In the framework of description logics, the theories and their related algorithms of conservative extensions, modularity and module extraction are the core notions and vital tools in engineering semantic Web construction, ontology construction, ontology merging and reuse. Among other important contributions in this area, Lutz, et al. have shown that the conservative extension problem for ALC is decidable but its complexity is 2ExpTime-complete while the complexity of the deciding algorithm for light-weight εL is 1ExpTime-complete. Their deciding algorithms are basically depends on tableau algorithm which is substantially a reasoning mechanism in first-order predicate logic. Although, theoretically speaking, those results and algorithms are significant and valuable, both existing theories and methods appear to be complicated, difficult to understand, and hard to implement by engineers working on the semantic Web and ontology construction. This paper will not discuss and analyze the current theories and their algorithms. Instead, it independently proposes a second-order linear reasoning mechanism for all members of DL-Lite family. A proof of the completeness of the second-order deduction system is provided. The proposed mechanism is intuitive, easy to manipulate, and much easier to implement in the engineering sector. It is uniformly applicable for members of DL-Lite family such as εL, FL₀, FL_ε, and vL. Most of all, this system is consistent with graph deduction that facilitates design and construction of the necessary graphs by using space to exchange with time cost. As a result, the time complexity is reduced significantly such that if the space and deduction graphs are sophisticatedly equipped, the deciding time can be reduced topolynomial.