere' Tying these together with the findings of the previous subsection, compare: 9 (20) mind Kati, mind Mari, mind (pedig) Peti ≈ mindenki (etc.)all Kati all Mari all pedig Peti everyone In contrast, the particle is that follows its host does not form quantifier words, in either order, see (21).The NC particle sem of course does participate in quantifier words but, given the double life it leads, there is every reason to believe that sen-ki, sem-mi, se-hol are simply instances of (19d). ( Is participates in the composition of NPIs and FCIs, see ( 22), but in that case it combines with a full quantifier word, which is a different matter (see Szabolcsi 2017).( 22) a. vala-ki is some-who too 'anyone, NPI' b. akár-ki is whether-who too 'anyone, NPI/FCI' The data just reviewed converge with the observations above.Mind-type particles must be part of a reiterated construction that is semantically equivalent to a quantifier, and they also form actual quantifier words with the indeterminate pronouns that correspond to the same domains as their hosts.Is-type particles on the other hand do not have to be part of a reiterated construction; when they are, those are "accidental" coordinations.They do not build quantifier words.

Strict vs. non-strict negative concord items
At this point we have evidence for the overall structures of the two constructions and for the quantificational role of mind-type particles; less so for the nature of is and the sem that patterns with is (follows its host).Negative concord (NC) provides some fine-grained evidence about those syntactic details.
The negative concord particle sem (more colloquially: se) occurs in both constructions under investigation but, interestingly, builds different kinds of NCIs in the two cases.
Hungarian is a negative concord language that is usually thought to be of the strict type, where the sentential negation marker nem 'not' is always mandatory, as in Russian.But Surányi (2006) showed that Hungarian NC is a hybrid: there is a set of NC-expressions that do not co-occur with nem when they are in preverbal position, mimicking non-strict NC languages like Italian.Consider the n-expressions senki 'n-one' and senki sem 'n-one nor' in preverbal position (which distinguishes strict vs. non-strict negative concord) and in postverbal position (which does not distinguish them).We see that senki has the distribution of a strict NCI like Russian nikto, whereas senki sem has the distribution of a non-strict NCI like Italian nessuno.Notice that in the strict NC version, the particle sem precedes its lexical hosts as well as the indeterminate pronoun ki 'who, viz.human' that it combines with, whereas in the non-strict NC version sem follows its lexical hosts as well as the n-word senki that it combines with.Szabolcsi's (2016) proposes a unified analysis for the hybrid negative concord facts involving senki and senki sem.It will be briefly reviewed and extended to the new data in Section 5.At this point, we note that Szabolcsi treats the sem in the non-strict NC construction as an overt counterpart of Chierchia's (2013) NEG, a functional head that invokes an abstract negation above its projection.The account of the contrast in ( 29)-( 30) converges with the overall syntactic analyses for the two constructions.

Interim summary
The preceding subsections substantiated the claim that the host + particle and particle + host reiterations are syntactically distinct, over and beyond linear order.Reiterations of host+particle represent the coordination of two or more independent propositions, with or without ellipsis.Since each of the propositions can stand on its own, reiteration is not mandatory.This contrasts with the case of particle+host, where reiteration is mandatory, and the construction can be seen as providing a set of partial answers to a question.The quantifier particles indicate whether each, some, or none of those partial answers is true; addition of pedig to the last junct marks the set as constituting a complete answer.Finally, with the particle sem the first type constitutes non-strict and the second, strict negative concord expressions.We anticipated that this squared with the claim that the particles following their hosts are heads on the clausal spine, whereas the particles preceding their hosts spell out a (propositional) quantifier.
Having presented and compared the basic data of the two constructions, Sections 3 and 4 zoom in on each construction in turn.Negative concord is relegated to Section 5.

