Lecture 2: Logic 2 Flashcards
x is a prime number
is an example of
A declarative sentence but NOt a proposition because its truth value varies along with x
“X is a prime number is an instance”
Of a predicate
Predicates express…
Properties of objects (unary predicates: require 1 input) or relations between objects (binary, ternary, etc.)
Predicates are usually denoted with
Uppercase letters, followed by their input labels in brackets
What are the two ways of turning a predicate into a proposition
- Evaluating the predicate, that is, replacing each variable with a constant value
- Quantifying the predicate, that is, asserting that a predicate is true for some, or for all, objects of the universe
Assigning a predicate values turns it into …
A proposition
Example of turning a predicate into a proposition
The alphabet of predicate logic is made of
Predicate logic is an extension of…
Propositional logic, it “contains” propositional logic
Propositions can be thought of as …
The preidates with arity 0
What is the precedence of predicates?
Quantifiers take precedence over all connectives
What is the translation of
“All men are mortal. Socrates is a man. THEREFORE Socrates is mortal”
into propositional logic?
What is the translation of
“All men are mortal. Socrates is a man. THEREFORE Socrates is mortal”
into predicate logic?
What is the translation of
“All men are mortal. Socrates is a man. THEREFORE Socrates is mortal”
into predicate logic? (Using more meaningful names)
