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Kevin PatersonSchool of PsychologyUniversity of Leicester

ESSLLI 2010

Quantifier Processing: Acquisition of Quantification

Kevin Paterson

Lecture 5 topics:o Quantifier Spreadingo Strong & weak quantifierso Focusing adverbso Quantificational anaphorao Quantifier scope ambiguity

Quantifier Spreadingo Widely observed that children make non-adult

errors when evaluating the meaning of statements that contain a universal quantifier.

o Errors appear to be restricted to universal quantifiers (but see section on focusing adverbs).

o Observed from at least 3 years until 7 years.

(Brooks & Braine, 1996; Bucci, 1978; Crain, 2000; Crain et al., 1994, 1996; Donaldson & Lloyd, 1974; Drozd, 2001; Drozd & van Loosbroek, 1998; Geurts, 2003; Inhelder & Piaget, 1959,1964; Philip, 1995; Philip & Lynch, 1999; Philip & Takahashi, 1991; Philip &Verrips 1994; Smith 1979, 1980).

Quantifier Spreading

Are all of the circles blue?

Child: No, there are two blue squares.

(Inhelder & Piaget,, 1959, see Geurts, 2003).

Quantifier Spreading

Are all of the children riding a bike?

(e.g., Donaldson & Lloyd, 1974; Philip &Takahashi 1991).

Child response: No. No-one is riding that bike.

Quantifier Spreading

Are all of the girls holding an umbrella?

(e.g., Philip &Verrips 1994).

Child response: No. The man is holding one too.

Quantifier Spreadingo Error widely attributed to children employing a

“symmetrical” reading, where they anticipate one-to-one correspondence between X and Y in statements of the form “Every X is a Y”.

o Essentially same as illicit conversion observed in (adults) syllogistic reading (e.g., Newstead, 1989).

o “All X are Y” is taken to mean that “All Y are X”.

Quantifier Spreadingo Drozd (2001) and Geurts (2003) argue that errors are due

to children misconstruing universal quantifiers as “weak”.o Geurts (2003): faulty mapping between syntactic and

semantic representations.o As a consequence, children prone to construing universals

as weak quantifiers and consequently often assign non-relational readings.

Strong & Weak Quantifiers.o Milsark (1977) argued for broad distinction between

determiners that encompasses well-known distinction between definite and indefinite expressions.

o “Strong” determiners are inherently relational but “weak” determiners aren’t.

o “Most X are Y” means that most individuals in given set of X’s are Ys.

o This also presuppose that set X is non-empty.

Strong & Weak Quantifiers.o Milsark (1977) used existential there-sentences as the

litmus test of this distinction, based on the argument that because strong determiners already presuppose existence, this will create a tautology that renders sentences unacceptable.

1. There is a boy in the garden.2. There are some boys in the garden.3. There are many boys in the garden.4. #There is the boy in the garden.5. #There is every boy in the garden.6. #There are most boys in the garden.

Strong & Weak Quantifierso Do children lack “strong” readings?o Can assess this by examining judgements about the

acceptability of quantifiers in there-sentences.o Recent data collected by Matt Passby at the University of

Leicester suggests that children (age 4-7 years) have difficulty rejecting there-sentences that contain “strong” quantifiers.

o See also Hsiang-Hua, Miller, & Schmitt (2004)

Strong & Weak Quantifiers

Focusing Adverbso Children also produce non-adult responses when

evaluating the meaning of sentences containing focus-sensitive particles such as “only”.

o Crain et al. (1996).― Children make errors by misinterpreting sentences with

preverbal “only” as having the same meaning as sentences with pre-subject “only”. Only the fireman is holding a hose. The fireman is only holding a hose.

― Children lack knowledge of syntactic restrictions.

Focusing AdverbsThe fireman is holding a hose.

Only the fireman is holding a hose.

The fireman is only holding a hose.

Children primarily make errors by failing to take account of contrast information.

Paterson et al. (2003)

Focusing Adverbs

Pollard & Paterson: The case of “even”.

Only the girl is holding a balloon.

The girl is only holding a balloon.

Even the girl is holding a balloon.

The girl is even holding a balloon.

“Even” is additive focus particle and requires that what is true of contrast set is true for focus set.

Evidently, children (and adults) have difficulty in evaluating meaning of “even”.

Focusing Adverbso Crain et al. (1996): Semantic Subset Principle

― Children initially adopt interpretation of pre-verbal quantifier as ranging over entire VP rather than just the direct object, because former interpretation is truer is narrowest set of circumstances.

The fireman is only holding a hose.