Is 'too' and sem 'nor' are heads on the clausal spine
The syntactic role of is/sem can be conveniently explicated in terms of the feature-checking theory of quantifier scope.See among others Beghelli & Stowell (1997); Szabolcsi (1997); É. Kiss (2002); Brody & Szabolcsi (2003); Lipták (2005), and an overview in Szabolcsi (2010: Chapter 11).On this view, in Hungarian, members of a sequence of functional heads overtly attract operator phrases to their specifiers.Because the movement is overt, it is reflected in linear order at spell-out.Linear order directly maps to c-command, determining the relative scope of the operators (with some complications extensively discussed in Brody & Szabolcsi 2003). 10or example, the Ref(erential) head attracts definites and indefinites, and the Dist(ributive) head attracts universals and existentials that receive a distributive interpretation in its specifier.Revising her earlier FocP analysis, Horvath (2010;2013) adds an unpronounced EI head (EI for exclusive identification) right above the final landing site of the verb.EI attracts a phrase modified by csak 'only' or by an unpronounced EI-operator to its specifier.These latter operators in turn attach to focus-accented phrases, accounting for the well-known correlation of focus accent, preverbal position, and exhaustive interpretation in Hungarian.
Is 'too' has been recognized as a head that attracts a focus-accented phrase to its specifier since Brody (1990).The sem that follows its host is the negative concord variant of is and has the same property.In principle, two analyses are possible.(i) IsP and SemP are operator phrases that occupy the specifier of some unpronounced functional head H somewhere in the Ref>Dist>Neg>EI>Neg sequence in the clausal spine.H might be Dist for IsP, and a variant of Neg that has the properties of Chierchia's (2013)  The particles is and sem would be the only phrase-internal particles to follow their sisters if analysis (i) were chosen. 11Second, focus-sensitive particles always allow for broad focus, even when only a focus-accented constituent of the larger unit appears in their specifier.Recall (2a), repeated as (32); the example works equally well with sem in the place of is.
(32) A hó is/sem esik, … a gyerek is/sem nyűgös.the snow too/nor falls … the child too/nor cranky 'The snow is falling, likewise the child is cranky.'/ 'The snow isn't falling, likewise the child isn't cranky.' Here each is and sem operates on a full proposition, which is better understood if they are heads with those propositions in their complements; this is only possible on analysis (ii).Third, the negative existential/locative verb nincs becomes sincs precisely in contexts where nem is replaced by sem.Likewise, A. Lipták (p.c.) suggests that complex particles such as még-is/még-sem 'nevertheless,' de-hogy-is/hogy-is-ne 'of course not' are compounded clausal heads, corroborating that status for is and sem.
The fact that Kati is and Kati sem can appear in either preverbal or postverbal position, see (9), might seem problematic for the clausal head analysis of is/sem.But Szabolcsi (1997) and Brody & Szabolcsi (2003) argued that the sequence of operator heads (except for Neg) repeats itself above each of TP, vP, VP, etc.Of these, only the highest sequence is preverbal at spell-out.Analysis (ii) does not require anything beyond this assumption.
As was anticipated in Section 1 and confirmed in Section 2, iterations of host+is/sem are Junction Phrases containing independent propositions, each of which can stand alone. 1211 Horvath (2013) observes that csak either precedes the focused XP (as in (31a)) or immediately follows the verb.She explicitly argues that in the latter case, csak is an overt version of the clausal EI-head, and not a stranded EI-operator.Her representations for two synonymous sentences are as follows.My analysis of is/sem as a clausal head is congruent with Horvath's (ii).
Mari only Kati-dat showed prt Laci-acc 'Mari only introduced Laci to Kati.' (ii) Mari Kati-nak j mutatta csak [be t V Laci-t t j ].Mari Kati-dat showed only prt Laci-acc 'Mari only introduced Laci to Kati.' 12 In line with the fact that the juncts are independent clauses, the presence of is/sem in the first junct is not obligatory.In its absence, the structure is similar to Kate was asleep, and Mary too was asleep.
The Junction head is optionally pronounced.When the complements of Is/Sem are identical, both backward and forward ellipsis are possible.Importantly to us, segments like Kati is/sem (és) Mari is/sem, which may seem like constituent coordinations, straightforwardly result from backward ellipsis in clausal coordination, cf.(34a).Comments on the semantics are in order; they are presented with reference to is 'too', but carry over to its negative concord variant sem 'nor'.
Is 'too' is an additive particle.It introduces the presupposition that a focus-alternative of the proposition it combines with (i.e., the asserted prejacent) is true. 13Following Kobuchi-Philip (2009), in the reiterated construction the two or more propositions mutually satisfy each other's presuppositions, and thus the construction as a whole does not project any presupposition to the global context.Here, Kati is 100 kg volt presupposes that someone other than Kati was 100 kg, which is satisfied by the assertion about Mari.And vice versa, Mari is 100 kg volt presupposes that someone other than Mari was 100 kg, which is satisfied by the assertion about Kati.Brasoveanu & Szabolcsi (2013) address a theoretical problem that arises here.Effortless presupposition satisfaction usually works left-to-right, but here it is computed symmetrically.They propose that the additive requirements introduced by is and its cross-linguistic relatives are in fact post-suppositions in the sense of Brasoveanu (2013).In brief, they are not-at-issue requirements whose satisfaction is delayed within a local domain.Therefore, the juncts wait for one another, and mutual satisfaction is possible.If however nothing in the local domain satisfies the additive requirement, it projects to the global context, and becomes a traditional presupposition.
Szabolcsi (2015: Section 3.1.2)discusses of the behavior of what she calls MO particles in some detail, exemplified by Hungarian is, Russian i, and Japanese mo.In all these languages, the reiterated construction implies a perceived similarity in the juncts.In the case of broad focus, the conjoined propositions are implied to bear on the same salient issue in a 13 For the derivation of the additive presupposition of English too and Hungarian is, based on focus alternatives, see Szabolcsi (2017).
where is 'too' sem 'nor' Kati too/nor 100 kg was and Mari too/nor 'Kati as well as Mari was 100 kg.' / 'Neither Kati nor Mari was 100 kg.' Comments on the semantics are in order; they are presented with reference to is 'too', but carry over to its negative concord variant sem 'nor'.
Is 'too' is an additive particle.It introduces the presupposition that a focus-alternative of the proposition it combines with (i.e., the asserted prejacent) is true. 13Following Kobuchi-Philip (2009), in the reiterated construction the two or more propositions mutually satisfy each other's presuppositions, and thus the construction as a whole does not project any presupposition to the global context.Here, Kati is 100 kg volt presupposes that someone other than Kati was 100 kg, which is satisfied by the assertion about Mari.And vice versa, Mari is 100 kg volt presupposes that someone other than Mari was 100 kg, which is satisfied by the assertion about Kati.Brasoveanu & Szabolcsi (2013) address a theoretical problem that arises here.Effortless presupposition satisfaction usually works left-to-right, but here it is computed symmetrically.They propose that the additive requirements introduced by is and its cross-linguistic relatives are in fact post-suppositions in the sense of Brasoveanu (2013).In brief, they are not-at-issue requirements whose satisfaction is delayed within a local domain.Therefore, the juncts wait for one another, and mutual satisfaction is possible.If however nothing in the local domain satisfies the additive requirement, it projects to the global context, and becomes a traditional presupposition.
Szabolcsi (2015: Section 3.1.2)discusses of the behavior of what she calls MO particles in some detail, exemplified by Hungarian is, Russian i, and Japanese mo.In all these languages, the reiterated construction implies a perceived similarity in the juncts.In the case of broad focus, the conjoined propositions are implied to bear on the same salient issue in a uniform way (typically, as all favorable or all unfavorable).To wit, example (2) could be used to present the snow's falling, the wind's blowing, and the child's being cranky as congruent facts bearing on whether we should start heading home.The expressions as well as and likewise in the idiomatic translations correspond to this not-at-issue contribution. 14zabolcsi (2015) also observes that reiterated examples like (34a) and their cross-linguistic relatives are always interpreted distributively.(34a) can only mean that Kati and Mari individually weigh 100 kg; it cannot mean that they do so collectively.The explanation comes from the additive requirement (post-supposition).If the joint weight of Kati and Mari were 100 kg, the contextual requirement would not be satisfied.The mere presence of the same particle on multiple DPs does not by itself impose this requirement.Japanese A-to B-to 'A-with B-with = A and B' allows for both distributive and collective readings; to is a reiterating particle but, semantically, not a "MO particle".

