Abstract
This paper continues the line of research on the representation and compilation of propositional knowledge bases with propositional directed acyclic graphs (PDAG), negation normal forms (NNF), and binary decision diagrams (BDD). The idea is to permit variables with more than two states and to explicitly represent them in their most natural way. The resulting representation languages are analyzed according to their succinctness, supported queries, and supported transformations. The paper shows that most results from PDAGs, NNFs, and BDDs can be generalized to their corresponding multi-state extension. This implies that the entire knowledge compilation map is extensible from propositional to multi-state variables.
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References
Akers, S.B.: Binary decision diagrams. IEEE Transactions on Computers 27(6), 509–516 (1978)
Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers 35(8), 677–691 (1986)
Bryant, R.E.: Symbolic Boolean manipulation with ordered binary decision diagrams. ACM Computing Surveys 24(3), 293–318 (1992)
Darwiche, A.: Decomposable negation normal form. Journal of the ACM 48(4), 608–647 (2001)
Darwiche, A., Marquis, P.: A knowlege compilation map. Journal of Artificial Intelligence Research 17, 229–264 (2002)
Wachter, M., Haenni, R.: Propositional DAGs: a new graph-based language for representing Boolean functions. In: Doherty, P., Mylopoulos, J., Welty, C. (eds.) KR’06, 10th International Conference on Principles of Knowledge Representation and Reasoning, Lake District, U.K., pp. 277–285. AAAI Press, Menlo Park (2006)
Hill, F.J., Peterson, G.R.: Introduction to Switching Theory and Logical Design. John Wiley and Sons, New York (1974)
Lukasiewicz, J., Tarski, A.: Untersuchungen über den Aussagenkalkül. Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie Cl. III 23, 30–50 (1930)
Rosser, J.B., Turquette, A.R.: Many-Valued Logics. North-Holland, Amsterdam (1952)
Wegener, I.: Branching Programs and Binary Decision Diagrams – Theory and Applications. Monographs on Discrete Mathematics and Applications, vol. 56. SIAM, Philadelphia (2000)
Chavira, M., Darwiche, A.: Compiling Bayesian networks with local structure. In: IJCAI’05, 19th International Joint Conference on Artificial Intelligence, Edinburgh, U.K. (2005)
Palacios, H., Bonet, B., Darwiche, A., Geffner, H.: Pruning conformant plans by counting models on compiled d-DNNF representations. In: ICAPS’05, 15th International Conference on Planning and Scheduling, Monterey, USA, pp. 141–150 (2005)
Sang, T., Beame, P., Kautz, H.: Solving Bayesian networks by weighted model counting. In: AAAI’05, 20th National Conference on Artificial Intelligence, Pittsburgh, USA, vol. 1, pp. 475–482 (2005)
Bollig, B., Sauerhoff, M., Sieling, D., Wegener, I.: Binary decision diagrams. In: Crama, Y., Hammer, P. (eds.) Boolean Functions, Volume II (to appear, 2006)
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Wachter, M., Haenni, R. (2007). Multi-state Directed Acyclic Graphs. In: Kobti, Z., Wu, D. (eds) Advances in Artificial Intelligence. Canadian AI 2007. Lecture Notes in Computer Science(), vol 4509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72665-4_40
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DOI: https://doi.org/10.1007/978-3-540-72665-4_40
Publisher Name: Springer, Berlin, Heidelberg
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