Predicate Logic Flashcards
What is predicate logic?
Logic that builds heavily upon the ideas of proposition logic to provide more
What do predicate logic consists of?
Predicates + Logical connective + Quantifies
What is a predicate?
A statement containing variables that describes a property of a thing or a relationship between things
Which is the subject and predicate in the sentence: Aquaman is a movie
Subject: Aquaman
Predicate: is a movie
Which is the subject/object and predicate in the sentence: Smith hates Cats
Subject/Object: Smith, Cats
Predicate: hates
What is the structure of a predication?
It starts with a predicate followed by a set of arguments
Give the predication if the proposition is: Aquaman is a movie
Movie(Aquaman) or M(a)
Give the predication if the proposition is: Smith hates Cats
Hates(Smith, Cats) or H(s,c)
What are arguments in predicate logic?
The letters or variables in the bracket
What are individual variables in predicate logic?
Single letters such as x, y and z in an argument with any value
What is a statement in predicate logic?
The predicate and argument together
What are individual constants in predicate logic?
Single letters representing specific entities (subject/object) in a predication
Individual variables vs Individual constants
Individual variables doesn’t have a constant reference to a specific entity. They can take any value
When does a predication become a proporsition?
When the variables are assigned to specific values, resulting true or false
What are logical connectives?
Connectives that combine predicates together
Examples of logical connectives
if, and, then, not, or, either or, if and only if…
Examples of quantifiers
some, no one, any, all, at least
What are the 2 types of quantifiers?
Existential and Universal
Existential quantifiers
∃ meaning at least one member
Universal quantifiers
∀ meaning all members
How would you write “There is at least one employee who is a programmer”
∃ e ∈ Emp: Programmer(e)
What’s the literal translation for “∃ e ∈ Emp: Programmer(e)”
at least one
employee
is an element/member of
set of employees
such that
employee is a programmer
Other ways to write “∃ e ∈ Emp: Programmer(e)”
There exists an employee, “e”, such that “e” is a programmer OR Some employees are a programmer
How would you write “Every student is at
least 18 years old”
∀ s ∈ Stud: Age(S)>=18
What’s the literal translation for “∀ s ∈ Stud: Age(s)>=18”
Every
student
is an element/member of
the set of students
such that
student is >= 18
