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Which property does Skolemization preserve when convertin... | QuestionStock

Representative image for question: Which property does Skolemization preserve when converting a first-order formula to Skolem normal form?

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Logic

Which property does Skolemization preserve when converting a first-order formula to Skolem normal form?

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Which property does Skolemization preserve when converting a first-order formula to Skolem normal form?

Options:

Logical equivalence to the original formula.
Satisfiability (i.e., equisatisfiability) with respect to the original formula.
Preservation of all models pointwise.
Preservation of the formula's free variables only.

Correct answer: Satisfiability (i.e., equisatisfiability) with respect to the original formula.

Explanation: Skolemization yields an equisatisfiable formula: it preserves satisfiability but not full logical equivalence, by replacing existentials with Skolem functions (Skolem, 1920s).

Created 2026-03-10T18:49:55.949Z. Updated 2026-03-10T18:49:55.949Z.