Semantics 1, SoSe 2016 (Sailer)
Additional material for 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.
Task 3 The sentence: Some Tybalt loved some Montague. is translated into the formula
∃ y (montague1(y) : love2(tybalt,y).
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
Additional material for week 5
Formulae with more than one connective
The video shows how the truth value of a more complex formula can be computed. The example contains two connectives:
kill(malcom,lady-macbeth) ∨ ¬thane(macbeth)
The video shows two different methods: top down and bottom up.
Truth tables
(The following exercises have been copied here from the page on exercises for truth tables.)
Truth tables for complex formulae
Truth tables are also useful to compute the truth value of complex formulae. This is shown in the following podcast, created by Lisa Günthner.
Preparation for week 5
- Read Levine et al (in prep.), Chapter 2, section 2.
- Using your model from last week,
- Give 1 formula with ⊃.
- Give 1 formule with 2 different connectives (both distinct from ⊃)
- Provide the step-by-step computation of the truth of your 2 formulae.
Additional material for week 4
The material can be found on the page Semantics 1, SoSe 2016 (Sailer): Week 4
Additional material for week 3
The material for week 3 can be accessed here