As children encounter situations in which initial hypothesis is incorrect, they acquire evidence for alternative analyses.

The woman is walking a dog.

The woman is only walking a dog.

The woman is walking only a dog.

Children and adults performance consistent with only ranging over VP.

Thus evidence relating to Semantic Subset Principle remains unclear (but see Musolino, 2006)

Paterson et al. (2006)Notley et al. (2009)

Focusing Adverbs

Quantificational Anaphorao Research on adults indicates a preference for the subset

reading of following ambiguity: There were six ships on the horizon. Three ships sank.

o Considerable evidence that children have difficulty in processing anaphora (e.g., Karmiloff-Smith, 1980).

o How do children deal with this ambiguity?

Wijnen, Roeper, & van der Meulen (2004).

Here’s a playground. It’s great to do all kinds of funny things when you’re out in

the playground, like swinging, making a sand castle or climbing on the monkey bars.

There are some kids playing in the sand box. Are two upside down?

o Children very likely (>80%) to say “yes” for picture of 2 kids doing handstands in sand box, compared to when 2 kids are doing handstands outside of box, or 2 adults are doing handstands.

Quantificational Anaphora

Mousoulidou & Paterson

Three cats were on a wall. Two (other, of the) cats caught a mouse.

Presuppositional Picture Existential Picture

Quantificational Anaphora

Experiment 1 Children and Adult's Existential Responses

59%68%70%

100%

0%

27%

0%

20%

40%

60%

80%

100%

UnambiguouslyExistential

Ambiguous UnambiguouslyPresuppositional

Sentence Type

ChildrenAdults

Quantificational Anaphorao Clear discrepancy in findings.o Wijnen et al. (2004) finding good evidence for discourse

integration – although >80% responses of this type exceeds normal adult performance.

o Mousoulidou & Paterson find none!o Clearly further work is needed to clarify children’s

capabilities and acquisition of processing strategies.

Quantifier Scope Ambiguityo Recall ambiguity nature of ambiguity.

“A boy kissed every girl.” Surface scope interpretation: one boy, many girls. ∃ x [ boy (x) & y [ girl (y) kissed (x,y) ] ]∀ → Inverse scope interpretation: many boys, many girls. ∀ x [ girl (x) & y [ boy (y) & kissed (x,y) ] ]∃

o How do children process this ambiguity?o How are alternative analyses acquired?

“Donald didn’t’ find two guys.”

1. It is not the case that Donald found two guys.

2. There are two guys Donald didn’t find.

o. Adults can assign either reading and respond to pictures appropriately.

o. Children have difficulty in reaching inverse scope reading of sentences.

Lidz & Musolino (2003)

Quantifier Scope Ambiguity

Scalar Implicatureo Argued that children produce non-adult patterns of scalar

implicature that, unlike adults, tend to be logical in nature (Noveck, 2004; see also Huang & Snedeker, 2009).

­ “Some boys kissed a girl”.­ In terms of logic, true if “all boys kissed a girl”.­ However, licences implicature that “not all boys kissed a girl”.

o Whereas 8-10 year olds will accept that “some x” can imply “all x”, adults are more circumspect (Noveck, 2001).

o Considerable evidence that children have difficulty in computing scalar implicature (Feeney et al., 2004; Pouscoulous et al., 2007; Papafragou & Musolino, 2003).

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Conclusionso Considerable evidence that young children assign non-adult

interpretations to quantifiers, including:- Full understanding of meaning of universal quantifiers

and focusing adverbs- Distinction between strong & weaker determiners- Inverse scope reading of quantifier scope ambiguity- Evidence for age differences in processing of scalar

implicature.o Evidently children must acquire semantic representations

for quantifiers over considerable period of time.

References• Brooks, P., & Braine, M. (1996). What do children know about the universal

quantifiers all and each? Cognition, 60, 235–268.• Bucci, W. (1978). The interpretation of universal affirmative propositions: a

developmental study. Cognition, 6, 55–77.• Crain, S., Ni, W., & Conway, L. (1994). Learning, parsing and modularity. In C. Clifton,

L. Frazier, & K. Rayner (Eds.), Perspectives on sentence processing. Hillsdale, NJ: Lawrence Erlbaum.

• Crain, S., & Thornton, R. (1998). Investigations in universal grammar: a guide to research on the acquisition of syntax and semantics. Cambridge, MA: MIT Press.

• Crain, S., Thornton, R., Boster, C., Conway, L., Lillo-Martin, D., & Woodams, E. (1996). Quantification without qualification. Language Acquisition, 5, 83–153.

