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??
$$ \forall $$
$$\forall x, …$$ 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??
$$ \forall x, \text{King}(x) \implies \text{Person}(x) $$
What is the symbol for existential quantification??
$$ \exists $$
$$\exists x, …$$ How can you pronounce something like this??
“There exists at least one $x$…”
How would you write the sentence that there exists at least one $\text{Crown}$ that is also on $\text{John’s}$ head??
$$ \exists x, \text{Crown}(x) \land \text{OnHead}(x, \text{John}) $$
$$\neg \exists x P$$ Can you rewrite using this a universal quantifier??
$$ \forall x,\neg P $$
$$\neg \forall x P$$ Can you rewrite this using an existential quantifier??
$$ \exists x, \neg P $$
$$\exists x P$$ Can you rewrite this using a universal quantifier??
$$ \neg \forall x, \neg P $$
$$\forall x P$$ Can you rewrite this using an existential quantifier??
$$ \neg \exists x, \neg P $$
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date: 2021-04-04 10:40
tags:
- '@?notes'
- '@?aima'
- '@?public'
title: 'AIMA: First-Order Logic'