A conditional knowledge base R contains defeasible rules of the form "If A, then usually B". For the notion of c-representations, a skeptical inference relation taking all c-representations of R into account has been suggested. In this paper, we propose a 3-phase compilation scheme for both knowledge bases and skeptical queries to constraint satisfaction problems. In addition to skeptical c-inference, we show that also credulous and weakly skeptical c-inference can be modelled as a constraint satisfaction problem, and that the compilation scheme can be extended to such queries. For each compilation step, we prove its soundness and completeness, and demonstrate significant efficiency benefits when querying the compiled version of R. These findings are also supported by experiments with the software system InfOCF that employs the proposed compilation scheme.
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