Semantics 1, SoSe 2017 (Sailer)
Olat course: https://olat-ce.server.uni-frankfurt.de/olat/auth/RepositoryEntry/4778393609
Mock exam
Open the page of the SoSe 2017 mock exam (with example solutions).
Assignment sheets
Assignment logic (due June 13): assignment-logic-SoSe17.pdf
Assignment LRS (due July 18): assignment-lrs-SoSe17.pdf
Material for week 13 (11.7.)
Example online grammar: http://141.2.159.95:7025/wt/
Basic combinatorics: Canonical examples
(the following exercises are adapted from the textbook material to [Chapter 5].
Possible EX-CONT values
Given the following PARTS lists, what are possible EX-CONT values (if we do not assume other restrictions)
1. PARTS < pat, alex,like, like(__,__) >
Check your answer
like(pat,alex)
like(alex,pat)
2. PARTS < alex,snore, snore(__), ¬(__) >
Check your answer
¬(snore(alex))
3. PARTS < alex,alex,snore >
Check your answer
There is no possible EX-CONT value because the three elements on the PARTS list cannot be combined.
3. PARTS < alex,alex,snore, snore(__) >
Check your answer
snore(alex)
4. PARTS < alex,alex,snore, snore(__), __ ∧ __ >
Check your answer
snore(alex) ∧ snore(alex)
Material for week 12 (4.7.)
Example online grammar: http://141.2.159.95:7025/wt/
Analysis of simple sentences
Feel free to send feedback on this exercise to Manfred Sailer.
Basic combinatorics: Canonical examples
(the following exercises are adapted from the textbook material to [Chapter 5].
Possible EX-CONT values
Given the following PARTS lists, what are possible EX-CONT values (if we do not assume other restrictions)
1. PARTS < pat, alex,like, like(__,__) >
Check your answer
like(pat,alex)
like(alex,pat)
2. PARTS < alex,snore, snore(__), ¬(__) >
Check your answer
¬(snore(alex))
3. PARTS < alex,alex,snore >
Check your answer
There is no possible EX-CONT value because the three elements on the PARTS list cannot be combined.
3. PARTS < alex,alex,snore, snore(__) >
Check your answer
snore(alex)
4. PARTS < alex,alex,snore, snore(__), __ ∧ __ >
Check your answer
snore(alex) ∧ snore(alex)
Material for week 11 (27.6.)
Lexical entries as Attribute-Value Matrix
Provide the required information on the lexical properties of the underlined words in the following sentences.
Note:
- Put a minus ("-") if a slot should not receive any filling
- Use det, noun, prep or verb for the HEAD values.
Feel free to send feedback on this exercise to Manfred Sailer.
Material for week 10 (20.6.)
Basic syntactic notions
Parts of speech
Feel free to send feedback on this exercise to Manfred Sailer.
Syntactic categories
Feel free to send feedback on this exercise to Manfred Sailer.
Material for week 8 (6.6.2017)
Input: Truth tables
Truth tables are also useful to compute the truth value of complex formulae. This is shown in the following podcast, created by Lisa Günthner.
Input: Determiners/quantifiers
Watch the following video on logical determiners:
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
Restricted Quantifiers
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.
Different types of Quantifiers
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
Which type(s) of quantifiers does the sentence below have?
2. Write down the logical formula(e) that correspond to the sentence Ramon signs every sculpture he makes.
Check your solutions here
Sentence: Ramon signs every sculpture he makes.
Universal Quantifier
∀x ((sculpture(x) ∧ make(ramon, x)) ⊃ sign(ramon, x))
Paraphrse: "For every thing x, if x is a sculpture and x is made by Ramon then x is signed by Ramon."
We use the name constant ramon for both the name (Ramon) and the personal pronoun he that referes to Ramon.
In restricted quantifier notation
∀x ((sculpture(x) ∧ make(ramon, x)) : sign(ramon, x))
Here, the N' is "sculpture he makes" and therefore its translation appears in the part before the colon.
Scopal Ambiguity
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
1. In which way is the following sentence ambiguous?
Everyone loves someone.
The following pictures may help you:
One Reading
Another Reading
Check your solutions here:
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:
∀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)
Material for week 6 (23.5.2017)
Video
The following video presents the step-by-step computation of the truth value of two formulae with connectives. The example uses a model based on Shakespeare's play Macbeth. The two formulae are:
- ¬ king(lady-macbeth)
- king(duncan) ∨ king(lady-macbeth)
The next 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.
Material for week 5 (16.5.2017)
Why it is too difficult to go directly from language to the world
The following architecture is extremely useful when talking about semantics:
- A natural language expressions: Daenerys loves Drogo.
