Revising and updating using a back-up semantics
We introduce a novel approach to revision and updating where two semantics are used for the same class of theories. One semantics, the intended semantics, is used to give a theory its intended meaning, while the other, the back-up semantics, is used as a fall back whenever the intended semantics fails to provide a meaning to the theory.
Almost nothing will be assumed about the exact properties of both the intended and the back-up semantics, except for the following relations between them: (i) the entailment relation based on the intended semantics is stronger than the entailment relation based on the back-up semantics and (ii) the back-up semantics is defined for a broader class of theories than the intended semantics.
In general, for revision, retraction is not suitable and, in many cases, minimal revision can only be achieved by applying revision by expansion.
When dealing with updating, retraction is not suitable for most nonmonotonic semantics. Even for nontrivial deletions, retracting information will not suffice if the back-up semantics satisfies some additional abstract properties.
We conclude by showing that this framework offers a possibility for refining some existing approaches to revision of nonmonotonic theories.
KeywordsTheory Revision Updating Nonmonotonic Reasoning
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- 1.P. Gärdenfors, Belief Revision, Cambridge University Press, 1992.Google Scholar
- 4.J. Dietrich and H. Herre, Outline of a nonmonotonic model theory. Technical Report NTZ-5:94, Universitaet Leipzig, Institut fuer Informatik, Leipzig, 1994.Google Scholar
- 5.K. Inoue, C. Sakama, Abductive Framework for Nonmonotonic Theory Change. Proceedings IJCAI'95, 1995.Google Scholar
- 6.D. Makinson, General Patterns in Nonmonotonic Reasoning, in: D.M. Gabbay, C.J. Hogger, J.A. Robinson (eds) Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 3, Nonmonotonic Reasoning, Oxford Science Publications, Oxford, 1994.Google Scholar
- 7.V. Marek and M. Truszczyński, Nonmonotonic Logic, Springer Verlag, Heidelberg, 1993.Google Scholar
- 8.Morris, P., Stable Closures, Defeasible Logic and Contradiction Tolerant Reasoning, Proceedings of the 7th National Conference on Artificial Intelligence, 1988.Google Scholar
- 9.L. M. Pereira, J. J. Alferes and J. N. Aparicio. Contradiction Removal within wellfounded semantics. In: A. Nerode, W. Marek and V. S. Subrahmanian, (eds.), First International Workshop on Logic Programming and Non-monotonic Reasoning, MIT Press, 1991.Google Scholar
- 10.C. Witteveen and W. van der Hoek, Revision by Communication. In: V. Marek, A. Nerode and M. Truszczyński, editors, Logic Programming and Non-Monotonic Reasoning, LNAI 928, pp. 189–202, Springer Verlag, 1995.Google Scholar
- 11.C. Witteveen and W. van der Hoek, Some Postulates for Nonmonotonic Theory Revision Applied to Logic Programming. In: R. Dyckhoff, H. Herre and P. Schroeder-Heister, editors, Extensions of Logic Programming, LNAI 1050, pp. 303–318, Springer Verlag, 1995.Google Scholar