Mind, vagy, akár and pre-host sem are quantifier-internal particles
Reiterations involving particles that precede their hosts involve a JP structure as well, but as a complement of an unpronounced propositional quantifier.The discussion will proceed as follows.4.1 presents the structure, with some remarks regarding how the particles get realized on the juncts.4.2 clarifies the neutrality of the J head.4.3 introduces the gist of the semantics in terms of propositional quantification, as in Kratzer & Shimoyama (2002).4.4 investigates propositional vs. constituent coordination, bringing in new data pertaining to Right Node Raising.

JP as a complement of an unpronounced quantifier
Section 2 enumerated descriptive arguments to the effect that the structure of mind_mind, vagy_vagy, akár_akár and (strict NC) sem_sem constructions is different from that of is_is and (non-strict NC) sem_sem ones.The juncts obligatorily come in tuples, each junct bears the same particle, and the connective és 'and' cannot be added.(Pedig might be a J head, with the initial quantifier particle adjoining to it, or it may be internal to the last junct.This paper uses pedig primarily as a diagnostic tool and does not attempt to settle its syntax.)I argue that a JP structure is involved but, unlike in (33), it is the complement of an unpronounced but contentful quantifier that is overtly realized in the form of identical particles on each of the juncts.The syntactic relation between Q and the particles can be seen as feature-checking, as indicated in (35), which repeats (3).( 35) Feature checking is a standard tool, and it captures the idea that Q is contentful, whereas the particles merely signal its presence.Feature checking ensures that each and every junct carries the appropriate particle if it is subject to an ATB-style condition. 15n alternative tool might be borrowed from Case concord, discussed in Bayırlı ( 2017), based on Pesetsky (2013).Case concord is specifically pertinent, because Case originates outside DP, not on the Num head (like plural) or on the N head (gender).The realization of the Q-feature can be seen to spread to the coordinates in the manner of Feature Assignment, subject to the intervention of phasal domains: (36) Feature assignment (FA) a. Copying: when  merges with , forming [  ], the grammatical features of  are immediately copied on  b.Realization: ... and are realized as morphology on all lexical head items dominated by .
where mind 'all' vagy 'or' akár 'whether' sem 'nor' Feature checking is a standard tool, and it captures the idea that Q is contentful, whereas the particles merely signal its presence.Feature checking ensures that each and every junct carries the appropriate particle if it is subject to an ATB-style condition. 15 An alternative tool might be borrowed from Case concord, discussed in Bayırlı (2017), based on Pesetsky (2013).Case concord is specifically pertinent, because Case originates outside DP, not on the Num head (like plural) or on the N head (gender).The realization of the Q-feature can be seen to spread to the coordinates in the manner of Feature Assignment, subject to the intervention of phasal domains: (36) Feature assignment (FA) a. Copying: when α merges with β, forming [ α α β], the grammatical features of α are immediately copied on β b.Realization: … and are realized as morphology on all lexical head items dominated by β.
(37) Phasal domains The overt manifestation of concord is suppressed by the intervention of phasal domains.
Imitating Bayırlı's notation, we may instantiate mind_mind constructions as follows, with the arc indicating a domain that is not penetrated by the copied particles.Read S as a variable over appropriate categories. (38)

17
(38) This paper will simply work on the assumption that some well-attested syntactic mechanism can account for the realization of the Q feature in the form of particles on each of the juncts.

