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We introduce negation into coinductive logic programming (coLP) via what we term Coinductive SLDNF (coSLDNF) resolution. We present declarative and operational semantics of coSLDNF resolution and present their equivalence under the restriction of rationality and its applications to Answer Set Programming (ASP). ASP is a powerful programming paradigm for performing nonmonotonic reasoning within logic programming. The current state of ASP solvers has been restricted to "grounded range restricted functionfree normal programs", with a "bottomup" evaluation strategy (that is, not goal driven) until now. The introduction of coLP with coSLDNF resolution has enabled the development of topdown goal evaluation strategies for ASP. We present a novel and innovative approach to solving ASP programs with coLP. Our method eliminates the need for grounding, allows functions, and effectively handles a large class of predicate ASP programs including possibly infinite ASP programs. Moreover, it is goaldirected and topdown execution method that provides an innovative and attractive alternative to current ASP solver technology.
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