predicaatvariabele

A predicate variable is a symbol used in logic and mathematics to represent a predicate. A predicate is a statement about a subject that can be either true or false. In formal logic, predicate variables are typically denoted by uppercase letters, often followed by a subscript if multiple predicates are being used. For example, P(x) might represent "x is a prime number," where P is the predicate variable and x is an argument.

Predicate variables allow for the generalization of logical statements. Instead of stating "If Socrates is a man, then Socrates is mortal," we can use a predicate variable to express a general truth: "For all x, if x is a man, then x is mortal." This is written as ∀x (Man(x) → Mortal(x)). Here, Man and Mortal are predicate variables.

In higher-order logic, variables can also range over predicates themselves. This means a variable can stand for a predicate that takes other predicates as arguments. This allows for more complex and abstract logical reasoning, enabling the expression of properties of properties or relationships between predicates. Predicate variables are fundamental to the expressive power of formal languages and are crucial in areas like automated theorem proving and the formalization of mathematics.