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?
- $\text{Head}(\text{Bob’s Head}, \text{Bob})$
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\[P(x, y)\]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?
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\[\forall x\, ...\]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?
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\[\exists x\, ...\]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?
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\[\neg \exists x P\]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??
\[\neg \exists x\, \neg P\]