Transitive Closure, Answer Sets and Predicate Completion

Esra Erdem and Vladimir Lifschitz

We prove that the usual logic programming definition of transitive closure is correct under the answer set semantics, and investigate under what conditions it is correct under the completion semantics. That definition is allowed here to be combined with an arbitrary set of rules that may contain negation as failure, not merely with a set of facts. This work is motivated by applications to answer set programming.

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