Predicate logic · Definition
Predicate
Before you start you need to know
A predicate is an expression with variables that, once given values, becomes a statement that is either true or false.
Definition
A predicate \(P(x)\) is an expression with free variables that becomes a proposition when values are assigned to them.
A predicate, also called a "function with truth values", is an expression whose truth value depends on one or more variables. As long as those variables remain free, the expression does not determine a complete proposition.
When values are assigned to all its variables, the predicate becomes a proposition and acquires a truth value.
Predicate logic extends propositional logic because it allows talking about objects, properties and relations within a domain.
Think about it
Why is x > 2 not yet a complete proposition?
Because its truth value depends on the value assigned to x.
Exercises 10
- The truth value of a predicate depends on...
- When all its variables are fixed, a predicate becomes...
- Which one is a predicate of two variables?
- In predicate logic, the variables at the start...
- Which example depends on the value of x?
- A predicate becomes a proposition when...
- P(x): x²=4 is a predicate because...
- Which one is an instance of the predicate P(x): x>0?
- Which of these expressions is an open predicate?
- When a free variable is quantified, the predicate becomes...
What comes next
References
- Frederic P. Schuller, Lectures on the Geometrical Anatomy of Theoretical Physics · Lecture 1, Introduction / Logic of Propositions and Predicates, YouTube, 2015.