# Assignmentsheet Logic Summer Term 2013

Choose one book from top 100 most loved books in 2003. This book will be the basis for your answers to the assignment sheet.

For the example solution we will use *Jane Eyre* by Charlotte Brontë.^{[1]}

- ↑ For a brief summary of the novel, see the wikipedia site of the novel.

## Contents

## Task 1: Ambiguous sentences (8 points)

1. Write down two ambiguous sentences with respect to the book’s content.

2. For each of these, provide an unambiguous paraphrase for the possible readings.

3. Classify the type of ambiguity.

4. For each of the readings: Is one of them more plausible in the context of the book than the other?

Example solution for ambiguous sentences in the context of ''Jane Eyre''.

## Task 2: Model (12 points)

1. Define a universe consisting of four main characters from your book.

2. Introduce names for your characters and provide their interpretations.

3. Introduce three property symbols relevant to the plot and provide their interpretations.

4. Introduce two 2-place relation symbols relevant to the plot and define their interpretations.

Example solution for defining a model in the context of ''Jane Eyre''.

## Task 3: Atomic formulae (8 points)

Write down two atomic formulæ and compute their truth value with respect to your model.

Examples for atomic formulae in the context of ''Jane Eyre''.

## Task 4: Complex formulae (8 points)

1. Combine your two formulæ from Task 3 into two complex formulæ. Use the connectives “¬”, “∧”, and “⊃”

2. Compute the truth value of these complex formulæ. (You don’t need to do the computation for the atomic formulæ again.)

Example solution for the ''Jane Eyre'' context.

## Task 5: Variables (5 points)

1. Provide a variable assigment function g which maps the variables *x _{1}, ..., x_{10}* to members of your
universe.

2. Provide one formula that contains two occurrences of variables.

3. Compute the truth value of this formula with respect to your assingment function g.

Example solution based on the novel ''Jane Eyre''.

## Task 6: Quantifiers (6 points)

1. Write down one formula with a quantifier.

2. For each individual in your universe, indicate whether the restrictor and the scope are true for that individual.

3. Given your results from (b), is the formula true in your model?

4. In which way would your model have to be different to make the formula false (or, in case the formula is false: to make it true in your model)?

Example with a quantifier for the ''Jane Eyre'' context.

## Task 7: Truth tables (6 points)

Compute the truth table for the following formulæ:

1. p ∧ (p ∧ q)

2. (p ∨ q) ⊃ ¬(q ∧ ¬r)