Nested expressions in logic programs

We extend the answer set semantics to a class of logic programs with nested expressions permitted in the bodies and heads of rules. These expressions are formed from literals using negation as failure, conjunction (,) and disjunction (;) that can be nested arbitrarily. Conditional expressions are introduced as abbreviations. The study of equivalent transformations of programs with nested expressions shows that any such program is equivalent to a set of disjunctive rules, possibly with negation as failure in the heads. The generalized answer set semantics is related to the Lloyd–Topor generalization of Clark’s completion and to the logic of minimal belief and negation as failure. This revised version was published online in June 2006 with corrections to the Cover Date.