@INPROCEEDINGS{And00transitiveclosure,
    author = {Esra Erdem And and Esra Erdem and Vladimir Lifschitz},
    title = {Transitive Closure, Answer Sets and Predicate Completion},
    booktitle = {Working notes of AAAI Spring Symposium},
    year = {2001},
    pages = {60-65},
    urlN = {tc.pdf},
    abstract = {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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