Model theory | Normal forms (logic)

Skolem normal form

In mathematical logic, a formula of first-order logic is in Skolem normal form if it is in prenex normal form with only universal first-order quantifiers. Every first-order formula may be converted into Skolem normal form while not changing its satisfiability via a process called Skolemization (sometimes spelled Skolemnization). The resulting formula is not necessarily equivalent to the original one, but is equisatisfiable with it: it is satisfiable if and only if the original one is satisfiable. Reduction to Skolem normal form is a method for removing existential quantifiers from formal logic statements, often performed as the first step in an automated theorem prover. (Wikipedia).

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Resolution (logic) | Scope (logic) | Up to | Herbrandization | Clause (logic) | Prime model | Automated theorem proving | Model theory | Elementary equivalence | Theory (mathematical logic) | Well-formed formula | Arity | Atomic model (mathematical logic) | Method of analytic tableaux | Second-order logic | Prenex normal form | Drinker paradox | Substructure (mathematics) | Existential quantification | Predicate functor logic | Mathematical logic | Universal quantification | Satisfiability | Logical equivalence | Thoralf Skolem | Model complete theory | First-order logic