Towards interpretation: Junction merely forms tuples (sets)
Den Dikken ( 2006) employs JP for either_or, neither_nor, and both_and structures.He does not specify what semantic contribution, if any, the J head makes, but his use of J in these varied cases indicates that it is meant to be semantically neutral.To make that idea precise, Szabolcsi (2015) couples JP with a proposal by Winter (1995).On that view, J merely forms an ordered tuple of the juncts.It is neither a conjunction, nor a disjunction.The tuple is converted to a set and, by default, an unpronounced operation interprets it as a conjunction, just as an unmarked sequence of sentences in a text is interpreted conjunctively.Additive (MO-)particles reinforce the conjunctive interpretation; in their presence, it is not merely a default.This is what happens in (33) above.But other particles on the juncts may override the default.Szabolcsi (2015) discusses KA-particles that invoke an unpronounced disjunctive operation.She argues that disjunctions are overtly marked, precisely because the conjunctive default needs to be overridden.
In what follows, I will likewise assume that J itself does not make JP a conjunction or a disjunction.It merely forms an ordered tuple, or set, of the juncts.What semantic operation is performed is determined by the particles on the juncts (i.e. by the unpronounced Q whose presence they signal).

Unpronounced Q is a contentful propositional quantifier
This paper will simply work on the assumption that some well-attested syntactic mechanism can account for the realization of the Q feature in the form of particles on each of the juncts.

Towards interpretation: Junction merely forms tuples (sets)
Den Dikken (2006) employs JP for either_or, neither_nor, and both_and structures.He does not specify what semantic contribution, if any, the J head makes, but his use of J in these varied cases indicates that it is meant to be semantically neutral.To make that idea precise, Szabolcsi (2015) couples JP with a proposal by Winter (1995).On that view, J merely forms an ordered tuple of the juncts.It is neither a conjunction, nor a disjunction.The tuple is converted to a set and, by default, an unpronounced operation interprets it as a conjunction, just as an unmarked sequence of sentences in a text is interpreted conjunctively.Additive (MO-)particles reinforce the conjunctive interpretation; in their presence, it is not merely a default.This is what happens in (33) above.But other particles on the juncts may override the default.Szabolcsi (2015) discusses KA-particles that invoke an unpronounced disjunctive operation.She argues that disjunctions are overtly marked, precisely because the conjunctive default needs to be overridden.
In what follows, I will likewise assume that J itself does not make JP a conjunction or a disjunction.It merely forms an ordered tuple, or set, of the juncts.What semantic operation is performed is determined by the particles on the juncts (i.e. by the unpronounced Q whose presence they signal).
English differs from Hungarian in that either is distinct from or, and either is optional.But *either p, q and *either p and q, etc. are not grammatical, so English also requires some efficient regulation.

Unpronounced Q is a contentful propositional quantifier
Recall from Section 2.4 that the same particles that appear in (35) also form quantifier words with indeterminate pronouns, yielding the parallelisms below, and similarly for akár and sem: The parallelism recalls an insight from Kratzer & Shimoyama (2002) and Kratzer (2005), presented for quantifier words that are built in the same way as mindenki and its brothers.
"Suppose we ... assumed that Indo-European indefinites, too, associated with independent quantificational operators.Their distinctive morphology might then tell us something about the nature of those operators.It might indicate syntactic agreement with matching non-overt propositional operators, as proposed in Beghelli and Stowell (1997) and thus create syntactic behavior not found with Japanese indeterminate pronouns.That speakers of Latvian, German, or Spanish, for example, perceive the pronouns and determiners of the kaut-, irgendein or algún series as existentials would now no longer mean that those expressions are themselves existentials.Their existential look would be the overt expression of syntactic agreement with propositional [∃], the true carrier of existential force.Those indefinites might have an uninterpretable but pronounced [∃] feature, then, that must enter an agreement relation with a matching interpretable feature that happens to be unpronounced."(Kratzer 2005: 131) The propositional quantifiers referred to above are defined as follows: (41) a.
[∃](A) = {the proposition that is true in all worlds in which some proposition in A is true} b. [∀](A) = {the proposition that is true in all worlds in which every proposition in A is true} Kratzer and Shimoyama apply (41) in the interpretation of sentences with quantifier words.There, A is the set of propositional alternatives generated off of indeterminate pronouns (who) in Hamblin-style alternative semantics: the set of propositions such that, for any human there is, the proposition that this human sleeps is in the set.In our case, A is the set of propositions that JP assembles from the juncts in it, as described in 4.2 above.Hamblin semantics can be used but does not play any particular role. 1716 The "≈" is motivated by the fact that the reiterated vagy_vagy construction is exhaustive (see Spector 2014 on soit_soit), whereas valaki is a vanilla indefinite like someone.However, Szabolcsi (2015: Section 3.2.5)points out that in many languages, reiterated disjunctions are not exhaustive: such are Sinhala (Slade 2011), Malayalam and Kannada (Jayaseelan, p.c.), as well as English either_or on many of its uses.While exhaustivity needs to be accounted for, it is not an inescapable property of reiterated disjunctions.It is with this grain of salt that I take vagy_vagy and valaki to be approximate counterparts. 17One of the anonymous reviewers notes that there is a large literature that points out problems with scope and binding in Kratzer & Shimoyama's version of alternative semantics and offers solutions.An early piece is Shan ( 2004), and a very recent one is Charlow ( 2018).
(43) { λw.sleeps(kati)(w), λw.sleeps(mari)(w), λw.sleeps(peti)(w) } For example, with particle mind 'all' attached to the juncts, the matching Q is ∀, and the result is the proposition that is true in all worlds where each of Kati sleeps, Mari sleeps, and Peti sleeps is true.Note that at the end of the day the following two sentences have the same truth conditions: The reason is that "every proposition in {p, q, r} is true" is logically equivalent to "p is true, and q is true, and r is true".The overall meaning of these sentences leaves us in the dark as to how that meaning might be composed.Only detailed analysis can help.This is especially important to bear in mind if one investigates a language in which, for some reason or other, even linear order does not distinguish between the two types of particles.

