# Difference between revisions of "WiSe 2020/21 (Sailer): Semantics 1"

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::: Formulate 1 complex formula with at least 2 logical connectives in it and compute its truth value. | ::: Formulate 1 complex formula with at least 2 logical connectives in it and compute its truth value. | ||

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+ | '''If you need your grade fast, submit as soon as possible!!!''' | ||

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=== Erasmus 3ECTS/CP no grade === | === Erasmus 3ECTS/CP no grade === |

## Revision as of 23:36, 15 February 2021

## Contents

# General information

**Please register at the olat course before the first meeting to get the information on the virtual meeting room!**

## Course description

Semantics is the study of the (literal) meaning of words and sentences. The meaning of a sentence is usually predictable from the words in the sentence and its syntactic structure. Yet, this relationship between form and meaning is not a simple one-to-one mapping. Instead, it is rich in ambiguities, pleonastic marking and elements without any identifiable meaning contribution. We will work on an account that is founded on classical tools of semantic research but still directly addresses these empirical challenges. After the class, the participants will be able to identify - and partly analyze - interesting semantic phenomena in naturally occurring texts. They will have acquired a basic working knowledge in formal logic, which they will be able to apply in the description of meaning

## Time and place

- Tuesday 08:15-9.45
- Starting: 3.11.2020
- online via zoom

## Olat course

Direct link: https://olat-ce.server.uni-frankfurt.de/olat/auth/RepositoryEntry/8836120582

Password: Sailer-WiSe2021

## Modules

- Lehramt Englisch (L2/5, L3): FW 2A, FW 2B
- BA English Studies: 3.4(1)
- BA Empirische Sprachwissenschaft: K 6.1

## Contact

Manfred Sailer

e-mail: sailer@em.uni-frankfurt.de

office: IG 3.214

office hours: *contact via e-mail!*

www: http://user.uni-frankfurt.de/~sailer/index.htm

# Course requirements

## L2 and L5

- regular attendance
- pass take home exam
- Modulprüfung (optional): grade on take home exam

## L3

- regular attendance
- pass take home exam
- Modulprüfung (optional): große Hausabeit (4 CP = 120h!!!) - please talk to me on time if you consider this option!
**Deadline: 10.5.**

## MSc Wirtschaftspädagogik

- regular attendance
- pass take home exam
- Modulprüfung: short term paper (9-11 pages, 1 CP) <- not ideal

## BA English Studies

- regular attendance
- pass take home exam
- literary scenario:

- Part 1: Extract 15 ambiguous sentences from the text such that all types of ambiguity covered in class are represented provide unambiguous paraphrases of the readings determine the type of ambiguity
- Part 2:
- Define a formal model consisting of 3 characters from your text, which contains 2 properties, 1 2-place relation
- Formulate 2 atomic formulae and compute their truth value.
- Formulate 4 complex formulae with at least 1 logical connective in each and compute their truth value.
- Formulate 1 complex formula with at least 2 logical connectives in it and compute its truth value.

**Deadline: 8.3.** (-> 5.4.)

## BA Empirische Sprachwissenschaft

### K 6.1

- regular attendance
- Modulprüfung (obligatory):
**take home exam**

**Deadline: 8.3.** (-> 5.4.)

### En 4.1

If you have to do K6.1: *not possible*: You have done this course as part of K6.1, so you can directly do *constraint-based Semantics 2*.
Otherwise:

- regular attendance
- pass take home exam
- literary scenario:

- Part 1: Extract 15 ambiguous sentences from the text such that all types of ambiguity covered in class are represented provide unambiguous paraphrases of the readings determine the type of ambiguity
- Part 2:
- Define a formal model consisting of 3 characters from your text, which contains 2 properties, 1 2-place relation
- Formulate 2 atomic formulae and compute their truth value.
- Formulate 4 complex formulae with at least 1 logical connective in each and compute their truth value.
- Formulate 1 complex formula with at least 2 logical connectives in it and compute its truth value.

