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We investigate the problem of reasoning in the propositional fragment ofMBNF, the logic of minimal belief and negation as failure introduced byLifschitz, which can be considered as a unifying framework for severalnonmonotonic formalisms, including default logic, autoepistemic logic,circumscription, epistemic queries, and logic programming. We characterize thecomplexity and provide algorithms for reasoning in propositional MBNF. Inparticular, we show that entailment in propositional MBNF lies at the thirdlevel of the polynomial hierarchy, hence it is harder than reasoning in all theabove mentioned propositional formalisms for nonmonotonic reasoning. We alsoprove the exact correspondence between negation as failure in MBNF and negativeintrospection in Moore's autoepistemic logic.

Reasoning about Minimal Belief and Negation as Failure