Propositional coordination and quantification
We have arrived at propositional quantification from two directions.On the one hand, Kratzer & Shimoyama use it for the equivalents of Someone/Everyone sleeps, for reasons related to Hamblin semantics.(In this paper, we are not specifically concerned with quantifier words.)On the other hand, the ellipsis-free versions of particle+host reiterations are straightforward representatives of propositional quantification.
'No matter which of {the snow is falling, the wind is blowing} is true, we are in trouble.' d.Sem a hó nem esik, sem a szél nem fúj.
'Not one of {the snow is falling, the wind is blowing} is true.' In other examples, the particles seemingly attach to smaller constituents (Mind Kati, mind Mari alszik, etc.).Starting with the introduction, I suggested that these are obtained by the optional ellipsis of shared material.The examples below provide further evidence that ellipsis or structure-sharing must be involved in some of the examples where the juncts are not complete propositions.I first illustrate the phenomenon with comparable examples from English: (46) a. Bring me both the blue __ and the green bottles.b.Bring me either every blue __ or every green bottle.c.Neither at least five blue __ nor more than six green bottles were provided.These examples bring to mind Right-Node Raising, which is often handled by movement.But neither bottle(s) in ( 46), nor -handed child(ren) in ( 47) could be shared by the two juncts as a result of rightward across-the-board extraction.I thank A. Lipták (p.c.) for directing me to work by V. Valmala that solves the problem.Using Right Node Raising as a pre-theoretical cover term, Valmala (2012;2013) distinguishes focal-pivot right-node raising and non-focal pivot right-node raising, and argues that the confusingly mixed properties of RNR can be neatly sorted out once this distinction is made.
Valmala proposes a set of diagnostics; see his work for details.Below I give a bird's eye review.
Focal-pivot RNR obtains when the shared string (the pivot) has focus accent.Focal pivots are always extractable expressions.For example: (48) I brought __ from the pantry and put __ on the table a ten-pound birthday cake.
Non-focal pivot RNR obtains when the last element before the pivot is focused and the pivot crucially is not.In this case the pivot may or may not be an extractable expression; non-extractable ones can only participate in this latter kind of RNR. ( 46) and ( 47) would be examples.Valmala argues that here the gap is not a result of movement; instead, interpretation is in-situ.He considers two possible mechanisms: ellipsis or structure-sharing (multidominance), without committing to a choice.I will not not address this theoretical issue, and simply use the label ellipsis.As A. Lipták (p.c.) observes, Hungarian never moves constituents to the right to be assigned stress, even pretheoretically and non-anti-symmetrically speaking, and so it does not exhibit focal-pivot RNR, although it allows non-focal-pivot RNR of the same string: Turning to the quantifier particle constructions, Hungarian exhibits a huge variety that exemplify the non-focal pivot RNR case.Verb-initial (50b), (51b) and ( 52) plausibly involve leftward across-the-board extraction of the verb, and (51b), the subsequent merger of negation.At least two works have recently called into question the availability of phrase-level coordination, arguing for conjunction reduction: Schein (2017) and Hirsch (2017).Schein's arguments primarily come from plurals and event semantics.Hirsch investigates semantically simpler cases and proposes that syntactic well-formedness and the availability of certain scope relations are best understood if coordinate structures are derived from vPcoordination, coupled with well-attested mechanisms for ellipsis, e.g.gapping.Importantly, he notes that as soon as generalized quantifiers are coordinated, semantically speaking we have propositional (type t) coordination (though not necessarily full-clausal coordination).Therefore, in the domain of data that he investigates, the general unavailability of constituent coordination must be a syntactic matter.
The same argument extends to the question of (53).If the formation of the generalizedquantifier level JP and QP is not possible even for such an innocent-looking case, that probably has to do with what syntactic mechanisms are available.At this point I cannot pinpoint any syntactically disastrous effects that would emerge if (53b) were allowed to coexist with the various possibilities for ellipsis.However, the data discussed in this paper will offer new grounds for hypothesis testing.

