Abstract
The ability to “define” propositions using default assumptions about the same propositions is identified as a significant source of computational complexity in nonmonotonic reasoning. If such constructs are not allowed, i.e. the knowledge base is stratified, a notable 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 the knowledge base. As an example quadratic and linear time algorithms are derived for specific subclasses of stratified autoepistemic theories. The results are shown to imply efficient reasoning methods for stratified cases of default logic, logic programs, truth maintenance systems, and nonmonotonic modal logics.
This paper was first published as (Niemelä and Rintanen, 1992).
Ilkka Niemelä gratefully acknowledges the support from the following foundations: Foundation of Technology, Jenny and Antti Wihuri Foundation, Emil Aaltonen Foundation, Alfred Kordelin Foundation, Heikki and Hilma Honkanen Foundation.
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Niemelä, I., Rintanen, J. (1994). On the impact of stratification on the complexity of nonmonotonic reasoning. In: Lakemeyer, G., Nebel, B. (eds) Foundations of Knowledge Representation and Reasoning. Lecture Notes in Computer Science, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58107-3_16
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DOI: https://doi.org/10.1007/3-540-58107-3_16
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