▁of ▁variables . ▁As ▁a ▁result , ▁equ isat isf i ability ▁is ▁different ▁ ▁from ▁logical ▁equivalence , ▁as ▁two ▁equivalent ▁formula e ▁always ▁have ▁the ▁same ▁models . ▁ ▁E quis atisf i ability ▁is ▁generally ▁used ▁in ▁the ▁context ▁of ▁transl ating ▁formula e , ▁so ▁that ▁one ▁can ▁define ▁a ▁translation ▁to ▁be ▁correct ▁if ▁the ▁original ▁and ▁resulting ▁formula e ▁are ▁equ isat isf i able . ▁Ex amples ▁of ▁transl ations ▁involving ▁this ▁concept ▁are ▁Sk ole m ization ▁and ▁some ▁transl ations ▁into ▁conj unct ive ▁normal ▁form . ▁ ▁Ex amples ▁ ▁A ▁translation ▁from ▁propos itional ▁logic ▁into ▁propos itional ▁logic ▁in ▁which ▁every ▁binary ▁dis j unction ▁ ▁is ▁replaced ▁by ▁, ▁where ▁ ▁is ▁a ▁new ▁variable ▁( one ▁for ▁each ▁replaced ▁dis j unction ) ▁is ▁a ▁transformation ▁in ▁which ▁satisf i ability ▁is ▁preserved : ▁the ▁original ▁and ▁resulting ▁formula e ▁are ▁equ isat isf i able . ▁Note ▁that ▁these ▁two ▁formula e ▁are ▁not ▁equivalent : ▁the ▁first ▁formula ▁has ▁the ▁model ▁in ▁which ▁ ▁is ▁true ▁while ▁ ▁and ▁ ▁are ▁false ▁( the ▁model ' s ▁truth ▁value ▁for ▁ ▁being ▁irrelevant ▁to ▁the ▁truth ▁value ▁of ▁the ▁formula ), ▁but ▁this ▁is ▁not ▁a ▁model ▁of ▁the ▁second ▁formula , ▁in ▁which ▁ ▁has ▁to ▁be ▁true ▁in ▁this ▁case . ▁ ▁References ▁ ▁Category : Met alog ic ▁Category : Model ▁theory ▁Category : Con cept s ▁in ▁logic <0x0A> </s> ▁World s ▁of