# AIMA - First-Order Logic

## Flashcards

What is the Sapir-Whorf hypothesis?

Our understanding of the world is strongly influenced by the language we speak.

What three things does first-order logic assume exists in the world?

- Facts
- Objects
- Relations

What one thing does propositional logic assume exists in the world?

Facts

What are the ontological commitments of a logic?

What it assumes about how reality is constructed.

What is a relation in first-order logic?

Some relationship or property expressed by one or more objects.

What’s a more natural way of thinking about unary relations?

Properties of an object.

What’s an example of a unary relation?

- $\text{Smelly}(\text{Zain})$
- $\text{Green}(\text{Grass})$

What’s an example of a binary relation?

- $\text{Head}(\text{Bob’s Head}, \text{Bob})$

## \[P(x, y)\]
How can you read a binary relation like this?

$x$ is a $P$ of $y$.

What is the arity of a relation?

The number of objects it connects.

What is a function in first-order logic?

A shorthand for representing the only existing related object for many-to-one relations.

Why is $\text{LeftLeg}(\text{Charlie})$ a valid function in first-order logic?

Because the relation $\text{LeftLeg}$ is many-to-one.

Why is the notation for functions and relations such as $\text{YoungestSibling}(\text{Bob})$ confusing?

Because it can represent two differet things:

- The sentence “Bob has a youngest sibling”
- The term representing Bob’s youngest sibling

Why are functions used in first-order logic?

Because they mean you don’t have to name every single object.

What is the symbol for universal quantification?

## \[\forall x\, ...\]
How can you pronounce something like this?

“For all $x$…”

How would you write the sentence that every $\text{King}$ is a $\text{Person}$ in first-order logic?

What is the symbol for existential quantification?

## \[\exists x\, ...\]
How can you pronounce something like this?

“There exists at least one $x$…”