A QUD-based theory of quantifier conjunction with but WCCFL 38, - PowerPoint PPT Presentation

A QUD-based theory of quantifier conjunction with but WCCFL 38, University of British Columbia Jing Crystal Zhong and James N. Collins 7 March 2020 University of Hawai‘i at Mānoa

Introduction Not just any two quantifiers can be conjoined by but in the subject position. (1) a. No syntactician but every phonologist attended the plenary talk. b. No syntactician but * no /?? few phonologists attended the plenary talk. 1

no man dance exactly.2 man dance Introduction every man dance exactly.2 man hula (5) Non-monotone quantifiers : exactly n NP , an even number of NP no man hula (4) Monotone decreasing quantifiers : no NP , few NP , at most two NP every man hula Barwise and Cooper [1] (hereaħter B&C) make the following (3) dance hula (2) Monotone increasing quantifiers : every NP , many NP , at least two NP able to mix increasing and decreasing quantifiers (p. 196) to use but in this way, it seems necessary or at least prefer- generalization: 2

no man dance exactly.2 man dance Introduction Monotone decreasing quantifiers : no NP , few NP , at most two NP exactly.2 man hula (5) Non-monotone quantifiers : exactly n NP , an even number of NP no man hula (4) 2 Barwise and Cooper [1] (hereaħter B&C) make the following (3) (2) Monotone increasing quantifiers : every NP , many NP , at least two NP able to mix increasing and decreasing quantifiers (p. 196) to use but in this way, it seems necessary or at least prefer- generalization: � hula � ⊑ � dance � � every ( man )( hula ) � ⊑ � every ( man )( dance ) �

exactly.2 man dance Introduction Barwise and Cooper [1] (hereaħter B&C) make the following exactly.2 man hula (5) Non-monotone quantifiers : exactly n NP , an even number of NP (4) Monotone decreasing quantifiers : no NP , few NP , at most two NP 2 (3) (2) Monotone increasing quantifiers : every NP , many NP , at least two NP able to mix increasing and decreasing quantifiers (p. 196) to use but in this way, it seems necessary or at least prefer- generalization: � hula � ⊑ � dance � � every ( man )( hula ) � ⊑ � every ( man )( dance ) � � no ( man )( dance ) � ⊑ � no ( man )( hula ) �

Introduction (3) (5) Non-monotone quantifiers : exactly n NP , an even number of NP (4) Monotone decreasing quantifiers : no NP , few NP , at most two NP Barwise and Cooper [1] (hereaħter B&C) make the following 2 (2) Monotone increasing quantifiers : every NP , many NP , at least two NP able to mix increasing and decreasing quantifiers (p. 196) to use but in this way, it seems necessary or at least prefer- generalization: � hula � ⊑ � dance � � every ( man )( hula ) � ⊑ � every ( man )( dance ) � � no ( man )( dance ) � ⊑ � no ( man )( hula ) � � exactly.2 ( man )( dance ) � ̸| = � exactly.2 ( man )( hula ) �

Monotonicity B&C’s monotonicity account explains the judgments in (6): (6) a. the keynote. b. attended the keynote. Where the monotonicity of the quantifier DPs difger , the conjunction is acceptable. 3 No syntactician ( ⇓ ) but every phonologist ( ⇑ ) attended No syntactician ( ⇓ ) but * no /?? few phonologists ( ⇓ )

Every pragmaticist ( ) but many phoneticians ( ) Few phoneticians ( ) but no pragmaticist ( ) attended the No pragmaticist ( ) but few phoneticians ( ) attended b. every many no few one. quantifiers, so long as the weaker quantifier precedes the stronger Generalization 1: Matching monotonicity is OK for scale-mate the keynote. Problem 1 keynote. However B&C’s mismatching-monotonicity condition is not necessary a. (8) attended the keynote. b. attended the keynote. Many phoneticians ( ) but every pragmaticist ( ) a. (7) (matching monotonicity is judged as OK sometimes): 4

Problem 1 However B&C’s mismatching-monotonicity condition is not necessary every many no few one. quantifiers, so long as the weaker quantifier precedes the stronger Generalization 1: Matching monotonicity is OK for scale-mate the keynote. b. 4 a. (8) attended the keynote. b. a. (7) (matching monotonicity is judged as OK sometimes): Many phoneticians ( ⇑ ) but every pragmaticist ( ⇑ ) attended the keynote. ≫≫ ?? Every pragmaticist ( ⇑ ) but many phoneticians ( ⇑ ) Few phoneticians ( ⇓ ) but no pragmaticist ( ⇓ ) attended the keynote. ≫≫ ?? No pragmaticist ( ⇓ ) but few phoneticians ( ⇓ ) attended

