Traditionally, a logic program is built up to reason about atomic first-order formulas. The key idea of parametrized logic program- ming is that, instead of atomic first-order formulas, a parametrized logic program reasons about formulas of a given parameter logic. Of course, the main challenge is to define the semantics of such general programs. In this work we introduce the novel definitions along with some motivating examples. This approach allows us to prove general results that can be instantiated for every particular choice of the parameter logic. Impor- tant general results we can prove include the existence of semantics and the alternating fix-point theorem of well-founded semantics. To reenforce the soundness of our general framework we show that some known approaches in the literature of logic programming, such as paraconsistent answer-sets and the MKNF semantics for hybrid knowledge bases, are obtained as particular choices of the parameter logic.