Primary Normal Forms Applied to Belief Fusion

• Jerusa Marchi UFSC
• Guilherme Bittencourt UFSC
• Laurent Perrussel Université Toulouse I

Abstract

In knowledge based systems, belief merging aims to aggregate possible conflicting pieces of information that arrive from different sources. The quality of the resulting set is usually considered in terms of a closeness criterion between the initial belief set and an integrity constraint with respect to the aim of the merging procedure. The notion of distance between belief sets is thus a crucial issue when we face the merging problem. The aim of this paper is twofold: introduce a syntactical way to calculate distances and propose a new distance that considers the importance of each proposicional symbol in the belief set.

References

Bittencourt, G. (1998). Concurrent inference through dual transformation. Logic Journal of the IGPL, 6(6):795–834.

Bittencourt, G., Marchi, J., and Padilha, R. S. (2003). A Syntactic Approach to Satisfaction. In Konev, B. and Schimidt, R., editors, 4th International Workshop on the Implementation of Logic (LPAR03), pages 18–32. University of Liverpool and University of Manchester.

Bittencourt, G., Perrussel, L., and Marchi, J. (2004). A syntactical approach to revision. In Mántaras, R. L. and Saitta, L., editors, Proceedings of the 16th Europ. Conf. on Artificial Intelligence (ECAI’04), pages 788–792, Valencia, Spain. IOS Press.

Dalal, M. (1988). Investigations Into a Theory of Knowledge Base Revision: Preliminary Report. In Rosenbloom, P. and Szolovits, P., editors, Proceedings of the 7th National Conference on Artificial Intelligence (AAAI’98), volume 2, pages 475–479, Menlo Park, California. AAAI Press.

Darwiche, A. and Marquis, P. (2001). A Perspective on Knowledge Compilation. In Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI’01), pages 175–182, Seattle, Washington, USA.

Fourman, M. (2000). Propositional planning. In AIPS-Workshop on ModelTheoretic Approaches to Planning, pages 10–17.

Konieczny, S. and Pérez, R. P. (2002). Merging information under constraints: a logical framework. Journal of Logic and Computation, 12(5):773–808.

Liberatore, P. and Schaerf, M. (1995). Arbitration: A commutative operator for belief revision. In Proceedings of the Second World Conference on the Fundamentals of Artificial Intelligence (WOCFAI’1995, pages 217–228.

Liberatore, P. and Schaerf, M. (1998). Arbitration (or how to merge knowledge bases). IEEE Transactions on Knowledge and Data Engineering, 10(1):76–90.

Lin, J. and Mendelzon, A. O. (1999). Knowledge base merging by majority. In In Dynamic Worlds: From the Frame Problem to Knowledge Management. Kluwer.

Marchi, J., Bittencourt, G., and Perrussel, L. (2005). A syntactical approach to belief update. In Gelbukh, A., Álvaro Albornoz, and Terashima-Marín, H., editors, Proceedings of the Mexican International Conference on Artificial Intelligence (MICAI’05), pages 142–151, Monterrey, Mexico. Springer Verlag LNAI 3789.

Perrussel, L., Marchi, J., and Bittencourt, G. (2008). Quantum-based belief merging. In Proceedings of the 11th Ibero-American Conference on AI (IBERAMIA’08), pages 21–30, Lisbon, Portugal. Springer-Verlag.

Revesz, P. Z. (1993). On the semantics of theory change: Arbitration between old and new information. In In Proceedings of the Twelfth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Databases, pages 71–82.