# Event pluralities - Day 2 - Distributive c ... The distributive relation In ﬁrst order logic, a...

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Event pluralities - Day 2 Distributive configurations

Patricia Cabredo Hofherr1 Lucia M. Tovena2

1UMR 7023 CNRS & Université Paris 8

2Université Sorbonne Paris Cité – Paris VII

ESSLLI 2015 Barcelona

Outline

1 Introducing distributivity Basic notions and empirical issues Refine the terminology

2 A typology of distributive configurations Features and combinations Type 1 Distrib (whole–unit) Marking distributivity

3 Type 2 Cumul (Whole–whole) Instances and properties Identity issues About sendos

4 Type 3 Ratio (Unit–unit) Introducing ratios Types of ratios

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 2 / 87

Introducing distributivity

Outline

1 Introducing distributivity Basic notions and empirical issues Refine the terminology

2 A typology of distributive configurations Features and combinations Type 1 Distrib (whole–unit) Marking distributivity

3 Type 2 Cumul (Whole–whole) Instances and properties Identity issues About sendos

4 Type 3 Ratio (Unit–unit) Introducing ratios Types of ratios

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 3 / 87

Introducing distributivity Basic notions and empirical issues

Readings

Consider the girls in (1). The sentence has two readings.

(1) The girls carried a box

COLLECTIVE READING: – the nominal in subject position is interpreted referentially – one situation where the girls as a group carried a box. DISTRIBUTIVE READING: – the nominal in subject position is interpreted referentially, but it is partitioned – possible multiplication effect on the nominal in object position – one situation where each individual girl carried a box (the same or not).

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 4 / 87

Introducing distributivity Basic notions and empirical issues

Readings

Consider sentence (1) and the additional dimension of events. – The collective reading a single carrying event – The distributive reading many events of carrying. CUMULATIVE READING: cf. (2)

(2) The girls carried the boxes

– the nominals in subject and object positions are both plural and are interpreted referentially and scopelessly – the sentence is not specific about the number of subevents and of participants in each of them, but implies some subdistribution resulting in a plurality of events

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 5 / 87

Introducing distributivity Basic notions and empirical issues

Readings

The trademark of the cumulative reading is that there is no multiplication of the nominals, but only their partition. Under the cumulative reading of (3), there are – all in all 3 girls – all in all 2 biscuits

(3) Three girls ate two biscuits

The difference wrt the collective reading, is that the sentence describes more than one event.

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 6 / 87

Introducing distributivity Basic notions and empirical issues

Example

Consider the readings of (3) from the point of view of events Three girls ate two biscuits a. 3 events, each one of one girl eating two biscuits dist b. 2 events, each one of three girls sharing and eating one biscuit dist c. 1 event of three girls sharing and eating two biscuits coll d. n events, each one of p girls eating m biscuits, n≥2, p≤3 and m

Introducing distributivity Basic notions and empirical issues

Example

Simple examples of predicative distributivity

(4) a. The men are bearded b. The girls slept

(5) The green players scored

(6) Every child ran to the door

The predicates in (4) and (6) necessarily distribute over the individuals, not so for (5). There may be a single event in (6). Predicative distributivity will not be studied further.

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 8 / 87

Introducing distributivity Basic notions and empirical issues

Distributive configuration

A distributive reading can be forced by adding extra material. Sentence (7) is not ambiguous.

(7) Three girls ate two biscuits each

For a distributive reading to hold, there has to be a pairing of key and share (Choe, 1987), although these expressions do not have to be explicit. (not in all languages) sorting KEY is what forces the plural reading. Its function is similar to that of a wide scope taking expression in this respect. It defines the domain over which distribution takes place. distributed SHARE designates the entity/entities that are distributed, thus resembling a narrow scope taking expression.

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 9 / 87

Introducing distributivity Basic notions and empirical issues

Varieties of distributive configurations

quantified sorting key, e.g. English

(8) The girls ate two biscuits each

marked distributed share, e.g. Korean (Choe, 1987)

(9) emma-ka mum+NOM

ai- tul-eke child+PLU+to

phwungsen-hana-ssik-ul balloon+one+ssik+ACC

sacwu-essta bought Mommy bought each child a balloon

ratios

(10) James Bond eats two olives per martini.

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 10 / 87

Introducing distributivity Basic notions and empirical issues

Identification of the components

Is the role of sorting key and distributed share reflected in their morphological form, semantic function, or syntactic positions? E.g. the sorting key c-command the distributed share. E.g. the sorting key is the domain that gets exhaustified in the distribution. Distributed shares might get reused.

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 11 / 87

Introducing distributivity Basic notions and empirical issues

Identification of the components

Distributive readings involve event pluralities. Is event plurality directly expressed, or is it a consequence of a partitioned plural participant? Are these readings definable in terms of pairs of individuals, pairs individual(s)–event, other? Are events part of the share? Are events always part of the distribution, be it as share or as key?

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 12 / 87

Introducing distributivity Refine the terminology

Distributivity

Languages go to considerable lengths to express distributivity. The distributive dependency may be established between whole sums or individual units. Whole sums are the domains from which the arguments of the distributive relation gets their values, individual units provide such values. We define a term for each component. These terms are used to refer to the linguistic expressions and to their semantic values.

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 13 / 87

Introducing distributivity Refine the terminology

key

The KEY is the domain over which distribution takes place It is semantically plural It has a countable domain The expression is used referentially

(11) a. Les/ Ces filles ont mangé deux biscuits chacune (Fr.) the/these girls ate two biscuits

b. Cinq filles ont mangé deux biscuits chacune (Fr.) some/five girls ate two biscuits

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 14 / 87

Introducing distributivity Refine the terminology

k-unit

The K-UNIT is the singular/plural unit of the key that enters an instance of the distributive relation All the k-units have the same cardinality/size. By default, the single entities in the key domain are the units for the distribution, e.g. (11). Default can be overridden by explicit information, e.g. (12).

(12) The girls sang a song two by two

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 15 / 87

Introducing distributivity Refine the terminology

sh-unit

The SH-UNIT is the singular/plural entity that get paired with k-units A sh-unit is not referential All the sh-units have the same cardinality. Numerals in the DP indicate the cardinality/size of each sh-unit

(13) a. Three girls ate a biscuit (each) b. Three girls ate many/several biscuits each c. Three girls ate a little pasta (each)

The cardinality of the domain from which the sh-unit is taken, minimally is function of the cardinality of the key’s domain (modulo issues of reusability).

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 16 / 87

Introducing distributivity Refine the terminology

sum-share

The SUM-SHARE is the plural expression that introduces the domain out of which the sh-unit are taken

(14) Los estudiantes han ganado sendos premios (Es.) the students won a prize each

Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities ESSLLI 2015 17 / 87

Introducing distributivity Refine the terminology

The distributive relation

A distributive relation can be viewed as a dependency involving entities from the domains of its arguments, e.g. having pairs of k-unit–sh-unit in its domain. The cardinality of k-units and sh-units need not match, but each set is homogeneous The relation may specify the granularity of the