2. What is the highest mountain on Earth?

3. Mountain-height problem Measured from the sea level: Mt. Everest (8,848 m) From the base to the peak: Mauna Kea (10,203 m) To the Earth centre: Chimborazo (6,384 km ) There are many different meanings of the expression “mountain height” as there are different procedures of measuring.

4. Meaning = Algorithm Meaning of an expression is a collection of procedures for computing its denotation. In particular, meaning of a sentence can be identified with a way of checking whether it is true or false.

5. Quantifiers Quantifiers occur very frequently in our speech. Every mountain is higher than 300 m. Some mountains are covered with snow. At least 14 summits reach above 8000 m. An even number of mountains are >8000 m. Most of Asia is covered by mountains. They underlie language expressivity.

6. In the Thesis What algorithms lie behind quantifiers? What is their complexity? How does it interplay with comprehension? Why is it interesting for linguistics? What are the relations with cognitive-science?

7. Classifying Quantifiers by Complexity An experiment

8. Some cars are black.

9. An even number of cars are black.

10. At least 8 cars are purple.

11. Most of the cars are red.

12. Most circles are connected with each other.

13. More than 1 square and more than 2 circles are connected by lines.

14. And… I bet you had a feeling of increasing difficulty. This is explained by computational complexity… and corroborated via experiments.

15. Summary I systematically drew a distinction between tractable and intractable quantifiers. Tractable QuantifiersIntractable Quantifiers MonadicCollective Standard polyadicBranching and Ramsey Weak reciprocalsStrong reciprocals More in the book!