What is the highest mountain on Earth?

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.

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.

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.

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?

Classifying Quantifiers by Complexity

An experiment

Some cars are black.

An even number of cars are black.

At least 8 cars are purple.

Most of the cars are red.

Most circles are connected with each other.

More than 1 square and more than 2 circles

are connected by lines.

And…

I bet you had a feeling of increasing difficulty.

This is explained by computational complexity…

and corroborated via experiments.

Summary

I systematically drew a distinction between tractable and intractable quantifiers.

Tractable Quantifiers Intractable Quantifiers

Monadic Collective

Standard polyadic Branching and Ramsey

Weak reciprocals Strong reciprocals

More in the book!