On the Impact of Stratification on the Complexity of Nonmonotonic Reasoning

This paper investigates the problem of finding subclasses of nonmonotonic reasoning which can be implemented efficiently. The ability to “define” propositions using default assumptions about the same propositions is identified as a major source of computational complexity in nonmonotonic reasoning. If such constructs are not allowed, i.e. stratified knowledge bases are considered, a significant computational advantage is obtained. This is demonstrated by developing an iterative algorithm for propositional stratified autoepistemic theories the complexity of which is dominated by required classical reasoning. Thus efficient subclasses of stratified nonmonotonic reasoning can be obtained by further restricting the form of sentences in a knowledge base. As an example quadratic and linear time algorithms for specific subclasses of stratified autoepistemic theories are derived. The results are shown to imply efficient reasoning methods for stratified cases of default logic, logic programs, truth maintenance systems, and nonmonotonic modal logics.