It is introduced a new algebra \((A, \otimes , \oplus , *, \rightharpoonup , 0, 1)\) called \(L_PG\)-algebra if \((A, \otimes , \oplus , *, 0, 1)\) is \(L_P\)-algebra (i.e. an algebra from the variety generated by perfect MV-algebras) and \((A,\rightharpoonup , 0, 1)\) is a Gödel algebra (i.e. Heyting algebra satisfying the identity \((x \rightharpoonup y ) \vee (y \rightharpoonup x ) =1)\). The lattice of congruences of an \(L_PG\) -algebra \((A, \otimes , \oplus , *, \rightharpoonup , 0, 1)\) is isomorphic to the lattice of Skolem filters (i.e. special type of MV-filters) of the MV-algebra \((A, \otimes , \oplus , *, 0, 1)\). The variety \(\mathbf {L_PG}\) of \(L_PG\) -algebras is generated by the algebras \((C, \otimes , \oplus , *, \rightharpoonup , 0, 1)\) where \((C, \otimes , \oplus , *, 0, 1)\) is Chang MV-algebra. Any \(L_PG\) -algebra is bi-Heyting algebra. The set of theorems of the logic \(L_PG\) is recursively enumerable. Moreover, we describe finitely generated free \(L_PG\)-algebras.

它引入了一个新的代数\((A, \otimes , \oplus , *, \rightharpoonup , 0, 1)\)称为\(L_PG\) -algebra if \((A, \otimes , \oplus , *, 0, 1)\)是\(L_P\) -代数（即由完美MV -代数生成的品种的代数）并且\((A,\rightharpoonup , 0, 1)\)是哥德尔代数（即 Heyting代数满足身份\((x \rightharpoonup y ) \vee (y \rightharpoonup x ) =1)\)。\(L_PG\) -代数\((A, \otimes , \oplus , *, \rightharpoonup , 0, 1)\) 的同余格同构于 Skolem 滤波器的格（即特殊类型的MV-filters) 的MV -algebra \((A, \otimes , \oplus , *, 0, 1)\)。\(L_PG\ ) -代数的多样性\(\mathbf {L_PG}\)由代数\((C, \otimes , \oplus , *, \rightharpoonup , 0, 1)\)生成，其中\(( C, \otimes , \oplus , *, 0, 1)\)是 Chang MV -代数。任何\(L_PG\) -代数都是双海廷代数。逻辑\(L_PG\)的定理集是递归可枚举的。此外，我们描述了有限生成的自由\(L_PG\) -代数。