| Summary: | <p>The purpose of this chapter is to report on work that has been done in the REWERSE project concerning hybrid reasoning with rules and ontologies. Two major streams of work have been pursued within REWERSE. They start from the predominant semantics of non-monotonic rules in logic programming. The one stream was an extension of non-monotonic logic programs under answer set semantics, with query interfaces to external knowledge sources. The other stream, in the spirit of the AL-log approach of enhanced deductive databases, was an extension of Datalog (with the well-founded semantics, which is predominant in the database area). The former stream led to so-called non-monotonic dl-programs and hex-programs, and the latter stream to hybrid well-founded semantics. Further variants and derivations of the formalisms (like a well-founded semantics for dl-programs, respecting probabilistic knowledge, priorities, etc.) have been conceived.</p>
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