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- Skolem_normal_form abstract "In mathematical logic, reduction to Skolem normal form (SNF) is a method for removing existential quantifiers from formal logic statements, often performed as the first step in an automated theorem prover. A formula of first-order logic is in Skolem normal form (named after Thoralf Skolem) if it is in prenex normal form with only universal first-order quantifiers. Every first-order formula can 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.The simplest form of Skolemization is for existentially quantified variables which are not inside the scope of a universal quantifier. These can simply be replaced by creating new constants. For example, can be changed to , where is a new constant (does not occur anywhere else in the formula).More generally, Skolemization is performed by replacing every existentially quantified variable with a term whose function symbol is new. The variables of this term are as follows. If the formula is in prenex normal form, are the variables that are universally quantified and whose quantifiers precede that of . In general, they are the variables that are universally quantified and such that occurs in the scope of their quantifiers. The function introduced in this process is called a Skolem function (or Skolem constant if it is of zero arity) and the term is called a Skolem term.As an example, the formula is not in Skolem normal form because it contains the existential quantifier . Skolemization replaces with , where is a new function symbol, and removes the quantification over . The resulting formula is . The Skolem term contains but not because the quantifier to be removed is in the scope of but not in that of since this formula is in prenex normal form, this is equivalent to saying that, in the list of quantifers, precedes while does not. The formula obtained by this transformation is satisfiable if and only if the original formula is.".
- Skolem_normal_form wikiPageExternalLink Skolemization.
- Skolem_normal_form wikiPageExternalLink Skolemization.html.
- Skolem_normal_form wikiPageID "421074".
- Skolem_normal_form wikiPageRevisionID "586710187".
- Skolem_normal_form date "August 2013".
- Skolem_normal_form hasPhotoCollection Skolem_normal_form.
- Skolem_normal_form id "p/s085740".
- Skolem_normal_form reason "If the formula is not in prenex form, also some existentially quantified variables may belong to the x, e.g. the formula ¬∃x ¬∃y. p should be skolemized to is equivalent to ¬∃x. ¬ p.".
- Skolem_normal_form title "Skolem function".
- Skolem_normal_form title "SkolemizedForm".
- Skolem_normal_form urlname "SkolemizedForm".
- Skolem_normal_form subject Category:Model_theory.
- Skolem_normal_form subject Category:Normal_forms_(logic).
- Skolem_normal_form comment "In mathematical logic, reduction to Skolem normal form (SNF) is a method for removing existential quantifiers from formal logic statements, often performed as the first step in an automated theorem prover. A formula of first-order logic is in Skolem normal form (named after Thoralf Skolem) if it is in prenex normal form with only universal first-order quantifiers.".
- Skolem_normal_form label "Forma normal de Skolem".
- Skolem_normal_form label "Skolem normal form".
- Skolem_normal_form label "Skolemform".
- Skolem_normal_form label "Skolemizacja".
- Skolem_normal_form label "Skolemização".
- Skolem_normal_form label "Skolemizzazione".
- Skolem_normal_form label "Skolémisation".
- Skolem_normal_form label "スコーレム標準形".
- Skolem_normal_form label "斯科伦范式".
- Skolem_normal_form sameAs Skolemform.
- Skolem_normal_form sameAs Forma_normal_de_Skolem.
- Skolem_normal_form sameAs Skolémisation.
- Skolem_normal_form sameAs Skolemizzazione.
- Skolem_normal_form sameAs スコーレム標準形.
- Skolem_normal_form sameAs Skolemizacja.
- Skolem_normal_form sameAs Skolemização.
- Skolem_normal_form sameAs m.026gh8.
- Skolem_normal_form sameAs Q1090524.
- Skolem_normal_form sameAs Q1090524.
- Skolem_normal_form wasDerivedFrom Skolem_normal_form?oldid=586710187.
- Skolem_normal_form isPrimaryTopicOf Skolem_normal_form.