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Abstract. We give an overview of the coinductive logic programming paradigm. We discuss its applications to modeling ω-automata, model checking, verification, non-monotonic reasoning, developing SAT solvers, etc. We also discuss future research directions.

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Answer Set Programming (ASP) is a powerful paradigm based on logic programming for non-monotonic reasoning. Current ASP implementations are restricted to "grounded range-restricted function-free normal programs" and use an evaluation strategy that is "bottom-up" (i.e., not goal-driven). Recent introduction of coinductive Logic Programming (co-LP) has allowed the development of topdown goal evaluation strategies for ASP. In this paper we present this novel goaldirected, top-down approach to executing predicate answer set programs with co-LP. Our method eliminates the need for grounding, allows functions, and effectively handles a large class of predicate answer set programs including possibly infinite ones.