Exercise Quantifiers: Difference between revisions

Revision as of 23:22, 16 December 2013

The following material is an adapted form of material created by student participants of the project e-Learning Resources for Semantics (e-LRS).
Involved participants: AnKa, Katharina, Lara

Find the right formula for the sentence below.

Which type(s) of Quantifiers does the sentence below have?

2. Write down the corresponding logical formula(s). Check your solutions here.

1. In which way is the following sentence ambiguous?

Everyone loves someone.

The following pictures may help you:

Check your solutions here:

In this sentence, the scopal ambiguity is created by the two quantifiers everyone and someone.

When looking at the two pictures that try to help you, you can see two possible readings:

1. For every person there is, there is at least one other person who loves him / her.

2. There is one person that is loved by everyone else.

2. Write down the two possible logical forms.

Check your solutions here:

1. For every person there is at least one person who loves him / her:

∀x (person(x) ⊃ ∃y (person(y) ∧ love(x,y)

Or, in restricted-quantifier notation: ∀x (person(x) : ∃y (person(y) : love(x,y)

2. There is one person that is loved by everyone:

∃y (person(y) ⊃ ∀x (person(x) ∧ love(x,y)

Or, in restricted-quantifier notation: ∀x (person(x) : ∃y (person(y) : love(x,y)

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 . There is one person that is loved by everyone else.</div>
 </div>
+<br/ >
+<br/ >
 '''2.''' Write down the two possible logical forms.
+<br/ >
 <div class="toccolours mw-collapsible mw-collapsed" style="width:800px">

	∃x (student(x) : (hear(x,concert) ∧ interview(holmes,x)))
	∃x ((student(x) ∧ hear(x,concert)) : interview(holmes,x))
	∃x (student(x) ∧ hear(x,concert) ∧ interview(holmes,x))
	∃x ((student(x) ∧ interview(holmes,x)) : hear(x,concert))