Session 08

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Quantifiers as Sets? The problems indicate: DPs do (in general) not denote an individual of type e. So maybe they denote sets of individuals (i.e. they are of type )? ’ Fred ÷ = { Fred } ’ everything ÷ = D e ’ nothing ÷ = ∅ ’ at most 2 people ÷ = an arbitrary set of at most 2 people Compositional rules (or the semantics of verbs) has to be changed accordingly. Assume: ’S ÷ = ’ DP VP ÷ = 1 iff ’ DP ÷ ⊆ ’ VP ÷ Alternatively, change the semantics of the VP: ’ lives in Osnabrück ÷ = λX ∈ Pow(D). X ⊆ {y: y lives in Osnabrück} 03.06.20<strong>08</strong> Slides based on semantics textbook from I. Heim & A. Kratzer and lecture notes from M. Krifka 34
Does this proposal yield adequate results for the following sentences? S Quantifiers as Sets? DP N Fred VP V lives in Osnabrück S { Fred } ⊆ {y: y lives in Osnabrück } iff Fred lives in Osnabrück DP Everybody VP V D e ⊆ {y: y lives in Osnabrück } iff every individual lives in Osnabrück lives in Osnabrück 03.06.20<strong>08</strong> Slides based on semantics textbook from I. Heim & A. Kratzer and lecture notes from M. Krifka 35
Page 1 and 2: Introduction to Semantics Session 8
Page 3 and 4: Homework Homework 03.06.2008 Slides
Page 5 and 6: Very Which class of adjectives can
Page 7 and 8: Very ’very÷ = λR λQ . R(R(Q)
Page 9 and 10: Very = λx. dog(x) & the meanness o
Page 11 and 12: Escalator: H&K What does our curren
Page 13 and 14: Escalator: intuitions What is empir
Page 15 and 16: (i) the leftmost apple in the row D
Page 17 and 18: (ii) the leftmost dark apple in the
Page 19 and 20: (iii) the apple that is both leftmo
Page 21 and 22: Lexical Semantics of leftmost • I
Page 23 and 24: (ii) the leftmost dark apple in the
Page 25 and 26: More DPs Do all DPs behave like pro
Page 28 and 29: More DPs A woman Somebody Everybody
Page 30 and 31: Quantifiers as Individuals? John li
Page 32 and 33: Quantifiers as Individuals? Tautolo
Page 36 and 37: Quantifiers as Sets? Does this prop
Page 38 and 39: Quantification Quantificational DPs
Page 40 and 41: What does it mean to change the typ
Page 42 and 43: Quantifiers as Sets of Sets GQs as
Page 44 and 45: Problematic Cases Solved Nobody liv
Page 46 and 47: Solving the Inference Problem Someb
Page 48 and 49: Quantificational Determiners Given
Page 50 and 51: Derivation of Truth Conditions Comp
Page 52 and 53: Functional and Relational View Trut
Page 54 and 55: Quantification Formal Properties of
Page 56 and 57: Symmetry Another example: Is every
Page 58 and 59: Monotonicity Monotonicity (a) No ba
Page 60 and 61: Monotonicity Monotonicity The examp
Page 62: Thank you! Thank you! 03.06.2008 Sl

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