We present a principled framework for modular Web rule bases, called MWeb. According to this framework, each predicate defined in a rule base is characterized by its defining reasoning mode, scope, and exporting rule base list. Each predicate used in a rule base is characterized by its requesting reasoning mode and importing rule base list. For legal MWeb modular rule bases S, the MWebAS and MWebWFS semantics of each rule base s ε S with respect to S are defined model-theoretically. These semantics extend the answer set semantics (AS) and the well-founded semantics with explicit negation (WFSX) on ELPs, respectively, keeping all of their semantical and computational characteristics. Our framework supports: (1) local semantics and different points of view, (2) local closed-world and open-world assumptions, (3) scoped negation-as-failure, (4) restricted propagation of local inconsistencies, and (5) monotonicity of reasoning, for fully shared predicates.