Propositional logic · Definition
Logical operator
Before you start you need to know
A logical operator is a rule that combines propositions to form others. Here we see what it does, how many inputs it takes and how it is classified.
Definition
A logical operator \(L\) is a function that, for some integer \(n\geq 1\), takes \(n\) propositions and produces a proposition.
A logical operator is a rule that takes one or more propositions and produces another proposition. The number of propositions it takes is called its arity.
When it takes one proposition it is unary; when it takes two it is binary. The symbols \(\neg P\), \(P\land Q\) and \(P\lor Q\) serve as examples of those two possibilities: one takes one input and the other two take two.
Arity describes the shape of the rule, not its truth value. To know what each operator does we must later study its particular tables and properties.
Think about it
If a rule takes three propositions, what does its arity indicate?
That it is a ternary operator: its input is made of three propositions.
Exercises 10
- What does a logical operator do?
- A unary operator takes...
- A binary operator takes...
- Which expression uses a unary operator?
- Which expression uses a binary operator?
- What is a logical operator used for inside a formula?
- Which one is a unary operator?
- Which of these symbols is a binary operator?
- The arity of an operator indicates...
- Which operator transforms a single proposition?
References
- Frederic P. Schuller, Lectures on the Geometrical Anatomy of Theoretical Physics · Lecture 1, Introduction / Logic of Propositions and Predicates, YouTube, 2015.