Abstract
In this article we explore multiple change operators, i.e., operators in which the epistemic input is a set of sentences instead of a single sentence. We propose two types of change: prioritized change, in which the input set is fully accepted, and symmetric change, where both the epistemic state and the epistemic input are equally treated. In both kinds of operators we propose a set of postulates and we present different constructions: kernel changes and partial meet changes.
Similar content being viewed by others
References
Alchourrón, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic, 50, 510–530.
Alchourrón, C., & Makinson, D. (1986). Maps between different kinds of contraction function: The finite case. Studia Logica, 45, 187–198.
Bienvenu, M. (2009). Prime implicates and prime implicants: From propositional to modal logic. Journal Artificial Intelligence Research (JAIR), 36, 71–128.
Bienvenu, M., Herzig, A., & Qi, G. (2008). Prime implicate-based belief revision operators. In 18th European conference on artificial intelligence, ECAI’2008 (pp. 741–742).
Bittencourt, G., Perrussel, L., & Marchi, J. (2004). A syntactical approach to revision. In 16th Eureopean conference on artificial intelligence, ECAI’2004 (pp. 788–792).
Darwiche, A., & Marquis, P. (2001). A perspective on knowledge compilation. In Seventeenth international joint conference on artificial intelligence, IJCAI 2001 (pp. 175–182).
Delgrande, J. P., Schaub, T., Tompits, H., & Woltran, S. (2008). Belief revision of logic programs under answer set semantics. In G. Brewka, & Lang, J. (Eds.), Proceedings of the eleventh international conference, KR 2008 (pp. 411–421). AAAI Press.
Doyle, J. (1979). A truth maintenance system. Artificial Intelligence, 12, 231–272.
Doyle, J. (1992). Reason maintenance and belief revision: Foundations versus coherence theories. In P. Gärdenfors (Ed.), Belief revision (pp. 29–51). Cambridge University Press.
Falappa, M. A., Fermé, E. L., & Kern-Isberner, G. (2006). On the logic of theory change: Relations between incision and selection functions. In Proceedings of ECAI 2006 (pp. 402–406).
Falappa, M. A., García, A. J., & Simari, G. R. (2004). Belief dynamics and defeasible argumentation in rational agents. In Proceedings of NMR 2004 (pp. 164–170).
Falappa, M. A., Kern-Isberner, G., & Simari, G. R. (2002). Belief Revision, Explanations and Defeasible Reasoning. Artificial Intelligence Journal, 141, 1–28.
Falappa, M. A., Kern-Isberner, G., & Simari, G. R. (2009). Argumentation in artificial intelligence. In I. Rahwan, G. R. Simari (Eds.), Belief revision and argumentation theory (pp. 341–360). New York: Springer.
Fermé, E. L., & Hansson, S. O. (1998). Selective revision. Studia Logica, 63, 331–342.
Fermé, E. L., Saez, K., & Sanz, P. (2003). Multiple kernel contraction. Studia Logica, 73(2), 183–195.
Friedman, N., & Halpern, J. (1999). Belief revision: A critique. Journal of Logic, Language and Information, 8(4), 401–420.
Fuhrmann, A. (1991). Theory contraction through base contraction. The Journal of Philosophical Logic, 20, 175–203.
Fuhrmann, A. (1997). An essay on contraction. Studies in logic, language and information. Stanford, California: CSLI Publications.
Fuhrmann, A., & Hansson, S. O. (1994). A survey of multiple contractions. The Journal of Logic, Language and Information, 3, 39–76.
García, A. J., & Simari, G. R. (2004). Defeasible logic programming: An argumentative approach. Theory and Practice of Logic Programming, 4(1), 95–138.
Gärdenfors, P. (1982). Rules for rational changes of belief. In Philosophical essays dedicated to L. ��qvist (pp. 88–101).
Gärdenfors, P. (1988). Knowledge in Flux: Modelling the Dynamics of Epistemic States. Cambridge, Massachusetts: The MIT Press, Bradford Books.
Gärdenfors, P., & Makinson, D. (1988). Revisions of knowledge systems using epistemic entrenchment. In Second conference on theoretical aspects of reasoning about knowledge (pp. 83–95).
Hansson, S. O. (1991). Belief base dynamics. Ph.D. thesis, Uppsala University, Department of Philosophy, Uppsala, Sweden.
Hansson, S. O. (1992). A dyadic representation of belief. In P. Gärdenfors (Ed.), Belief revision (pp. 89–121). Cambridge University Press.
Hansson, S. O. (1993). Reversing the Levi identity. The Journal of Philosophical Logic, 22, 637–669.
Hansson, S. O. (1994). Kernel contraction. The Journal of Symbolic Logic, 59, 845–859.
Hansson, S. O. (1997). Semi-revision. Journal of Applied Non-Classical Logic, 7, 151–175.
Hansson, S. O. (1998). Revision of belief sets and belief bases. Handbook of Defeasible Reasoning and Uncertainty Management Systems, 3, 17–75.
Hansson, S. O. (1999). A textbook of belief dymanics: Theory change and database updating. Kluwer Academic Publishers.
Hansson, S. O., Fermé, E., Cantwell, J., & Falappa, M. (2001). Credibility limited revision. The Journal of Symbolic Logic, 66(4), 1581–1596.
Konieczny, S., & Pino Pérez, R. (1998). On the logic of merging. In Proceedings of the sixth international conference on principles of knowledge representation and reasoning, KR 1998 (pp. 488–498).
Konieczny, S., & Pino Pérez, R. (2002). Merging information under constraints: A logical framework. Journal of Logic and Computation, 12(5), 773–808.
Liberatore, P., & Schaerf, M. (1995). Arbitration: A commutative operator for belief revision. In WOCFAI (pp. 217–228).
Liberatore, P., & Schaerf, M. (1998). Arbitration (or how to merge knowledge bases). IEEE Transactions on Knowledge and Data Engineering, 10(1), 76–90.
Makinson, D. (1997). Screened revision. Theoria: Special Issue on Non-Prioritized Belief Revision, 63, 14–23.
Newell, A. (1982). The knowledge level. Artificial Intelligence, 18, 87–127.
Niederée, R. (1991). Multiple contraction: A further case against Gärdenfors’ principle of recovery. Lecture Notes in Computer Science, 465, 322–334.
Papadimitriou, C. H. (1994). Computational complexity. Addison-Wesley.
Peppas, P. (2004). The limit assumption and multiple revision. Journal of Logic and Computation, 14(3), 355–371.
Quine, W. V. O. (1959). On cores and prime implicants of truth functions. American Mathematics Monthly, 66, 755–760.
Simari, G. R., & Loui, R. P. (1992). A mathematical treatment of defeasible reasoning and its implementation. Artificial Intelligence, 53, 125–157.
van der Hoek, W., & de Rijke, M. (1999). Interleaved contractions. Logic, Language and Computation, 2, 106–127.
Weiss, G. (Ed.) (1999). Multiagent systems: A modern approach to distributed artificial intelligence. Cambridge, Massachussetts: The MIT Press.
Zhang, D., & Foo, N. (2001). Infinitary belief revision. Journal of Philosophical Logic, 30(6), 525–570.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Falappa, M.A., Kern-Isberner, G., Reis, M.D.L. et al. Prioritized and Non-prioritized Multiple Change on Belief Bases. J Philos Logic 41, 77–113 (2012). https://doi.org/10.1007/s10992-011-9200-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-011-9200-8