- ... is mapped to some expression from a formal language (here: predicate logic): love2(daenerys,drogo)
- This logical expression is then interpreted with respect to our scenario/world: The formula love2(daenerys,drogo) is true, because, in our scenario, Daenerys loves Drogo.
The following properties of natural language make it useful to use the intermediate step of a logical language:
- The same expression can have different meanings (ambiguity).
- Different expressions can have the same meaning (synonyms, paraphrases)
Find examples for the above-mentioned properties (ambiguity, synonymy, paraphrases).
Check your answers
1. one form, two meaingns: Ambiguity: (see earlier in this meeting and the slides of last week's meeting)
1.a Ambiguous words: date (fruit or point in time); bank (financial institute or bank of a river)
1.b. Ambiguous sentences: Sycorax and Prospero were stranded on the island with their children.
2. two forms, one meaning:
2.a Synonymous words: couch - sofa; instant - moment
2.b Paraphrases:
- active-passive pairs: Prospero set Ariel free. - Ariel was set free by Prospero.
- cleft sentences: Prospero set Ariel free. - It was Prospero who set Ariel free.
- different ways to express a possessor: Sycorax was the first inhabitant of the island. and Sycorax was the island's first inhabitant.
Towards a formal model
First steps
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: Lisa, Marthe, Elisabeth, Isabelle.
You can think of building a formal model like being the producer of a film who has to collect everything that should be included in the film.
Here is a very simple story from which we can derive an example model.
The universe and name symbols
Task: Assume three individuals from our Game of Thrones-scenario.
Formally we collect the individuals of our model in a so-called universe (U). For the fairy-tale story, we can define the universe as follows:
U = {Redridinghood, Grandmother, Wolf}
Do a similar definition for your own scenario.
We can introduce name symbols for some of our individuals. For example: redridinghood, grandmother, wolf.
We link the name symbols to the individuals in our modal. To do this, we introduce the interpretation function. We will written the interpretation function as as I.
This function can be defined in the following way:
I(grandmother) = Grandmother
I(redridinghood) = Red Riding Hood
I(wolf) = Wolf
Relations and predicate symbols
In the fairy-tale scenario we express a relation between Little Red Riding Hood and the Wolf, namely that Little Red Riding Hood is the Wolf's afternoon snack. To formalize this, we collect all pairs of individuals which are such that the first element in the pair is the afternoon snack of the second. Note: A pair is written in between pointy brackets.
Formally we can write this down as follows:
{< x, y > | x is y 's afternoon snack} = { < Redridinghood, Wolf >, < Grandmother, Redriding hood >.}
We can also assume empty relations:
{< x, y > | x is y 's father } = { }
Note, if a relation works both ways, two pairs must be added:
{< x, y > | x talks with y} = { <Redridinghood, Wolf >, < Wolf, Redridinghood >}
Just like with names, we want to have symbols that we can use in the logical language. For our example, let's take the predicate symbols afternoon-snack-of_2 and father-of_2, and talks-with_2. (The number 2 indicates that the interpretation consists of pairs, not just of single individual) There interpretation is defined as follows:
I(afternoon-snack-of_2) = { < x, y > | x is y 's afternoon snack } = { <Redridinghood, Wolf >, <Grandmother, Wolf > }.
Task: For each of your properties, invent an appropriate predicate symbol. Define its interpretation.
Properties and predicate symbols
A property is a specification that either holds of an individual or not. In the little story, having a big mouth is a property of the Wolf, but of noone else in the story. Being female holds of both Little Red Riding Hood and the Grandmother.
We can think of a property as the set of individuals that have this property. Under this view, the property of being female would be the set {Redridinghood, Grandmother}.
Alternatively it is convenient to think of properties as 1-place relations. Under this view, the property of being female would be a set of lists of length 1. This is what the property of being female then looks like: { <Redridinghood>, <Grandmother> }
Task: Using your Game of Thrones universe, define two properties in the format of 1-place relations.
Just like before, we want to have symbols that we can use in the logical language. For our example, let's take the predicate symbols female_1 and has-big-mouth_1. There interpretation is defined as follows:
I(female_1) = { < x > | x is female } = { <Redridinghood>, <Grandmother> }.
Task: For each of your properties, invent an appropriate predicate symbol. Define its interpretation.
Computing the truth value of atomic formulae
The following video presents the step-by-step computation of the truth value of two atomic formulae. The example uses a model based on Shakespeare's play Macbeth. The two formulae are:
- kill(macbeth,duncan)
- kill(lady-macbeth,macbeth)
Back to the course page.