### DH 6.1

*not possible*: You have done this course as part of K6.1, so you can directly do *constraint-based Semantics 2*.

## Optionalbereich

Teilnahmenachweis with 3CP, no grade:

- regular attendance
- all attendance tasks
- small literary scenario:

- Part 1: Extract 4 ambiguous sentences from the text such that different types of ambiguity covered in class are represented provide unambiguous paraphrases of the readings determine the type of ambiguity
- Part 2:
- Define a formal model consisting of 3 characters from your text, which contains 2 properties, 1 2-place relation
- Formulate 2 atomic formulae and compute their truth value.
- Formulate 2 complex formulae with at least 1 logical connective in each and compute their truth value.
- Formulate 1 complex formula with at least 2 logical connectives in it and compute its truth value.

**Deadline: 8.3.** (-> 5.4.)

## Erasmus

### Erasmus 6ECTS/CP with grade

- regular attendance
- graded take home exam
- small literary scenario:

- Part 1: Extract 4 ambiguous sentences from the text such that different types of ambiguity covered in class are represented provide unambiguous paraphrases of the readings determine the type of ambiguity
- Part 2:
- Formulate 2 atomic formulae and compute their truth value.
- Formulate 2 complex formulae with at least 1 logical connective in each and compute their truth value.
- Formulate 1 complex formula with at least 2 logical connectives in it and compute its truth value.

The grade will be determined by the result of the take home exam.

**If you need your grade fast, submit as soon as possible!!!**
**Latest deadline: 8.3.** (-> 5.4.)

### Erasmus 3ECTS/CP no grade

- regular attendance
- all attendance tasks
- small literary scenario:

- Part 1: Extract 4 ambiguous sentences from the text such that different types of ambiguity covered in class are represented provide unambiguous paraphrases of the readings determine the type of ambiguity
- Part 2:
- Formulate 2 atomic formulae and compute their truth value.
- Formulate 2 complex formulae with at least 1 logical connective in each and compute their truth value.
- Formulate 1 complex formula with at least 2 logical connectives in it and compute its truth value.

# Meeting 10

## 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**, __ (__,__) >

Check your answer

**like**(**pat**,**alex**)

**like**(**alex**,**pat**)

2. PARTS < **alex**,**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**, __ (__) >

Check your answer

**snore**(**alex**)

4. PARTS < **alex**,**alex**,**snore**, __ (__), __ ∧ __ >

Check your answer

**snore**(**alex**) ∧ **snore**(**alex**)

# Meeting 9

The following video (21') introduces the way we will write down lexical entries in our course.

The next video shows the HPSG analysis of sentences (38').

# Meeting 8

Watch the following video (33') on the basic step in a syntactic analysis as we need it in our course.

The next video (14') introduces the way we talk about syntactic trees. Please watch it.

# Meeting 7

## Video

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*

*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 (**montague _{1}**(

*y*) :

**love**(

_{2}**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.

# Meeting 6

Homework from week 6 (preparation for week 7): Watch the video on logical determiners.

# Meeting 5

## Formulae with one connective

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)**

## Formulae with two connectives

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.

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.

## 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.

## Variable assignment funcion

**Task** 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*

# Meeting 4

## Computing the truth value of complex formulae

### Connectives

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)**

Back to the course page.

# Meeting 3

## 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:

**kill2(macbeth,duncan)****kill2(lady-macbeth,macbeth)**

# Meeting 2

## Our literary scenario

Literary scenario for this course: book and movie series *Harry Potter*, https://en.wikipedia.org/wiki/Harry_Potter

## 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:
*Harry meets Hagrid.* - ... is mapped to some expression from a formal language (here: predicate logic):
**meet2**(**harry**,**hagrid**) - This logical expression is then interpreted with respect to our scenario/world: The formula
**meet2**(**harry**,**hagrid**) is true, because, in our scenario, Harry meets Hagrid.

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 *Harry Potter*-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*

## 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.

# Meeting 1

Literary scenario of our class: **Harry Potter**

Check the plot summaries of the books/movies for example on wikipedia: