Abstract
We consider problems of reasoning with a knowledge-base, which is represented by an ordered binary decision diagram (OBDD), for two special cases of general and Horn knowledge-bases. Our main results say that both finding a model of a knowledge-base and deducing from a knowledge-base can be done in linear time for general case, but that abduction is NP-complete even if the knowledge-base is restricted to be Horn. Then, we consider the abduction when its assumption set consists of all propositional literals (i.e., an answer for a given query is allowed to include any positive literals), and show that it can be done in polynomial time if the knowledge-base is Horn, while it remains NP-complete for the general case. Some other solvable cases are also discussed.
This research was partially supported by the Scientific Grant-in-Aid from Ministry of Education, Science, Sports and Culture of Japan.
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Horiyama, T., Ibaraki, T. (2000). Reasoning with Ordered Binary Decision Diagrams. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_11
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DOI: https://doi.org/10.1007/3-540-40996-3_11
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