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 ∈ S w.r.t. S are defined model-theoretically.
These semantics extend the answer set semantics (AS) and the well-founded semantics with ex-
plicit negation (WFSX) on ELPs, respectively, keeping all of their semantical and computational
characteristics. Our framework supports: (i) local semantics and different points of view, (ii) local
closed-world and open-world assumptions, (iii) scoped negation-as-failure, (iv) restricted propa-
gation of local inconsistencies, and (v) monotonicity of reasoning, for “fully shared” predicates.
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