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5.3 Deriving scope ambiguities

  1. Start simple
    1. [ $ {}_{\mathrm{S}}$ Every man$ _{x}$ walks.]
    2. [ $ {}_{\mathrm{S}}$ [Every man]$ _{x}$ [ $ {}_{\mathrm{S}}$ x walks.]]
    3. [ $ {}_{\mathrm{S}}$ Every$ {}_{x}$ [x man]$ {}_{x}$ [ $ {}_{\mathrm{S}}$ x walks.]]
    4. $ \mathrm{\:Every\:}\:x\:\lbrack\mathrm{\:man\:}(x) \rightarrow \mathrm{\:walk\:}(x)\rbrack$
  2. Two NPs
    1. [ $ {}_{\mathrm{S}}$ [Every man]$ _{x}$ loves [some woman]$ {}_{y}$]
    2. [ $ {}_{\mathrm{S}}$ [Every man]$ _{x}$ [ $ {}_{\mathrm{S}}$ x loves [some woman]$ {}_{y}$.]]
    3. [ $ {}_{\mathrm{S}}$ Every$ {}_{x}$ [x man]$ {}_{x}$ [ $ {}_{\mathrm{S}}$ x loves some woman$ {}_{y}$.]]
    4. [ $ {}_{\mathrm{S}}$ [some woman$ {}_{y}$] [ $ {}_{\mathrm{S}}$ Every$ {}_{x}$ [x man]$ {}_{x}$ [ $ {}_{\mathrm{S}}$ x loves y.]]]
    5. [ $ {}_{\mathrm{S}}$ some$ {}_{y}$ [y woman]$ {}_{y}$ [ $ {}_{\mathrm{S}}$ Every$ {}_{x}$ [x man]$ {}_{x}$ [ $ {}_{\mathrm{S}}$ x loves y.]]]
    6. $ \mathrm{\:Some\:} y \lbrack \mathrm{\:woman\:}(y) \wedge \mathrm{\:Every\:}\:x\:\lbrack \mathrm{\:man\:}(x) \rightarrow \mathrm{\:love\:}(x,y)\rbrack \rbrack$
  3. Two NPs another way
    1. [ $ {}_{\mathrm{S}}$ [Every man]$ _{x}$ loves [some woman]$ {}_{y}$]
    2. [ $ {}_{\mathrm{S}}$ [Some woman]$ _{y}$ [ $ {}_{\mathrm{S}}$ [every man]$ {}_{x}$ loves y.]]
    3. [ $ {}_{\mathrm{S}}$ Some$ {}_{y}$ [y woman]$ _{y}$ [ $ {}_{\mathrm{S}}$ [every man]$ {}_{x}$ loves y.]]
    4. [ $ {}_{\mathrm{S}}$ [every man$ {}_{x}$] [ $ {}_{\mathrm{S}}$ some$ {}_{x}$ [y woman]$ {}_{x}$ [ $ {}_{\mathrm{S}}$ x loves y.]]]
    5. [ $ {}_{\mathrm{S}}$ every$ {}_{x}$ [x man]$ {}_{x}$ [ $ {}_{\mathrm{S}}$ some$ {}_{y}$ [y woman]$ {}_{x}$ [ $ {}_{\mathrm{S}}$ x loves y.]]]
    6. $ \mathrm{\:Every\:} x \lbrack \mathrm{\:man\:}(x) \rightarrow \mathrm{\:some\:}...
...\lbrack \mathrm{\:woman\:}(y) \rightarrow \mathrm{\:love\:}(x,y)\rbrack \rbrack$
  4. So now this IS a syntactic ambiguity

  5. A new architecture for grammar
    1. Classical aspects model (c. 1965)
      ALT=
    2. T-model (c. 1976)
      ALT=


next up previous contents index
Next: 6 Logical Entailments Up: 5 Quantifiers Previous: 5.2 Every and All   Contents   Index
Jean Mark Gawron 2009-02-16