Equisatisfiability

Erfüllbarkeitsäquivalenz is a property that can apply between predicate logic formulas.

Two formulas F and G are precisely then erfüllbarkeitsäquivalent if:

Or vice versa:

The two formulas need not be equivalent, and also do not need to be fulfilled by the same interpretations. Erfüllbarkeitsäquivalenz is thus a rather weak property.

Relevant is the Erfüllbarkeitsäquivalenz on proof of unsatisfiability of a predicate logic formula using the Herbrand theory. For this purpose, the formula must first be converted into Skolem, which is only erfüllbarkeitsäquivalent the output formula.

Example

It is a formula ( with the condition that they have neither a tautology nor unsatisfiable ). Then the formulas and erfüllbarkeitsäquivalent but not equivalent.

Transformation into satisfiability 3 -CNF formula

For each formula in m -CNF, that is, So the mold with a maximum literals per disjunction, a satisfiability formula can be constructed in 3 -CNF in polynomial time.

Be with this. As long as there has a clause of this by replacing with

Is a new variable. Any interpretation that and fulfilled fulfilled. Any interpretation that satisfies can be converted to an interpretation which and fulfilled.

• Logic