Negative concord
Finally, we come back to the strict vs. non-strict negative concord facts observed in 2.5.To attack them, we must first know how NC works in Hungarian.
At least two works have recently called into question the availability of phrase-level coordination, arguing for conjunction reduction: Schein (2017) and Hirsch (2017).Schein's arguments primarily come from plurals and event semantics.Hirsch investigates semantically simpler cases and proposes that syntactic well-formedness and the availability of certain scope relations are best understood if coordinate structures are derived from vP-coordination, coupled with well-attested mechanisms for ellipsis, e.g.gapping.Importantly, he notes that as soon as generalized quantifiers are coordinated, semantically speaking we have propositional (type t) coordination (though not necessarily full-clausal coordination).Therefore, in the domain of data that he investigates, the general unavailability of constituent coordination must be a syntactic matter.
The same argument extends to the question of ( 53).If the formation of the generalizedquantifier level JP and QP is not possible even for such an innocent-looking case, that probably has to do with what syntactic mechanisms are available.At this point I cannot pinpoint any syntactically disastrous effects that would emerge if (53b) were allowed to co-exist with the various possibilities for ellipsis.However, the data discussed in this paper will offer new grounds for hypothesis testing.

Negative concord
Finally, we come back to the strict vs. non-strict negative concord facts observed in 2.5.To attack them, we must first know how NC works in Hungarian.Szabolcsi (2016) proposes a unified account of the hybrid negative concord data in ( 23)-( 24), as follows.Senki 'n-one' is an existential that must occur within the immediate scope of clause-mate semantic negation.The negation may be contributed by the Neg head nem 'not'.The requisite scope relation automatically holds when senki is in postverbal position, cf.(25).When senki occurs preverbally, as in ( 23), it is in the specifier of the Neg head nem.It moves there by remnant movement, by itself or possibly along with another NCI or a minimizer like egy szemhunyás 'a wink'.Remnant movement reconstructs, so the moved item or sequence continues to be in the scope of nem.The structure in (54) contains a phonetically null operator O ALT .Szabolcsi ( 2016) follows Chierchia's (2013) explanation of why negative polarity and negative concord items must be within the immediate scope of a suitable decreasing operator (here: negation).The explanation is that these items have obligatorily active alternatives, which by definition must be exhaustified.O ALT is an exhaustifier.The exhaustification of positive alternatives leads to a contradiction, but the exhaustification of negated alternatives is innocuous.See Chierchia (2013) for details.Crucially, Szabolcsi (2016) also adopts, and adapts, Chierchia's analysis of non-strict, Italian-style negative concord.Chierchia argues that Italian has a phonetically null functional head that he calls NEG that has two critical properties: (i) it must agree with an NCI in its specifier, (ii) it is capable of invoking a contentful but abstract (disembodied) negation, ¬ at the edge of its projection.Preverbal nessuno 'n-one' sits in the specifier of null NEG, and the contradiction O ALT would produce is averted by the disembodied negation, ¬.Szabolcsi (2016) argues that in examples like (32), Hungarian sem 'nor' is an overt counterpart of Chierchia's NEG, and so a functional head above TP. (55) Senki sem aludt.'No one slept.'Non-strict NC Abstract ¬ right above SemP-above-TP sem 'nor' needs a focus-accented XP in its spec, and to be in the immediate scope of ¬ senki 'n-one', existential, NCI One aspect of this analysis that is important to us is that the sem 'nor' that follows its host is now established as a functional head on the clausal spine.Szabolcsi (2016) identifies sem 'nor' as the negative concord counterpart of is 'too'.Both is and sem are focus-sensitive and therefore attract focus-accented elements to their specifiers (not restricted to NCIs).
We can now turn to the negative concord structures that involve reiterations.The reiterated construction in (56) represents non-strict negative concord, because it is a conjunction of two clauses, with ellipsis in the first.Each of those clauses contains the functional head Sem with a focus-accented DP in its specifier and an abstract negation, cf. ( 55 (57a) can be derived by across-the-board movement of the verb from sem Kati alud-, sem (pedig) Mari alud-, adjoining it to T, with the subsequent merging of nem 'not'.In (57b), those steps are followed by remnant movement of sem Kati, sem (pedig) Mari to the specifier of nem.
The two particles sem ultimately compose the same meanings, in two different ways.The strict/non-strict distinction is a consequence of the structures.In particular, the nonstrict NC property is due to the fact that the sem that follows its host is a counterpart of Chierchia's NEG head that is capable of invoking an abstract negation.The sem that is instantiated preceding its host on every member of a tuple is an existential quantifier that requires to be in the scope of negation but is not capable of pulling one out of thin air; hence the need for overt nem, a hallmark of strict negative concord.
In sum, the negative concord facts square with the analyses of the two constructions discussed in Sections 3 and 4.
As a supplement, I comment on strict-NC iterations that include the verb (i.e.where the verb is not ATB extracted, cf. ( 57)).These are notoriously complicated and difficult to account for in Russian, for example (e.g.Tiskin 2017).In Hungarian, pattern (58) without nem 'not' only exists as a frozen idiomatic expression that preserves a stage of the Jespersen cycle from more than 500 years ago (É.Balusu (2017) proposes that the Telugu particle -VV (harmonizing long vowel) primarily forms polarity sensitive expressions with wh-pronouns, and the availability of the universal reading is a result of subsequent exhaustification (limited to eppuD-uu in Telugu).If the same analysis can be extended to Japanese and the generally available universal reading for wh+mo is obtained by exhaustification, then it may be possible to maintain that both -VV and -mo are heads on the clausal spine that have the ability to accommodate wh-pronouns in their specifiers.That would in turn provide a link to the analysis of the Hungarian string senki sem, analyzed with senki in the specifier of the clausal head sem; see the discussion of ( 55 It remains an open question why Telugu -VV and Japanese -mo combine with bare whpronouns and Hungarian is/sem with ones that have (uninterpreted) existential particles.
(Note that senki sem and valaki/akárki is are strings, not single "quantifier words".)Szabolcsi ( 2017) proposes a semantics for Hungarian is/sem that subsumes the additive, scalar, negative polarity and free choice readings.In brief, is/sem seeks out a set of alternatives induced by its host and activates them.These may be focus alternatives or subdomain/scalar alternatives.Activation in the sense of Chierchia (2013) entails that the alternatives must be incorporated into the meaning of the sentence by way of some strengthening (e.g.exhaustification) mechanism, typically with the assistance of further, overt or covert operators.According to Szabolcsi (2017), English too and either fall under the same generalizations, although they apparently specialize in working with focus-alternatives.This is in the same spirit as Balusu (2017), although the latter only investigated combinations with wh-pronouns.
With this last ingredient added and generalized cross-linguistically, it appears that the apparently contradictory properties of -mo and -VV can be reconciled.

