first-order logic

Well-Formed Formula (WFF)

A well-formed formula (WFF) is a syntactically correct expression in a formal language. It adheres to the established rules, ensuring…

4 days ago

Variable Assignment in Formal Logic

A variable assignment, sometimes called a variable assignment function, is a crucial interpretation in formal languages for first-order or higher-order…

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Upward Löwenheim–Skolem Theorem

The upward Löwenheim–Skolem theorem states that if a first-order theory has an infinite model, it has models of arbitrarily large…

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Skolem Normal Form in First-Order Logic

Skolem Normal Form (SNF) simplifies first-order logic by eliminating existential quantifiers. It replaces them with Skolem functions, ensuring only universal…

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Skolem-Lowenheim Theorem

A fundamental theorem in first-order logic. It asserts that if a theory has an infinite model, it possesses models for…

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Skolemization in First-Order Logic

Skolemization is a crucial technique in first-order logic for eliminating existential quantifiers. It involves introducing Skolem functions to preserve logical…

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Pure Predicate Logic

Pure predicate logic, also known as pure first-order logic, is a formal system for reasoning about propositions and their relationships.…

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Pure First-Order Logic

Pure first-order logic is a foundational system in logic, characterized by its exclusion of function symbols and identity. It relies…

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Prenex Normal Form

A standardized structure for first-order logic where all quantifiers (universal and existential) are moved to the beginning of the formula,…

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Polyadic First-Order Logic

An extension of first-order logic that incorporates predicates with multiple arguments. This allows for the representation of complex relationships between…

4 days ago