A Trichotomy in the Complexity of Propositional Circumscription

Circumscription is one of the most important and well studied formalisms in the realm of nonmonotonic reasoning. The inference problem for propositional circumscription has been extensively studied from the viewpoint of computational complexity. We prove that there exists a trichotomy for the complexity of the inference problem in propositional variable circumscription. More specifically we prove that every restricted case of the problem is either \(\Pi_{\rm 2}^{\rm P}\)-complete, coNP-complete, or in P.

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