A survey of Bosnian, French, Japanese, Mandarin, Persian, Russian, Sinhala, Telugu and Turkish
The present paper cannot undertake a thorough descriptive and theoretical investigation of the questions raised above, but as a starting point, this subsection presents the results of a small cross-linguistic survey.The data establish the prevalence of two distinct constructions, even though cross-linguistically, the distinction does not track the relative order of the particles and their hosts.
The data were solicited from semanticists and syntacticians. 20The survey did not ask them to commit to syntactic or semantic analyses, although sometimes I was able to rely on their closely related publications; see especially Kobuchi-Philip (2009); Slade (2011); but dispreferred in comparison with John, Mary and Bill.For the same reason, the single and may indicate the completion of the list, but that is probably a Gricean inference.The Japanese and Bosnian data can be interpreted in the same way, but caution is in order.Almost all the languages in the sample have one or more 'either_or' constructions that seem to exemplify quantifier-phrase internal particles.As above, whether the particle precedes or follows its host is not cross-linguistically consistent.The diagnostic properties are the following: (74) Quantifier-phrase internal Or_Or a.The particle and its host must be part of a tuple.b1.The optional connective, if it exists, is typically a specialized item that has contrastive or adversative uses, similarly to Hung.pedig discussed in the paper.It occurs only before the last junct and indicates that the list is complete.b2.Alternatively, the optional connective is an exclusive disjunction particle and can occur between all the juncts.c.The same particle often forms an indefinite (existential quantifier word) with a wh-pronoun.(The epistemic specificity properties are not examined here.) Consider the following schematic data in Table 2; comments follow below.The optional connective often intervenes between the particle and its host, indicated by a caret (^) in the column for junct Z. 22 22 Russian uses two distinct contrastive "connectives", a vs. zhe (only zhe intervenes between the particle and the host).M. Esipova (p.c.) comments that a goes with conjunctive (to) constructions (all juncts have to be true), and zhe with disjunctive ones.On the other hand, i_i and negative concord ni_ni are not contrastive, so they are not compatible with either a or zhe.Usually, medial 'or' is inclusive and reiterated 'or_or' is exclusive/exhaustive, but there are two exceptions that show that the correlation is not necessary.Sinhala X-hari Y-hari and Telugu X-oo Y-oo are inclusive; Telugu X leeda Y 'X if-not Y' is exclusive/exhaustive. Turkish and Persian in general do not build quantifier words from particles and whpronouns, as noted above; in Bosnian and Russian, only some particles fail to participate.
Note that Turkish dA leads a double life as an additive clausal head (Table 1) and as a "contrastive" connective (Table 2), calling for a semantic or pragmatic unification.
There are further examples of the "quantifier-phrase internal" construction, although in fewer languages in my sample.Syntactically, they come from the same mold as the disjunctions in Table 2: tuples are necessary; the optional connective is the same "contrastive" item that occurs in Table 2 and indicates the completion of the list; quantifier-word formation is possible.
At least Russian, Turkish, and Hungarian have two "alternation" constructions, whose semantics is analyzed in Esipova (2016;2017). 23The first one involves particles, see Table 3.The second one involves wh-words.Lipták (2001;p.c.) suggests that it might be possible to bring them into the fold by postulating null particles; I will not pursue an analysis here.But notice the same general pattern.See Table 4.
Table 5 recaps the discussion of Persian ham_ham and Turkish hem_hem in Section 6.1.
French and other Romance languages have reiterating constructions that may represent the two types, but the analysis is not straightforward.See Table 6.
Finally, we turn to negative concord, so far as it involves specialized particles and/or optional connectives.Recall that Hungarian sem has both clausal head and quantifierphrase internal versions, each of which solidly patterns with the other representatives of ≈ sometimes visited by American and sometimes by German tourists … people were happy.' its type.Given this duality, it is not surprising that both types seem to be represented in the data, based on the optional particles, for example.But the properties are fairly mixed, and so it would be rash to attempt labels at this point.See Table 7.
Seeing how difficult 'nor_nor' type negative concord is to analyze in many languages, it is unsurprising but at the same time somewhat disappointing that our diagnostics do not straightforwardly point to one analysis or another.But they probably provide some useful starting points.