• Donaldson, M., & Lloyd, P. (1974). Sentences and situations: children’s judgments of match and mismatch. In F. Bresson (Ed.), Problemes actuels en psycholinguistique. Paris: Centre National de Recherche Scientifique.

References• Drozd, K. (2001). Children’s weak interpretations of universally quantified questions.

In M. Bowerman & S.C. Levinson (Eds.), Language Acquisition and Conceptual Development. Cambridge University Press: Cambridge. pp. 340–376.

• Drozd, K., & van Loosbroek, E (1998). Dutch children’s interpretations of focus particle constructions. Poster presented at the 23rd annual Boston University Conference on Language Development, Boston, MA.

• Feeney, A., Scrafton, S., Duckworth, A., & Handley, S. J. (2004). The story of some: Everyday pragmatic inferences by children and adults. Canadian Journal of Experimental Psychology, 58, 121–132.

• Filik, R., Paterson, K. B., & Liversedge, S. P. (2009). The influence of only and even on on-line semantic interpretation. Psychonomic Bulletin & Review, 16 678-683.

• Freeman, N. H., & Stedmon, J. A. (1986). How children deal with natural language quantification. In I. Kurcz, G. W. Shugar, & J. H. Danks (Eds.), Knowledge and language. Amsterdam: Elsevier.

References• Huang, Y. T., Snedeker, J. (2009). Semantic Meaning and Pragmatic Interpretation in

5-Year-Olds: Evidence From Real-Time Spoken Language Comprehension, Developmental Psychology, 45, 1723-1739.

• Hsiang-Hua, C., Miller, K., & Schmitt, C. (2004). Acquisition of the strong and weak quantifiers in’ there’-existentials. Poster presented at Generative Approach to Language Acquisition North America conference (GALANA 2004). Inhelder, B., & Piaget, J. (1964). The early growth of logic in the child. London: Routledge.

• Karmiloff-Smith, A. (1980) "Psychological processes underlying pronominalization and non-pronominalization in children's connected discourse". In J.Kreiman & E.Ojedo (Eds.) Papers from the Parasession on Pronouns and Anaphora. Chicago: Chicago Linguistics Society, 231-250.

• Lidz, J., & Musolino, J. (2002). Children’s command of quantification. Cognition, 84, 113–154.

• Neimark, E. D., & Chapman, R. H. (1975). Development of the comprehension of logical quantifiers. In R. J. Falmagne (Ed.), Reasoning: representation and process in children and adults. Hillsdale, NJ: Erlbaum.

References• Noveck, I. (2001). When children are more logical than adults: experimental

investigations of scalar implicature. Cognition, 78, 165–188. • Musolino, J. (2006). On the semantics of the subset principle. Language Learning and

Development, 2, 195-218.• Papafragou, A., & Musolino, J. (2002). Scalar implicatures: Experiments at the

semantics- pragmatics interface, Cognition, 86, 253–282. • Paterson, K. B., Liversedge, S. P., Rowland, C., & Filik, R. (2003). Children’s

comprehension of sentences with focus particles. Cognition, 89, 263-294. • Paterson, K. B., Liversedge, S. P., White, D., Filik, R., & Jaz, K. (2006). Children's

interpretation of ambiguous focus in sentences with "only". Language Acquisition, 13, 253-284.

• Philip, W., & Lynch, E. (1999). Felicity, relevance, and acquisition of the grammar of every and only. In S. C. Howell, S. A. Fish, & T. Keith-Lucas (Eds.), Proceedings of the 24th annual Boston University conference on language development, Somerville, MA: Cascadilla Press.

References• Philip, W., & Takahashi, M. (1991). Quantifier spreading in the acquisition of every. In

T. L. Maxfield, & B. Plunkett (Eds.), University of Massachusetts occasional papers: papers in the acquisition of WH. Amherst, MA: GLSA.

• Philip, W. & M. Verrips (1994) Dutch preschoolers’ elke. Paper presented at the 1994 Boston University Conference on Language Development. Pouscoulous, N., Noveck, I. A., Politzer, G., & Bastide, A. (2007). A developmental investigation of processing costs in implicature production. Language Acquisition, 14, 347–375.

• Smith, C.L. (1979). Children’s understanding of natural language hierarchies. Journal of Experimental Child Psychology 27, 437-458.

• Smith, C.L. (1980) Quantifiers and question answering in young children. Journal of Experimental Child Psychology 30, 191-205.

• Wijnen, F., Roeper, T., & van der Meulen, H. (2004). Discourse binding: Does it begin with nominal ellipsis? Proceedings of GALA 2003. Utrecht: LOT.