Background • Determiners are words like every/some/most • They express a relation between two sets An investigation of • Conservativity is a property that such a Conservativity relation may or may not have Tim Hunter Anastasia Conroy Background Research Question • Descriptive typological fact: Every determiner attested in natural languages is Do children carry expectations of conservative (Barwise and Cooper, 1981) conservativity (a typological generalization) when learning determiners? • Widely known in semantics but most standard theories predict conservative and nonconservative determiners equally likely (Montague 1974, Heim and Kratzer 1998) Hypotheses • Hypothesis 1: Children’s learning of determiners is constrained to consider only conservative meanings • Hypothesis 2: Children’s learning of determiners is not constrained to consider only conservative meanings
Theoretical details What is conservativity? • A relation R between sets is conservative iff – R(X)(Y) ⇔ R(X)(X ∩ Y) John is/are brown likes Mary • Example: “Every dog is brown” every dog(s ) – Truth condition: D ⊆ B some • Intuitively: most – It is OK to limit your attention to the dogs – Brown things that aren’t dogs are irrelevant • A determiner expresses a relation • Formally: between the sets denoted by its internal D ⊆ B ⇔ D ⊆ (D ∩ B) – – Every dog is brown ⇔ Every dog is a brown dog and external arguments What is conservativity? What is conservativity? • A relation R between sets is conservative iff • A relation R between sets is conservative iff – R(X)(Y) ⇔ R(X)(X ∩ Y) – R(X)(Y) ⇔ R(X)(X ∩ Y) • Example: “Some dog is brown” • Example: “Equi dogs are brown” – Truth condition: D ∩ B ≠ ∅ – Truth condition: |D| = |B| • Intuitively: • Intuitively: – It is not OK to limit your attention to the dogs – It is OK to limit your attention to the dogs – Brown things that aren’t dogs are relevant – Brown things that aren’t dogs are irrelevant • Formally: • Formally: D ∩ B ≠ ∅ ⇔ D ∩ (D ∩ B) ≠ ∅ |D| = |B| ⇔ |D| = | D ∩ B | – – – Some dog is brown ⇔ – Equi dogs are brown ⇔ Some dog is a brown Equi dogs are brown dog dogs Previous Research on Novel word learning • Most research on children’s learning of novel words focuses on nouns and verbs • Few studies on the acquisition of determiner meanings • Studies that investigate children’s knowledge of determiner meanings (Philip and Drozd) , are silent with respect to conservativity
Research Question Desiderata of experiment • Experiment must test young children • Novel determiner word Do children carry expectations of • Novel determiner meaning to avoid conservativity (a typological mapping to known determiner generalization) when learning • Way to expose children to meanings of a determiners? conservative and non conservative determiner • The two meanings must be cognitively similar Design Our novel determiner: ‘gleeb’ • Gleeb [girls] [like pizza] • Picky puppet task, accessible to young • Conservative meaning: children and fun – ``not all girls like pizza’’ – ``at least one girl dislikes pizza’’ • Novel determiner word, and meaning – Ignoring pizza-likers who aren’t girls is OK • Create cards that depict a true instance of • Non conservative meaning: – ``not all pizza likers are girls’’ determiner meaning, visually available to – ``at least one non-girl likes pizza’’ kids – Ignoring pizza-likers who aren’t girls is not OK • Meanings are direct of inverses of each • Recognising whether the required condition holds other should be equally easy on either meaning Picky Puppet • Koala likes some things, but not others. He only likes things that are yellow. Can you help us put cards into piles?
Modify the Picky Puppet • The picky puppet task doesn’t work because we are teaching children a new word • Modify the task to teach new words by giving examples Example/Warm up • Koala likes some cards but not others. Can you help me figure out what kind of cards he likes? He said he only likes cards that are splurfy Experimental design: picky puppet • For this experiment, we want children to sort cards with scenes • Each scene is either true on the meaning of the determiner being taught or not
Cards Cards • Need cards that can represent determiner • Beach/Park meanings • Boys/Girls • “Gleeb girls are on the beach” • To make things clear, being a girl and being on the beach need to be clearly binary Cards Conservative true • Gleeb girls are on the beach • “Gleeb [girls] [are on the beach]” • Nonconservative false • Conservative version: – Not all girls are on the beach • Nonconservative version: – Not all beach-goers are girls Nonconservative true Design • Gleeb girls are on the beach • Each child is exposed to only one novel determiner • Conservative false • How does an experimental session work? – Warm ups (3 items) – Training Phase (5 cards) – Testing Phase (5 cards)
Scoring Method • An experimenter recorded which pile the • 2 conditions: children were taught that the child placed the target card into puppet liked cards consistent either with the conservative or nonconservative • Children were scored as ‘correct’ on that meaning of the determiner card if the pile corresponded to the determiner meaning taught in training • Same stimuli cards and test sentence was phase used across conditions • Children randomly assigned to condition Participants Hypotheses • Hypothesis 1: Children’s learning of determiners is • 20 children constrained to consider only conservative • 4;5 – 5;6 meanings • Mean 5;0 • Prediction: children should be able to learn a novel conservative quantifier, but not a novel nonconservative one • By condition: • Hypothesis 2: Children’s learning of determiners is – Conservative: 4;5 – 5;5, mean 4;11 not constrained to consider only conservative – Nonconservative: 4;11 – 5;3, mean 5;1 meanings • Prediction: children should do equally well at learning novel conservative determiners and novel nonconservative determiners Results Results Results Non- Non- Conservative Conservative conservative conservative Number of Number of 4.1 3.1 4.1 3.1 cards correctly cards correctly sorted sorted out of 5 out of 5 Not different Percentage Greater than 10% 50% from chance 100% chance (2.5) (2.5) p = correctly 0.07 p < 0.001 sorted p > 0.17
Results summary Research Question Conservative • Hypothesis 1: Children’s learning of determiners is constrained to consider only conservative Number of cards properly sorted meanings Out of 5 • Prediction: children should do be able to learn a 4.1 novel conservative quantifier, but not a novel Greater than chance (2.5) nonconservative one p < 0.001 • Hypothesis 2: Children’s learning of determiners is • Kids do learn the novel conservative not constrained to consider only conservative determiner meanings • No evidence of learning nonconservative • Prediction: children should do equally well at version learning novel conservative determiners and novel • Very early mirroring of the typological nonconservative determiners generalisation Who learned the nonconservative Who learned the nonconservative one? one? • One child ‘learned’ the nonconservative • “Gleeb girls are on the beach” determiner (10% perfect) • Target (nonconservative) meaning: • 4;11 – not all beach-goers are girls • What did she do? – at least one boy is on the beach • She told the puppet he was confused, because he thought that the boys were girls • Since the puppet had girls/boys reversed, this is consistent with “gleeb” meaning “some” let’s look at how this indicates the learning of a conservative determiner meaning… • Therefore, a conservative determiner was learnt Conclusion • No evidence for learning of the nonconservative determiner meaning in these subjects • Early learning of the constraint is still a possible explanation
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