This paper describes a simple new semantics for logic rules, foundedsemantics, and its straightforward extension to another simple new semantics,constraint semantics. The new semantics support unrestricted negation, as wellas unrestricted existential and universal quantifications. They are uniquelyexpressive and intuitive by allowing assumptions about the predicates and rulesto be specified explicitly. They are completely declarative and easy tounderstand and relate cleanly to prior semantics. In addition, foundedsemantics can be computed in linear time in the size of the ground program.
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