First-order logic (relevant) Flashcards
What does the FOL do?
Add to the language of TFL
Names =
Lowercase letters
Predicates are…
Not complete sentences by themselves, usually say something about the object
Predicates =
Uppercase letter followed by ‘x,’ e.g. Fx, Gx
Quantifiers
The universal quantifier, the existential quantifier
The universal quantifier
‘Upside down A’x
The existential quantifier
‘Backwards E’x
What does the universal quantifier read as?
For all x/for every x
What does the existential quantifier read as?
For some x/for at least one x
What are predicates usually?
Properties of individuals, they combine with singular terms to make sentences
If a predicate has one gap it is called…
A one place predicate
How can we form two-place predicates?
Removing two singular terms and using two different variables (‘x’ or ‘y’) to represent the two gaps
What are two-place predicates known as?
Relations
Are the terms: nothing/everybody/someone/something names?
No, they aren’t names/singular terms so are expressed by quantifiers
What are domains?
The set of things that we are talking about. Quantifiers range over the domain
