A well-formed formula (WFF) is a syntactically correct expression in a formal language. It adheres to the established rules, ensuring…
A variable assignment, sometimes called a variable assignment function, is a crucial interpretation in formal languages for first-order or higher-order…
The upward Löwenheim–Skolem theorem states that if a first-order theory has an infinite model, it has models of arbitrarily large…
Skolem Normal Form (SNF) simplifies first-order logic by eliminating existential quantifiers. It replaces them with Skolem functions, ensuring only universal…
A fundamental theorem in first-order logic. It asserts that if a theory has an infinite model, it possesses models for…
Skolemization is a crucial technique in first-order logic for eliminating existential quantifiers. It involves introducing Skolem functions to preserve logical…
Pure predicate logic, also known as pure first-order logic, is a formal system for reasoning about propositions and their relationships.…
Pure first-order logic is a foundational system in logic, characterized by its exclusion of function symbols and identity. It relies…
A standardized structure for first-order logic where all quantifiers (universal and existential) are moved to the beginning of the formula,…
An extension of first-order logic that incorporates predicates with multiple arguments. This allows for the representation of complex relationships between…