Conclusion
This paper argued that there exists a cross-linguistically prevalent distinction between two types of quantifier particles.One type is a head on the clausal spine, the other is an uninterpreted pointer to an unpronounced but meaningful propositional quantifier.Highly regular linear order with respect to the host and the availability of a full slew of corresponding quantifier words make the two types straightforward to study in Hungarian; the data and discussion in Section 6 shows that many other languages exhibit distinctions that are consistent with the Hungarian ones.Although this research has benefited from the existence of important syntactic and/or semantic literature on some of those languages, both the syntax of reiterated constructions and the internal syntax of the quantifier words at hand have received scarce attention so far.It is hoped that this report will contribute to changing that.
adapted this proposal to Hungarian, identifying the sem in (1) as an overt where mind 'all' vagy 'or' akár 'whether' sem 'nor' (4) a. Vagy a hó esik, vagy a szél fúj, vagy a gyerek nyűgös.or the snow falls or the wind blows or the child cranky 'Either the snow is falling, or the wind is blowing, or the child is cranky.' b.Vagy a hó esett, vagy az eső esett.or the snow fell or the rain fell 'Either the snow or the rain was falling.'
hallottés Mari olvasott minden Nobel-díjas-ról.'Peti heard and Mari read about every Nobelist.' Mind egy magasmind hat alacsony gyerek-et meghívtam.all one tall all six short child-acc invited-1sg 'I invited both one tall and six short children.' b.Meghívtam mind egy magasmind hat alacsony gyerek-et.invitedSem a jobb--sem a bal-kezes gyerekek nem sírt-ak.nor the right-nor the left-handed child-pl not cried-3pl 'Neither the right-nor the left-handed children cried.' b.Nem sírtak sem a jobb--sem a bal-kezes gyerek-ek.not cried-pl nor the right-nor the left-handed child-pl four blue vagy minden lány-nak hat zöld golyót.or every girl-dat six green marble-acc 'Give either every boy four blue __ or every girl six green marbles.'These examples most likely derive from propositional coordination and quantification.The question arises whether the simpler ones involve DP-level (generalized quantifier) coordination and quantification, e.g.: or every boy-DAT four blue vagy minden lány-nak hat ZÖLD golyót.or every girl-DAT six green marble-ACC 'Give either every boy four blue __ or every girl six green marbles.'These examples most likely derive from propositional coordination and quantification.The question arises whether the simpler ones involve DP-level (generalized quantifier) coordination and quantification, e.g.: (53) a. Vagy sok fiú, vagy kevés lány aludt.or many boy or few girl slept 'Either many boys or few girls slept.' b.
nem aludt.'No one slept.'Strict NC nem 'not', ¬ senki 'n-one', existential, NCI people were happy 'At each ski resort that was… a.≈ alternately visited by American and German tourists b.
Hungarian is 'too' is historically a reduction of és 'and'.(És and is have not been interchangeable for many centuries.)I do not believe that the analysis should pursue this connection.As Szabolcsi (2017) points out, is also has an indispensable role in productively building negative polarity and free choice items.It is difficult to imagine that the J head or the conjunction 'and' has any relevance there.Is and és will thus be kept apart.The relation between these items, in Hungarian and cross-linguistically, is left for future research.
4In many languages, the particle 'too' and the connective 'and' are homophonous, e.g.Russian i, Romanian şi.
All three examples below mean 'No one slept'.
I observe that the two types of reiterated sem construction differ in that the "particle precedes host" one builds a strict NC expression, and the "particle follows host" one builds a non-strict one.(26) Sem Kati, sem Mari *(nem) aludt.pre-V, strict NC, nor Kati nor Mari not slept requires nem (27) Kati sem, Mari sem (*nem) aludt.pre-V, non-strict NC, Kati nor Mari nor not slept rejects nem (28) Nem aludt sem K, sem M / K sem, M sem.post-V, strict/non-strict, not slept nor K nor M K nor M nor require nem NEG for SemP.Alternatively, (ii) Is and Sem themselves are functional heads in the clausal spine.Some reasons to prefer (ii) are as follows.First, phrase-internal operator particles invariably precede their sisters in Hungarian:(31) a. csak Mari 'only Mari', vagy tíz 'some ten = ca.10', majdnem tíz 'almost 10' b. minden fiú 'every boy', mindenki 'everyone'  c. mind Kati, mind Mari 'both K and M', vagy Kati, vagy Mari 'either K or M' ).It effectively says, 'Kati didn't sleep and likewise Mari didn't sleep'.The reiterated construction in (57) represents strict negative concord.Sem Kati, sem Mari being analogous to senki 'n-one', (57) contains one large existential quantifier over propositions, within the scope of nem 'not'.It effectively says, 'It is not the case that there is a true proposition in the set {Kati slept, Mari slept}'.