**Introduction to First-Order Logic**

First-order logic, also known as predicate logic, extends propositional logic by introducing variables, quantifiers, and predicates. It allows for a more expressive and precise representation of knowledge and relationships between objects.

**Variables, Quantifiers, and Predicates**

First-order logic uses variables to represent objects, quantifiers such as ∀ (for all) and ∃ (there exists) to quantify objects, and predicates to express properties or relations between objects.

**Syntax and Semantics**

First-order logic has a formal syntax defining the structure of well-formed formulas (WFFs) and semantics specifying the meaning of these formulas in terms of interpretations and truth assignments.

**Inference Rules**

Inference rules in first-order logic allow for deriving new logical consequences from existing premises. Examples include Universal Instantiation, Existential Generalization, Modus Ponens, and Modus Tollens.

**Applications of First-Order Logic**

First-order logic is widely used in artificial intelligence, database systems, automated theorem proving, natural language processing, and formal verification of software and hardware systems.