Problem 1 (8) one. quantifiers, so long as the weaker quantifier precedes the stronger Generalization 1: Matching monotonicity is OK for scale-mate the keynote. b. However B&C’s mismatching-monotonicity condition is not necessary a. attended the keynote. b. a. (7) (matching monotonicity is judged as OK sometimes): 4 Many phoneticians ( ⇑ ) but every pragmaticist ( ⇑ ) attended the keynote. ≫≫ ?? Every pragmaticist ( ⇑ ) but many phoneticians ( ⇑ ) Few phoneticians ( ⇓ ) but no pragmaticist ( ⇓ ) attended the keynote. ≫≫ ?? No pragmaticist ( ⇓ ) but few phoneticians ( ⇓ ) attended � few � ⊒ � no � , � many � ⊒ � every �

Problem 2 B&C’s mismatching-condition, is not suffjcient (mismatching monotonicity is judged as not-OK sometimes): (9) a. b. Generalization 2: Difgering monotonicity is not OK if the quantifiers overlap in reference. 5 At least two thirds of Democrats ( ⇑ ) but fewer than half of Republicans ( ⇓ ) voted for the bill. ≫≫ ?? / ∗ At least a third of Democrats ( ⇑ ) but fewer than half of Republicans ( ⇓ ) voted for the bill.

Monotonicity vs. overlap fewer than half at least two thirds of at least a third of 0 1 Fig. 1. Overlapping and non-overlapping determiners 6

Monotonicity vs. overlap (10) a. b. Generalization 2: Difgering monotonicity is not OK if the quantifiers overlap in reference. — ‘at least 2/3 of’ and ‘fewer than half’ don’t overlap, so but -conjunction is licensed. — ‘at least 1/3 of’ and ‘fewer than half’ overlap on a scale of proportions, so but -conjunction is degraded. 7 At least 2/3 of Democrats ( ⇑ ) but fewer than half of Republicans ( ⇓ ) voted for the bill. ≫≫ ?? / ∗ At least 1/3 of Democrats ( ⇑ ) but fewer than half of Republicans ( ⇓ ) voted for the bill.

Monotonicity vs. overlap (10) a. b. Generalization 2: Difgering monotonicity is not OK if the quantifiers overlap in reference. — ‘at least 2/3 of’ and ‘fewer than half’ don’t overlap, so but -conjunction is licensed. — ‘at least 1/3 of’ and ‘fewer than half’ overlap on a scale of proportions, so but -conjunction is degraded. 7 At least 2/3 of Democrats ( ⇑ ) but fewer than half of Republicans ( ⇓ ) voted for the bill. ≫≫ ?? / ∗ At least 1/3 of Democrats ( ⇑ ) but fewer than half of Republicans ( ⇓ ) voted for the bill.

The empirical picture To summarize, (11) Generalization 1: Matching monotonicity is OK for scale-mate quantifiers, so long as the weaker quantifier precedes the stronger one. (12) Generalization 2: Difgering monotonicity is not OK if the quantifiers overlap in reference. Relevant factors — Ordering of determiners — Difgerent vs. same monotonicity — Overlapping vs. non-overlapping reference 8

The empirical picture To summarize, (11) Generalization 1: Matching monotonicity is OK for scale-mate quantifiers, so long as the weaker quantifier precedes the stronger one. (12) Generalization 2: Difgering monotonicity is not OK if the quantifiers overlap in reference. Relevant factors — Ordering of determiners — Difgerent vs. same monotonicity — Overlapping vs. non-overlapping reference 8

Experiment 1: Ordering b. - 24 English native speaker participants - 4 point Likert scale judgment task - equal number of fillers - 4 conditions, 18 critical items, Latin square design 2 factorial design crossing Same/DiffMono & Order - 2 No girl but every boy skipped class. 9 Is there an efgect from the order of determiners? a. (14) b. ??Every girl but many boys skipped class. a. (13) monotonicity. Otherwise, order doesn’t matter. — Order matters for scale-mate quantifiers w/ matching Many girls ( ⇑ ) but every boy ( ⇑ ) skipped class. Every girl ( ⇑ ) but no boy ( ⇓ ) skipped class.

Experiment 1: Ordering Is there an efgect from the order of determiners? - 24 English native speaker participants - 4 point Likert scale judgment task - equal number of fillers - 4 conditions, 18 critical items, Latin square design No girl but every boy skipped class. b. a. (14) b. ??Every girl but many boys skipped class. a. (13) monotonicity. Otherwise, order doesn’t matter. — Order matters for scale-mate quantifiers w/ matching 9 Many girls ( ⇑ ) but every boy ( ⇑ ) skipped class. Every girl ( ⇑ ) but no boy ( ⇓ ) skipped class. - 2 × 2 factorial design crossing Same/DiffMono & Order

Results Fig. 2. Results of experiment 1. Error bars represent standard error. 10

Experiment 2: Overlap vs. Same/difg. monotonicity Table 1. Experimental stimuli - 21 English native speaker participants - 4 point Likert scale judgment task - 16 fillers (8 grammatical, 8 ungrammatical) 4), Latin-square design - 4 conditions, 16 critical items ( k 2 factorial design crossing SameMono & Overlap - 2 No No Yes No exactly two X but an odd number of Y No Yes exactly two X but an even number of Y Yes Yes Example Overlap? SameMono? 11 at least 1 / 3 of X but fewer than half of Y at least 2 / 3 of X but fewer than half of Y