Slides / Bullets

• Mixed quantifiers
  • The order of quantifiers makes a difference:
    • ’àÄx’àÉy(Hates(x,y)) vs ’àÉx’àÄy(Hates(x,y))
    • ’àÄx’àÉy(SameCol(x,y)) vs ’àÉx’àÄy(SameCol(x,y))
• The step-by-step method of translation
  • This is very useful for sentences that contain several quantified noun phrases.
  • EG: ’ÄòEvery dog lives in some kennel’Äô
    • Step one: ’àÄx(Dog(x) ’Üí lives-in-some-kennel(x))
    • Step two: ’àÄx(Dog(x) ’Üí ’àÉy(Kennel(y) ’àß LivesIn(x,y))
• • EG: ’ÄòEvery dog who lives in a kennel has an owner who lives in a house’Äô.
    • Step One: ’àÄx(Dog(x)’àßlives-in-a-kennel(x) ’Üí has-an-owner-who-lives-in-a-house(x)).
    • Step Two: ’àÄx(Dog(x)’àß’àÉy(Kennel(y) ’àß LivesIn(x,y)) ’Üí ’àÉz(Owns(x,z) ’àß lives-in-a-house(z)).
    • Step Three: ’àÄx(Dog(x)’àß’àÉy(Kennel(y) ’àß LivesIn(x,y)) ’Üí ’àÉz(Owns(x,z) ’àß ’àÉy(House(y) ’àß LivesIn(z,y))).
• Ambiguity
  • Quantifiers in English are a rich source of ambiguity.
    • ’ÄòSome poor sucker is mugged every minute’Äô.
      • ? ’àÉx(Poor(x)’àßSucker(x)’àßmugged-every-minute(x))
      • ’àÄx(Minute(x)’Üísome-poor-sucker-is-mugged-during(x))
  • Often this ambiguity is resolved by context.