Predicate Logic

Predicate logic, also known as predicate calculus or first-order logic, is a formal system in mathematical logic that is distinguished from propositional logic by the inclusion of quantifiers and predicates.

Predicates

In predicate logic, a predicate is a symbol or string of symbols that can be true or false, depending on the values of its variables. Predicates are often thought of as functions that return a truth value.

For example, we could have a predicate P(x) that represents "x is a cat". If x is "Fluffy", and Fluffy is a cat, then P(Fluffy) is true.

Quantifiers

Quantifiers are used to describe variables in mathematical statements. The two main quantifiers are:

2. Existential Quantifier (∃): This is read as "there exists". For example, ∃x P(x) means "there exists an x such that P(x) is true", or "P(x) is true for at least one x".

Usage

Predicate logic is used in a wide range of fields, including mathematics, philosophy, linguistics, and computer science. In mathematics, it's often used to state theorems and definitions. In computer science, it's used in database systems, programming languages, and artificial intelligence.

The introduction of predicates and quantifiers allows us to express more complex ideas than we can with propositional logic alone.