Quantifier Polarity and Verification Quantifier Polarity, Numerosity, and Verification Procedures: Experimental Explorations ¡ Yosef ¡Grodzinsky ¡ Safra ¡Brain ¡Research ¡Center, ¡ Language, ¡Logic ¡and ¡Cogni;on ¡Center, ¡ Cogni;ve ¡Science ¡ The ¡Hebrew ¡University ¡of ¡Jerusalem, ¡Israel ¡ ¡ Ins;tute ¡for ¡Neuroscience ¡and ¡Medicine ¡(INM-‑1) ¡ Forschungszentrum ¡Jülich, ¡Germany ¡ ¡ ¡ ¡ 1 Budapest Workshop, Oct. 2015 / 38
Quantifier Polarity and Verification Goal • To gain insights on quantification through the study of verification Specifically • To look for processing differences between quantifier types • To see whether processing differences between quantifier types extend to the non-linguistic domain • To see whether these differences interact with perceptual factors • To distinguish between syntactic and semantic accounts of quantifier polarity Experimental Paradigm • Verification with quantifiers and non-linguistic symbols 2 Budapest Workshop, Oct. 2015 / 38
Quantifier Polarity and Verification Multi-Modal Measurements • RT, fMRI signal intensity, errors in aphasia Take home message I (Modularity) • Linguistic processes are not affected by perceptual factors Take home message II (language vs. math) • Processing distinctions found in the linguistic domain do not extend to math Take home message III (syntax vs. semantics) • With some luck, the results may adjudicate between views on the “negative” aspect of negative quantifiers 3 Budapest Workshop, Oct. 2015 / 38
Verification in numerosity experiments Verification with degree quantifiers and numerosity-containing scenarios (1) a. Many of the dots are black b. Few of the dots are red J&C: • Decomposition Many dots are red Neg (many) dots are red • Fixed verification strategy Focus on larger set of objects in image Focus on larger set Just & Carpenter, JVLVB, 1971 4 Budapest Workshop, Oct. 2015 / 38
Properties of negative quantifiers Arguments for J&C’s view on negation in few : negative quantifiers license NPIs (2) a. * Many of the students ever NPI climbed Mount Everest b. Few of the students ever NPI climbed Mount Everest (3) a. * More-than-half of the students lifted a finger NPI to help me b. Less-than-half of the students lifted a finger NPI to help me negative quantifiers reverse entailment patterns (4) a. > ½ of the students worked hard ⇒ b. > ½ of the students worked (5) a. < ½ of the students worked hard ⇐ b. < ½ of the students worked 5 Budapest Workshop, Oct. 2015 Klima, 1964; Fauconier, 1975; Ladusaw, 1980 / 38
Verification in numerosity experiments questions • Is the processing effect specific to many/few ? • Is it specific to language? • If subjects focus on the larger set, does its (relative) size matter? • What is the source of the contrast? Structure of the experimental argument • Extend the linguistic domain – generality of effect • Set up parallel linguistic and non-linguistic instructions – specificity • Set up a verification paradigm where scenarios depict variable proportions – perceptual-linguistic interactions 6 Budapest Workshop, Oct. 2015 / 38
Verification in numerosity experiments Verification in the context of quantities: an example from numerical cognition a . Stream of habituation of r eference stimuli r =16 b . Occasional deviant c omparandum stimulus of varying numerosity C=8, … 32 different same different c. Instructions: indicate whether the fourth set was (global) - larger or smaller than the preceding ones - same as the preceding ones - different from the preceding ones d. Expectations: - Weber’s Law - no effect of instructions on performance: r>c=c<r 7 Budapest Workshop, Oct. 2015 Piazza et al., Neuron , 2003 / 38
Verification in numerosity experiments An example experiment r eference c omparanda different same % “different” judgment Results: - Performance is a non-monotone function of r / c proportion r=16 r=32 - Best fit to symmetrical curves is obtained after log compression - Similar σ across r -values Log C - no reported effect of instruction probes on performance 8 Budapest Workshop, Oct. 2015 Piazza et al., Neuron , 2003 / 38
