Expressiveness vs. Complexity in Nonmonotonic Knowledge Bases: Propositional Case

We study the trade-off between the expressive abilities and the complexity of reasoning in propositional nonmonotonic knowledge bases. We first analyze, in an expressive epistemic modal framework, the most popular forms of nonmonotonic mechanisms used in knowledge representation: in particular, we prove that epistemic queries and epistemic integrity constraints are naturally expressed through the notion of negation as failure. Based on the above analysis, we then characterize the complexity of reasoning with different subsets of such nonmonotonic constructs. This characterization induces a complexity based classification of the various forms of nonmonotonic reasoning considered: in particular, we prove that negation as failure is computationally harder than epistemic disjunction, which apparently contradicts previous complexity results obtained in the logic programming setting.