predikátlogikában

Predikátlogika, also known as first-order logic, is a formal system used in logic and mathematics to study quantified and predicate statements. Unlike propositional logic, which deals with simple propositions and their logical connectives, predikátlogika introduces the concepts of predicates, variables, and quantifiers.

Predicates are properties or relations that can be applied to objects. For example, in the statement "Socrates is mortal," "is mortal" is a predicate. Variables, such as x or y, represent objects in a domain. Quantifiers, specifically the universal quantifier (for all, denoted by $\forall$) and the existential quantifier (there exists, denoted by $\exists$), allow us to make statements about collections of objects. For instance, "For all x, if x is a human, then x is mortal" is a statement that can be expressed in predikátlogika.

The language of predikátlogika consists of terms (variables, constants, and functions applied to terms), predicates, logical connectives (and, or, not, implies), and quantifiers. Formulas are built from these components. Predikátlogika provides a framework for expressing complex logical relationships and is fundamental to fields such as computer science, artificial intelligence, and mathematical proof. Its expressive power allows for a more nuanced analysis of statements than propositional logic.