Towards a new research program But instructions DO matter. So: • An attempt to reproduce J&C’s result with different quantifier pairs < many, few >; < more-than-half, less-than-half > An attempt to generalize to r/c proportions beyond 2:14, 14:2 • • A comparison with parallel non-linguistic instructions ( < , > ) • A comparison with parallel comparatives < there are more Xs than Ys, there are fewer Xs than Ys> • An attempt to provide a theoretical account of the effects – a syntactic vs. a semantic account 9 Budapest Workshop, Oct. 2015 / 38
The Parametric Proportion Paradigm An RT experiment with the Parametric Proportion Paradigm (PPP) (with Isabelle Deschamps, McGill. Galit Agmon & Yonatan Loewenstein, HUJI) POS : r More-than-half of the circles are blue c NEG: r c Less-than-half of the circles are yellow Auditory sentence 10 Budapest Workshop, Oct. 2015 Deschamps et al., Cognition , 2015 / 38
The Parametric Proportion Paradigm A non-verbal PPP: verification with symbols “Your task is to determine whether the instruction matches the scenario in the image, and do so as quickly as you can“ > > n n > n n L Image sequence 11 Budapest Workshop, Oct. 2015 Deschamps et al., Cognition , 2015 / 38
The Parametric Proportion Paradigm Factors in this design < No Non-linguistic: : > • Expression type Linguistic : Q of the circles are blue Li POS : More-than-half of the circles are blue Fixed Fi ed • Quantifier Type NEG: Less-than-half of the circles are yellow sta stand ndard POS : Many of the circles are blue and Monotonicity Degree NEG: Few of the circles are yellow • ˘ r= r=16 16 • Proportion and 4:16 8:16 12:16 16:16 24:16 34:16 46:16 Numerosity r=24 8:24 12:24 16:24 24:24 34:24 46:24 58:24 • Truth-value T More-than-half of the circles are blue F 12 Budapest Workshop, Oct. 2015 Deschamps et al., Cognition , 2015 / 38
PPP results – RT First PPP result: RTs abide by Weber’s Law 17 subjects X 2 quantifier types X 16 T/F = 544 trials RT RT #yellow #yellow RT RT #yellow #yellow Improvement of gaussian fit to mean RT fit on log compression (across all sentence types) 13 Budapest Workshop, Oct. 2015 Deschamps et al., Cognition , 2015 / 38
PPP results – RT Second PPP result: Polarity matters – RT functions Less than half of the circles are blue Splitting the previous graph: More than half of the circles are blue 17 subjects X 2 quantifiers X 16 RT T/F =272 trials NB: same results for r =24, and for the many / few contrast p<.023 #yellow/16 Blue 14 Budapest Workshop, Oct. 2015 See also: Cummins & Katsos, Cognition , 2010 / 38
PPP results – RT Polarity matters even in individual subjects! Less-than-half of the circles are blue More-than-half of the circles are blue 15 Budapest Workshop, Oct. 2015 / 38
PPP results – RT Third PPP result: verification with analogous symbols 272 trials RT NB: same results for r =24 #yellow/16 Blue 16 16 Budapest Workshop, Oct. 2015 / 38
PPP results – RT Fourth PPP result: Polarity X ±linguistic interaction Less than half of the circles are blue More than half of the circles are blue 17 17 Budapest Workshop, Oct. 2015 / 38
PPP results – RT Fifth PPP result: the Polarity effect is additive Possible relations between curves Additive: Polarity effect Non-additive: Polarity effect is independent from proportion is not independent from proportion RT RT RT diff RT diff prop prop Permutation tests indicate that the effect is additive. RT diff is independent of r/c . ⇒ Verification is unaffected by proportion; contrary to the focus-on-the-larger set strategy 18 Budapest Workshop, Oct. 2015 / 38
PPP results – RT Results and conclusions so far • Weber’s Law : Performance curves on the PPP is more symmetric on logarithmic compression • Quantifier Polarity : RT few , less-than-half > RT many , more-than-half • No symbolic Polarity : RT < ≈ RT > • Modularity I : Polarity effects are exclusive to Language: a Polarity X instruction type (±linguistic) interaction effect • Modularity II : the Polarity effect is additive (RT diff is independent of proportion) 19 Budapest Workshop, Oct. 2015 / 38
PPP results – RT Do participants respond on partial information: a view from comparatives POS : There are more blue circles than Yellow circles NEG: There are fewer blue circles than Yellow circles 22 subjects X 16 T/F = 352 trials 20 Budapest Workshop, Oct. 2015 / 38
A semantic account and some tests Informal comparison of RT abs across numerosities (and quantifier types) 21 Budapest Workshop, Oct. 2015 / 38
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