Abstract
We study syntactical merging operations that are defined semantically by means of the Hamming distance between valuations; more precisely, we investigate the Σ-semantics, Gmax-semantics and max-semantics. We work with a logical language containing merging operators as connectives, as opposed to the metalanguage operations of the literature. We capture these merging operators as programs of Dynamic Logic of Propositional Assignments DL-PA. This provides a syntactical characterisation of the three semantically defined merging operators, and a proof system for DL-PA therefore also provides a proof system for these merging operators. We explain how PSPACE membership of the model checking and satisfiability problem of star-free DL-PA can be extended to the variant of DL-PA where symbolic disjunctions that are parametrised by sets (that are not defined as abbreviations, but are proper connectives) are built into the language. As our merging operators can be polynomially embedded into this variant of DL-PA, we obtain that both the model checking and the satisfiability problem of a formula containing possibly nested merging operators is in PSPACE.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Balbiani, P., Herzig, A., Troquard, N.: Dynamic logic of propositional assignments: A well-behaved variant of PDL. In: Kupferman, O. (ed.) Logic in Computer Science (LICS), New Orleans, June 25-28, IEEE (2013), http://www.ieee.org/
Baral, C., Kraus, S., Minker, J., Subrahmanian, V.S.: Combining knowledge bases consisting of first-order theories. Computational Intelligence 8, 45–71 (1992)
Darwiche, A., Pearl, J.: On the logic of iterated belief revision. Artificial Intelligence 89(1), 1–29 (1997)
Delgrande, J.P., Schaub, T., Tompits, H., Woltran, S.: On computing belief change operations using quantified boolean formulas. Journal of Logic and Computation 14(6), 801–826 (2004)
Gorogiannis, N., Hunter, A.: Implementing semantic merging operators using binary decision diagrams. International Journal of Approximate Reasoning 49(1), 234–251 (2008)
Gorogiannis, N., Hunter, A.: Merging first-order knowledge using dilation operators. In: Hartmann, S., Kern-Isberner, G. (eds.) FoIKS 2008. LNCS, vol. 4932, pp. 132–150. Springer, Heidelberg (2008)
Harel, D.: Dynamic logic. In: Gabbay, D.M., Günthner, F. (eds.) Handbook of Philosophical Logic, vol. II, pp. 497–604. D. Reidel, Dordrecht (1984)
Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press (2000)
Herzig, A., Lorini, E., Moisan, F., Troquard, N.: A dynamic logic of normative systems. In: Walsh, T. (ed.) International Joint Conference on Artificial Intelligence (IJCAI), IJCAI/AAAI, Barcelona, pp. 228–233 (2011), Erratum at http://www.irit.fr/~Andreas.Herzig/P/Ijcai11.html
van der Hoek, W., Walther, D., Wooldridge, M.: On the logic of cooperation and the transfer of control. J. of AI Research (JAIR) 37, 437–477 (2010)
van der Hoek, W., Wooldridge, M.: On the dynamics of delegation, cooperation and control: A logical account. In: Proc. AAMAS 2005 (2005)
van der Hoek, W., Wooldridge, M.: On the logic of cooperation and propositional control. Artif. Intell. 164(1-2), 81–119 (2005)
Konieczny, S.: On the difference between merging knowledge bases and combining them. In: KR, pp. 135–144 (2000)
Konieczny, S., Pérez, R.P.: Logic based merging. Journal of Philosophical Logic 40(2), 239–270 (2011)
Konieczny, S., Pérez, R.P.: On the logic of merging. In: Proc. 6th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 1998), pp. 488–498. Morgan Kaufmann (1998)
Konieczny, S., Pino Pérez, R.: Merging with integrity constraints. In: Hunter, A., Parsons, S. (eds.) ECSQARU 1999. LNCS (LNAI), vol. 1638, pp. 233–244. Springer, Heidelberg (1999)
Lang, J., Marquis, P.: Reasoning under inconsistency: A forgetting-based approach. Artificial Intelligence 174(12), 799–823 (2010)
Liberatore, P., Schaerf, M.: Brels: A system for the integration of knowledge bases. In: KR, pp. 145–152. Citeseer (2000)
Lin, J., Mendelzon, A.: Knowledge base merging by majority. In: Pareschi, R., Fronhoefer, B. (eds.) Dynamic Worlds: From the Frame Problem to Knowledge Management, Kluwer Academic (1999)
Revesz, P.Z.: On the semantics of theory change: arbitration between old and new information. In: Proceedings of the Twelfth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, PODS 1993, pp. 71–82. ACM, New York (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Herzig, A., Pozos-Parra, P., Schwarzentruber, F. (2014). Belief Merging in Dynamic Logic of Propositional Assignments. In: Beierle, C., Meghini, C. (eds) Foundations of Information and Knowledge Systems. FoIKS 2014. Lecture Notes in Computer Science, vol 8367. Springer, Cham. https://doi.org/10.1007/978-3-319-04939-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-04939-7_19
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04938-0
Online ISBN: 978-3-319-04939-7
eBook Packages: Computer ScienceComputer Science (R0)