We introduce negation into coinductive logic programming (co-LP) via what we term Coinductive SLDNF (co-SLDNF) resolution. We present declarative and operational semantics of co-SLDNF 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 non-monotonic reasoning within logic programming. The current state of ASP solvers has been restricted to "grounded range- restricted function-free normal programs", with a "bottom-up" evaluation strategy (that is, not goal- driven) until now. The introduction of co-LP with co-SLDNF resolution has enabled the development of top-down goal evaluation strategies for ASP. We present a novel and innovative approach to solving ASP programs with co-LP. 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 goal-directed and top-down execution method that provides an innovative and attractive alternative to current ASP solver technology.

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