Semantics 1, SoSe 2016 (Sailer): Weeks 6 and 7

Quantifiers

Video introducing determiners into our logical language. (The video is based on the scenario of Romeo and Juliett.)

(copied from Wiki-ch2#Logical_determiners.2Fquantifiers)

Exercises

After having watched the video, work on the following tasks.

Task 1 Identify the determiners in the following sentence.

(a) Juliet talked to some stranger at the party.

(b) Every Capulet is an enemy to some Montague.

(c) Many people in Verona are not happy about the Capulet-Montague feud.

Check your solutions here:

(a) some

(b) every, some

(c) many

Task 2 Identify the formula that corresponds to the translation of the sentence.

Some Montague who was at the party fell in love with Juliet.

	∃x (montague1(x) : (at-party1(x) ∧ fall-in-love-with2(x,juliet)))
	∃x ((montague1(x) ∧ at-party1(x)) : fall-in-love-with2(x,juliet))
	∃x (montague1(x) : (at-party1(x) ∧ fall-in-love-with2(x,juliet))
	∃x ((montague1(x) ∧ fall-in-love-with2(x,juliet)) : at-party1(x))

Task 3 The sentence: Some Tybalt loved some Montague. is translated into the formula
∃ y (montague₁(y) : love₂(tybalt,y).

Mark all the cells in the table that stand for a true statement.

montague1(y) zwisch	love2(tybalt,y)zwisch
		Romeo
		Mercutio
		Juliet
		Tybalt
		Laurence
		Paris

Given this table, is the overall formula true or false? (Give a reason for your answer.)

Check your solutions here:

The formula is false, because there is no individual in our model for which both the restrictor and the scope are true.

Task 4 Variable assignment function
Start with the following variable assigment function g: g(u) = Romeo, g(v) = Juliet, g(w) = Romeo, g(x) = Laurence, g(y) = Mercutio, g(z) = Juliet

Provide the changed variable assignment function g[v/Paris].

Check your solutions here:

g[v/Paris](u) = g(u) = Romeo
g[v/Paris](v) = Paris
g[v/Paris](w) = g(w) = Romeo
g[v/Paris](x) = g(x) = Laurence
g[v/Paris](y) = g(y) = Mercutio
g[v/Paris](z) = g(z) = Juliet

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